The logarithmic eqaution log₂ 4 + log₂ (c-9) = 5 has its solution to be 17
How to evaluate the logarithmic eqautionFrom the question, we have the following parameters that can be used in our computation:
log₂ 4 + log₂ (c-9) = 5
Apply the product rule of logarithm
So, we have
log₂(4 * (c-9)) = 5
This can then be expressed as
(4 * (c-9)) = 2⁵
Divide both sides by 4
c - 9 = 2³
So, we have
c - 9 = 8
When evaluated, we have
c = 17
Hence, the logarithmic eqaution has its solution to be 17
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answer the following questions
The values of the identity are;
a. tan Z = 3/4
b. sin C = 4/10
c. tan Z = 20/21
d. cos A = 5/13
e. tan Z = 9/12
How to determine the valueTo determine the value, we need to know the different trigonometric identities, we have;
sinecosinetangentcotangentsecantcosecantFrom the information given, we have that;
a. tan Z = opposite/adjacent
substitute the values
tan Z = 24/32 = 3/4
b. sin theta = opposite/hypotenuse
sin C = 24/40 = 4/10
c. tan Z = opposite/adjacent
tan Z = 20/21
d. cos theta = adjacent/hypotenuse
cos X = 20/15 = 4/3
e. cos A = 15/39 = 5/13
d. tan Z = 27/36
tan Z = 9/12
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Dan spent 15% of his savings account a new phone. If he spent $150 on his new phone how much did he have in savings?
Solve 3x²2 - 2x + 4 = 0.
A)
B)
C)
D)
1± √√√11
3
1± √√√13
3
1 ±i√√11
3
1+1√√13
3
Answer:
To solve the equation 3x²2 - 2x + 4 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b² - 4ac)) / (2a)
In this case, a = 3, b = -2, and c = 4. Substituting these values into the quadratic formula, we have:
x = (-(-2) ± √((-2)² - 4(3)(4))) / (2(3))
x = (2 ± √(4 - 48)) / 6
x = (2 ± √(-44)) / 6
Since the discriminant (-44) is negative, the solutions involve imaginary numbers. Therefore, the answer is:
1 ± i√11
3
Hence, the correct answer is 1 ± i√√11/3.
the nth term of 1,7,13,19
The nth term of the sequence 1, 7, 13, 19 is given by the formula: nth term = 1 + (n - 1) * 6 = 19
To discover the nth time period of the sequence 1, 7, 13, 19, we want to become aware of the sample or rule that governs the sequence.
In this case, we look at that every time period will increase by way of 6 in contrast to the preceding term.
We can categorical this sample in the following equation:
nth time period = 1 + (n - 1) * 6
Let's follow this equation to discover the nth term:
For n = 1:
nth time period = 1 + (1 - 1) * 6
= 1 + zero * 6
= 1
For n = 2:
nth time period = 1 + (2 - 1) * 6
= 1 + 1 * 6
= 1 + 6
= 7
For n = 3:
nth time period = 1 + (3 - 1) * 6
= 1 + two * 6
= 1 + 12
= 13
For n = 4:
nth time period = 1 + (4 - 1) * 6
= 1 + 3 * 6
= 1 + 18
= 19
As we can see, the equation efficiently generates the given phrases of the sequence.
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(07.03 MC)
Find the area of the sector of the circle with central angle of 225° and radius of 5 cm. Use 3.14 for pi(π) and round to the nearest hundredth.
Rounding to the nearest hundredth, the area of the sector is approximately 49.06 cm².
To find the area of the sector of a circle, you can use the formula:
Area = (θ/360) * π * r²,
where θ is the central angle in degrees, π is the mathematical constant pi (approximately 3.14), and r is the radius of the circle.
In this case, the central angle is 225° and the radius is 5 cm. Plugging these values into the formula, we get:
Area = (225/360) * 3.14 * (5 cm)²
Area = (0.625) * 3.14 * 25 cm²
Area ≈ 49.0625 cm²
Rounding to the nearest hundredth, the area of the sector is approximately 49.06 cm².
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The function shown in the graph is vertically stretched by a factor of 8 to produce a new graph. Which function represents the new graph?
Answer:
[tex]f(x)=8\sin(2\pi x)[/tex]
Step-by-step explanation:
The explanation is attached below.
Answer: f(x)=8sin(2πx)
Step-by-step explanation
Hope this explanation helps. Please see the attachment.
9. A sample of the amount of rents paid for one bedroom apartment of similar sizes ear EBKUST campus are: Le 335,000, Le 385,000, Le 635,000, Le 578,000, Le 00,000, Le 535,000 Le 462,000, Le 410,000, Le 373,000, Le 410,000, Le 430,000 and = 515,000. Compute the: i. ii. iii. V. range (interpret your result) mean median mode
The results are:
i. Range: Le 635,000
ii. Mean: Le 445,666.67
iii. Median: Le 420,000
iv. Mode: None
We have,
To compute the range, mean, median, and mode of the given data set, let's first arrange the rent amounts in ascending order:
Le 00,000, Le 335,000, Le 373,000, Le 385,000, Le 410,000, Le 410,000, Le 430,000, Le 462,000, Le 515,000, Le 535,000, Le 578,000, Le 635,000
i. Range:
The range is calculated by subtracting the minimum value from the maximum value in the data set:
Range = Maximum value - Minimum value
Range = Le 635,000 - Le 00,000
Range = Le 635,000
ii. Mean:
The mean is the average of the rent amounts. We sum up all the values and divide by the number of values in the data set:
Mean = (Sum of all rent amounts) / (Number of rent amounts)
Mean = (Le 00,000 + Le 335,000 + Le 373,000 + Le 385,000 + Le 410,000 + Le 410,000 + Le 430,000 + Le 462,000 + Le 515,000 + Le 535,000 + Le 578,000 + Le 635,000) / 12
Mean = Le 5,348,000 / 12
Mean = Le 445,666.67
iii. Median:
The median is the middle value in the sorted data set. In this case, since we have 12 rent amounts, the median will be the average of the 6th and 7th values:
Median = (Le 410,000 + Le 430,000) / 2
Median = Le 420,000
iv. Mode:
The mode is the value that appears most frequently in the data set. In this case, there is no rent amount that appears more than once, so there is no mode.
Therefore,
The results are:
i. Range: Le 635,000
ii. Mean: Le 445,666.67
iii. Median: Le 420,000
iv. Mode: None
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You are a doctorate student in biology doing a dissertation about the insect Desmolithica Geogebra. This insect causes serious damage to plums, apricot and flowering cherries. The female insect lays as many as thirty to sixty eggs on the leaves of the host trees. The time when the insect larva hatches from its egg up to the moment in finding its host tree is called the searching period. Once the insect finds the plum, it squirms into the fruit and begin to ruin it. After approximately four weeks, the insect will crawl back under the bark of the plum tree or directly to the soil where it forms a cocoon. The observation regarding the behavior of the insect demonstrate the length of the searching period S(t), and the percentage of the larvae that survive this period N(t), depend on the air temperature denoted by t. The data from the observations suggest that if the air temperature is measure in degree celsius, where 20
S(t) = (-0.03t^2+1.6t-13.65)^(-1) days and N(t)= -0.85t^2+45.4t-547
S(25) in days N(25) in % T when ds/dt=0
0.1316 56.75 26.67
1. Explain comprehensively the models for S(t) and N(t). Elaborate mathematically these formulae in predicting for the length of searching period and percentage of larvae surviving the searching period when t=25.
2. Find the rate of change of the searching period with respect to temperature t. When does this rate equal to zero? What will happen when t=0?
3. Find the rate of change of the percentage of larvae surviving the searching period with respect to length of the searching period. What information does this provide?
The model for S(t) is given as:
S(t) = (-0.03t^2 + 1.6t - 13.65)^(-1)
This model predicts the searching period length in days. It is an inverse function of the quadratic equation (-0.03t^2 + 1.6t - 13.65). As the temperature increases, the searching period decreases, indicating that the larvae are more efficient at finding the host tree at higher temperatures.
To calculate S(25), we substitute t = 25 into the equation:
S(25) = (-0.03(25)^2 + 1.6(25) - 13.65)^(-1)
= (-0.03(625) + 40 - 13.65)^(-1)
= (-18.75 + 26.35)^(-1)
= 7.6^(-1)
= 0.1316 days
Therefore, when the air temperature is 25 degrees Celsius, the predicted length of the searching period is approximately 0.1316 days.
The model for N(t) is given as:
N(t) = -0.85t^2 + 45.4t - 547
This model predicts the percentage of larvae surviving the searching period. It is a quadratic function (-0.85t^2 + 45.4t - 547). As the temperature increases, the percentage of larvae surviving the searching period may increase or decrease depending on the behavior of the quadratic function.
To calculate N(25), we substitute t = 25 into the equation:
N(25) = -0.85(25)^2 + 45.4(25) - 547
= -0.85(625) + 1135 - 547
= -531.25 + 1135 - 547
= 56.75%
Therefore, when the air temperature is 25 degrees Celsius, the predicted percentage of larvae surviving the searching period is 56.75%.
2. The rate of change of the searching period S(t) with respect to temperature t can be found by taking the derivative of the function S(t) with respect to t, which is denoted as ds/dt.
ds/dt = d/dt [(-0.03t^2 + 1.6t - 13.65)^(-1)]
To find when ds/dt = 0, we set the derivative equal to zero and solve for t:
ds/dt = 0
However, without the specific equation of S(t) in its original form, it is not possible to provide an exact value of t when ds/dt equals zero.
Regarding the behavior when t = 0, we cannot determine this without further information or the specific form of the function S(t). The behavior at t = 0 depends on the equation itself and how it is defined.
3. The rate of change of the percentage of larvae surviving the searching period N(t) with respect to the length of the searching period S(t) can be found by taking the derivative of the function N(t) with respect to S(t), denoted as dN/dS.
dN/dS = d/dS [(-0.85t^2 + 45.4t - 547)]
This rate of change provides information about how the percentage of larvae surviving the searching period changes with respect to the length of the searching period. It gives insight into the sensitivity
Nelson takes out a loan of R530 000 to start his own business. The interest charged on the loan is 8% p.a. compounded monthly. At the end of 6 months he repays R120 000, and 12 months later he repays another R27 000. He makes a final payment 2 years after he started his business. How much money did he make in his final payment that paid off the loan?
The final payment that paid off the loan was , R235,891.64.
Now, We can use the formula,
FV = P [(1 + r/n)^(nt) - 1] / (r/n)
where FV is the future value, P is the periodic payment, r is the interest rate (as a decimal), n is the number of compounding periods per year, and t is the number of years.
Let's first calculate the interest rate per month:
r = 8% / 12 = 0.0066667
Next, the future value of the loan after 6 months:
n = 12 (compounding monthly)
t = 6/12 = 0.5 years
P = 0 (no payment made)
Hence,
FV1 = 530000 [(1 + 0.0066667/12)^(120.5) - 1] / (0.0066667/12)
FV1 ≈ 545,978.61
After 6 months, the loan balance is, R545,978.61.
Next, the future value of the loan after 18 months;
n = 12 (compounding monthly)
t = 1.5 years
P = 120000
Hence, FV2 = (530000 - 120000) [(1 + 0.0066667/12)^(121.5) - 1] / (0.0066667/12)
FV2 ≈ 307,329.33
After 18 months, the loan balance is ,R307,329.33.
Finally, we need to calculate the future value of the loan after 2 years:
n = 12 (compounding monthly)
t = 2 years
P = 27000
Hence, FV3 = (530000 - 120000 - 27000) [(1 + 0.0066667/12)^(122) - 1] / (0.0066667/12)
FV3 ≈ 235,891.64
Therefore, the final payment that paid off the loan was approximately R235,891.64.
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.................................................................................................................................................................
Answer:
2f+15
Step-by-step explanation:
f toy cars
toy dolls : 2f+15
option number 4
8. Consider the D.E. yy'= -x +
1/2
a. Find the implicit general solution of this
equation. What is the condition that c
should satisfied? (c is the constant that
appears in the solution).
b. (T) is the family of curves of the
general solution in an orthonormal
system. What is the nature of this graph?
(such curves are called integral curves of
the D.E.)
c. Find the graph (T) that passes through
the origin O(0, 0).
The implicit general solution is 0.5y² = -0.5x² + 0.5x + C, here C should pass through the origin of the circle. The family of curves (T) represents the integral curve. The graph (T) is represented below.
a. To find the implicit general solution of the given differential equation, we can integrate both sides with respect to x. Let's start by rewriting the equation:
yy' = -x + 1/2
Integrating both sides:
∫ yy' dx = ∫ (-x + 1/2) dx
Using integration by parts on the left side, let u = y and dv = y' dx:
[tex]\int u dv = uv - \int v du\\\\y\int dy = \int (-x + 1/2) dx\\\\1/2 y^2 = -1/2 x^2 + 1/2 x + C\\\\0.5y^2 = -0.5x^2+0.5x+C[/tex]
Where C is the constant of integration. This is the implicit general solution of the given differential equation.
b. The family of curves (T) that represents the general solution in an orthonormal system is known as the integral curves of the differential equation.
c. To find the graph (T) that passes through the origin O(0, 0), we substitute the point (x, y) = (0, 0) into the implicit general solution and solve for C:
[tex]1/2(0)^2 = -1/2(0)^2 + 1/2(0) + C\\\\0 = 0 + 0 + C\\\\\C = 0[/tex]
So the graph (T) that passes through the origin is given by:
[tex]1/2 y^2 = -1/2 x^2 + 1/2 x[/tex]
This equation represents the specific curve that satisfies both the differential equation and the condition of passing through the origin.
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A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 3, 4. Column 2 is labeled y with entries 11, 22, 33, 44. What relationship between the quantities is shown in the table? The relationship between quantities is +10. The relationship between quantities is ×11. The relationship between quantities is – 30. The relationship between quantities is + 20. A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 3, 4. Column 2 is labeled y with entries 11, 22, 33, 44. What relationship between the quantities is shown in the table? The relationship between quantities is +10. The relationship between quantities is ×11. The relationship between quantities is – 30. The relationship between quantities is + 20. A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 3, 4. Column 2 is labeled y with entries 11, 22, 33, 44. What relationship between the quantities is shown in the table? The relationship between quantities is +10. The relationship between quantities is ×11. The relationship between quantities is – 30. The relationship between quantities is + 20. A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 3, 4. Column 2 is labeled y with entries 11, 22, 33, 44. What relationship between the quantities is shown in the table? The relationship between quantities is +10. The relationship between quantities is ×11. The relationship between quantities is – 30. The relationship between quantities is + 20.
The relationship between the quantities shown in the table is +10. The values in column 2 (y) are obtained by adding 10 to the corresponding values in column 1 (x).
How to explain the relationshipIn the given table, the values in column 1 (labeled "x") are 1, 2, 3, and 4. The values in column 2 (labeled "y") are 11, 22, 33, and 44.
To determine the relationship between the quantities in the table, we can compare the values in column 2 (y) with the corresponding values in column 1 (x).
If we subtract each value in column 1 from the corresponding value in column 2, we find that:
11 - 1 = 10
22 - 2 = 20
33 - 3 = 30
44 - 4 = 40
By observing these results, we can see that the difference between each value in column 2 and its corresponding value in column 1 is always 10.
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pls ansdwer
woth 30 poitnsss
Answer:
The Correct answer is 1.53m=153cm
Step-by-step explanation:
1m=100cm
1.53m=x
[tex]x = 100 \times 1.53m[/tex]
x=153m
4. A video game set can be bought on hire purchase by making a deposit of $190 and 12 monthly instalments of $171 each. Calculate the hire purchase cost of the video game set. The actual marked price of the video game set is $1900. This includes a sales tax of 15%. Calculate the selling price of the video game set if no sales tax is included.
Answer: $1652.17
Step-by-step explanation:
First, let's calculate the hire purchase cost of the video game set.
The hire purchase cost is the initial deposit plus the total cost of the monthly installments.
The total cost of the monthly installments is $171 * 12 = $2052.
So, the total hire purchase cost is $190 (deposit) + $2052 (total monthly payments) = $2242.
Now, let's calculate the selling price of the video game set if no sales tax is included.
If the marked price of $1900 includes a 15% sales tax, we can calculate the pre-tax price (the selling price without the tax) by dividing the marked price by 1 plus the tax rate.
The tax rate in decimal form is 15% = 0.15.
So, the selling price without the tax would be $1900 / (1 + 0.15) = $1900 / 1.15 = approximately $1652.17.
ious
6 ♥
Next → Chapter 6 Post Test
6
Select the correct answer.
Which expression is equivalent to 10√5?
A. /500
OB. √105
C. /50
D. √15
An expression that is equivalent to 10√5 include the following: A. √500.
What is an expression?In Mathematics and Geometry, an expression simply refers to a type of mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number), without an equal to sign (symbol).
In this scenario and exercise, the non-simplified form of the given expression 10√5 can be determined or calculated by taking the square of both numerical value as follows;
Expression² = (10√5)²
Expression² = 10² × (√5)²
Expression² = 100 × 5
Expression² = 500
Expression = √500
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Complete Question:
Which expression is equivalent to 10√5?
A. √500
B. √105
C. √50
D. √15
insert parenthesis to make each equality true.
1+2*3+4*5=65
Answer:To make the equality 1+23+45=65 true by inserting parentheses, you can group the numbers and operations in the following way:
(1+2)*(3+4)*5 = 65
This can be calculated as:
3 * 7 * 5 = 65
So, by adding parentheses as (1+2)(3+4)5, the equality 1+23+45=65 becomes true.
Find the y-intercept of the line y = 15/2x - 13/10.
4) Write your answer as an integer or as a simplified proper or improper fraction, not as an
ordered pair.
Answer:
The y-intercept of a function is the point where the function crosses the y-axis, which is when x = 0.
Therefore, to find the y-intercept of the given line, we must set x equal to zero. This will result in the value of y when x = 0, which is our y-intercept.
[tex]y = \frac{15}{2}x - \frac{13}{10} \\[/tex]
[tex]y = \frac{15}{2}(0) - \frac{13}{10} \\[/tex]
[tex]y = -\frac{13}{10} \\[/tex]
The y-intercept is at [tex](0, -\frac{13}{10} )[/tex].
Answer: [tex]-\frac{13}{10}[/tex]
-------------------------------------------------------------------------------------------------------------
We could also identify that this is a linear function that is in the form
y = mx+b
where m is the value of the slope, and b is the value of the y-intercept.
In this case, [tex]\frac{15}{2}[/tex] is the slope and [tex]- \frac{13}{10} \\[/tex] is the y-intercept.
Determine the open intervals on which the function is increasing, decreasing, or constant. (Enter your answers using interval notation.)
t + 2, t<0
F(t) = 2, 0 ≤ t ≤ 2
-t + 4, t > 2
increasing: ____________
decreasing: ___________
constant: ______________
The Function is increasing (-∞, 0), decreasing (2, ∞), and constant [0, 2].
The intervals on which the function is increasing, decreasing, or constant, we need to analyze the behavior of the function in each interval.
1. Interval t < 0:
In this interval, the function is given by f(t) = t + 2. Since the coefficient of t is positive (1), the function is increasing. Therefore, the interval t < 0 is an interval of increasing values.
2. Interval 0 ≤ t ≤ 2:
In this interval, the function is constant and given by f(t) = 2. The value of the function remains constant at 2 for all values of t in this interval.
3. Interval t > 2:
In this interval, the function is given by f(t) = -t + 4. Since the coefficient of t is negative (-1), the function is decreasing. Therefore, the interval t > 2 is an interval of decreasing values.
To summarize:
Increasing interval: t < 0
Decreasing interval: t > 2
Constant interval: 0 ≤ t ≤ 2
Using interval notation, we can express the intervals as follows:
Increasing interval: (-∞, 0)
Decreasing interval: (2, ∞)
Constant interval: [0, 2]
In interval notation, (a, b) denotes an open interval, which means it includes all values between a and b, but excludes the endpoints. [c, d] denotes a closed interval, which includes both endpoints c and d.
Therefore, the function is increasing on the interval (-∞, 0), decreasing on the interval (2, ∞), and constant on the interval [0, 2].
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What is the equation of the circle with center (0,0) that passes through the point (-6,-6)? need answers now
○ (x+6)² + (y+6)² = 72
Ox² + y² = 0
Ox² + y² = 72
○ (x+6)² + (y+6)² = 0
The equation of the circle with center (0,0) that passes through the point (-6,-6) is x^2 +y^2 = 72. So, the correct option is A.
To find the equation of a circle, we need to know the center coordinates and the radius. In this case, the center of the circle is given as (0,0), which means the x-coordinate and y-coordinate of the center are both 0.
The radius can be determined by calculating the distance between the center and the given point on the circle, (-6,-6). We can use the distance formula, which is:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Plugging in the coordinates of the center (0,0) and the given point (-6,-6), we get:
d = √((-6 - 0)² + (-6 - 0)²)
= √((-6)² + (-6)²)
= √(36 + 36)
= √72
= 6√2
The radius of the circle is 6√2.
Now we can use the standard form equation of a circle, which is:
(x - h)² + (y - k)² = r²
Where (h, k) represents the center coordinates and r represents the radius. Substituting the values, we have:
(x - 0)² + (y - 0)² = (6√2)²
x² + y² = 72
So, the equation of the circle with center (0,0) that passes through the point (-6,-6) is: x^2 +y^2 = 72
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Find the volume of each figure. Round to the nearest hundredth. PLEASE HELP SOON :(
Answer:
20579.53 m³
Step-by-step explanation:
You want the volume of a sphere 34 m in diameter.
VolumeThe formula for the volume of a sphere is ...
V = (4/3)πr³ . . . . . where r is half the diameter
In terms of diameter, this is ...
V = (4/3)π(d/2)³ = (π/6)d³
V = (π/6)(34 m)³ ≈ 20,579.53 m³
The volume of the sphere is about 20,579.53 cubic meters.
<95141404393>
hello
the answer to the question is:
[tex]p = 2\pi \: r \\ 36 = 2 \times 3.14 \times r \\ r = 5.7 \: m \\ \\ v = \frac{4}{3} \pi {r}^{3} \\ v = \frac{4}{3} \times 3.14 \times {5.7}^{3} \\ = 775.3 \: {m}^{3} [/tex]
Flying against the wind, an airplane travels 8910 kilometers in 9 hours. Flying with the wind, the same plane travels 5080 kilometers in 4 hours. What is the rate of the plane in still air and what is the rate of the wind?
The rate of the plane in still air is 1130 km/hr and the rate of the wind is: 140 km/hr
What is the relative wind speed?Let the speed of plane in still air be p km/hr and wind speed be w km/hr.
The speed of plane with air is (p + w) km/hr and speed of plane against air is (p − w) km/hr
Flying with air: (p + w)⋅4 = 5080
or p + w = 1270 ----(1)
Flying against air: (p − w)⋅9 = 8910
or p − w = 990;(2)
Adding equations (1) & (2) we get,
(p + w) + (p − w) = 1270 + 990
or 2p = 2260
∴ p = 2260/2
= 1130 km/hr.
Putting p = 1130 in equation (1)
we get,
1130 + w = 1270
or
w = 1270 − 1130
w = 140 km/hr.
The speed of plane in still air is 1130 km/hr and wind speed is 140 km/hr.
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What is the relationship of the two lines?
y=3x-7 y=3x+1
Answer:
The two lines are parallel to each other.
Step-by-step explanation:
We see that the two lines are both in slope-intercept form, whose general equation is y = mx + b, where
m is the slope,and b is the y-interceptWhen two lines have the same slope, they are parallel to each other.
Carly and Annie are making string bracelets. Carly's design needs 3.5 meters of string, Annie's needs 2.7 meters of string. How much string do they need together?
Answer:
6.2 meters
Step-by-step explanation:
Carly needs 3.5 meters of string.
Annie needs 2.7 meters of string.
Adding these two values together:
3.5 meters + 2.7 meters = 6.2 meters
The Americans with disabilities
The Americans with Disabilities Act (ADA) is a landmark civil rights law enacted in the United States in 1990.
What is the Act about?Its purpose is to protect individuals with disabilities from discrimination and ensure equal opportunities in various aspects of life, including employment, public accommodations, transportation, and telecommunications.
The ADA defines a disability as a physical or mental impairment that substantially limits one or more major life activities, such as walking, seeing, hearing, speaking, or learning. The law prohibits discrimination against individuals with disabilities in both the private and public sectors.
Under the ADA, employers with 15 or more employees are required to provide reasonable accommodations to qualified individuals with disabilities, as long as it does not impose an undue hardship on the employer.
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Explain the Americans with Disabilities Act
Question 1(Multiple Choice Worth 2 points)
(Similar Triangles MC)
Triangle ABC ~ triangle DEF.
triangle ABC with side AB labeled 11, side CA labeled 7.6 and side BC labeled 7.9 and a second triangle DEF with side DE labeled 3.3
Determine the measurement of FD.
FD = 1.1
FD = 1.39
FD = 2.28
FD = 2.37
Question 2(Multiple Choice Worth 2 points)
(Experimental Probability MC)
An experiment is conducted with a coin. The results of the coin being flipped twice 200 times is shown in the table.
Outcome Frequency
Heads, Heads 40
Heads, Tails 75
Tails, Tails 50
Tails, Heads 35
What is the P(No Heads)?
85%
75%
50%
25%
Question 3(Multiple Choice Worth 2 points)
(Scatter Plots MC)
Data was collected on the price per cupcake on orders of different amounts from a bakery. The scatter plot shows the data that was gathered.
scatter plot titled cupcake pricing with the x axis labeled number of cupcakes and the y axis labeled cost per cupcake in dollars with points at 1 comma 6, 1 comma 5.5, 2 comma 5, 2 comma 5.5, 3 comma 4, 3 comma 4.5, 4 comma 3.5, 5 comma 3, 6 comma 2.5, 7 comma 2.5, 8 comma 2, and 9 comma 1.5
Which of the following describes the pattern of association for the scatter plot?
There is a strong, positive nonlinear association.
There is a weak, positive nonlinear association.
There is a strong, negative linear association.
There is a weak, negative linear association.
Question 4(Multiple Choice Worth 2 points)
(Line of Fit LC)
A scatter plot is shown on the coordinate plane.
scatter plot with points plotted at 1 comma 9, 3 comma 7, 4 comma 5, 4 comma 6, 5 comma 3, 6 comma 4, 7 comma 4, 8 comma 4, 9 comma 2, and 10 comma 1
Which of the following graphs shows a line on the scatter plot that fits the data?
scatter plot with points plotted at 1 comma 9, 3 comma 7, 4 comma 5, 4 comma 6, 5 comma 3, 6 comma 4, 7 comma 4, 8 comma 4, 9 comma 2, and 10 comma 1, with a line drawn through 7 comma 4 and 9 comma 2
scatter plot with points plotted at 1 comma 9, 3 comma 7, 4 comma 5, 4 comma 6, 5 comma 3, 6 comma 4, 7 comma 4, 8 comma 4, 9 comma 2, and 10 comma 1, with a line drawn through 4 comma 6 and 9 comma 2
scatter plot with points plotted at 1 comma 9, 3 comma 7, 4 comma 5, 4 comma 6, 5 comma 3, 6 comma 4, 7 comma 4, 8 comma 4, 9 comma 2, and 10 comma 1, with a line drawn through 4 comma 5 and 8 comma 1
scatter plot with points plotted at 1 comma 9, 3 comma 7, 4 comma 5, 4 comma 6, 5 comma 3, 6 comma 4, 7 comma 4, 8 comma 4, 9 comma 2, and 10 comma 1, with a line drawn through 6 comma 4 and 7 comma 4
Question 5(Multiple Choice Worth 2 points)
(Identifying Transformations LC)
Polygon ABCD is rotated to get polygon A′B′C′D′.
Graph of polygon ABCD in quadrant 1 with point A at 1 comma 5, point B at 6 comma 8, point C at 6 comma 4, and point D at 4 comma 3 and polygon A prime B prime C prime D prime in quadrant 4 with point A prime at 5 comma negative 1, point B prime at 8 comma negative 6, point C prime at 4 comma negative 6, and point D prime at 3 comma negative 4
Determine the direction and angle of rotation.
270° clockwise rotation
180° counterclockwise rotation
90° counterclockwise rotation
90° clockwise rotation
Question 6(Multiple Choice Worth 2 points)
(Linear Relationships LC)
Which linear equation shows a proportional relationship?
y = −2
y = 3x + 1
y equals three halves times x
y equals one half times x minus 3
Question 7(Multiple Choice Worth 2 points)
(Reflections MC)
Use the graph to answer the question.
Graph of polygon ABCDE with vertices at negative 3 comma 3, negative 3 comma 6, 1 comma 6, 1 comma 3, negative 1 comma 1. A second polygon A prime B prime C prime D prime E prime with vertices at 11 comma 3, 11 comma 6, 7 comma 6, 7 comma 3, 9 comma 1.
Determine the line of reflection.
Reflection across x = 4
Reflection across y = 4
Reflection across the x-axis
Reflection across the y-axis
Question 8(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)
New homeowners hire a painter to paint rooms in their house. The painter pays $60 for supplies and charges the homeowners $20 for each room they want painted.
Which of the following graphs shows the relationship between the amount of money the painter earns, in dollars, and the number of rooms he paints?
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 60 through the point 3 comma 0
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 60 through the point 3 comma 120
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma negative 60 through the point 3 comma 0
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma negative 60 through the point 3 comma negative 120
The answers to the questions are as follows: 1: FD = 1.1. 2: 25%. 3: There is a weak, negative linear association. 4: scatter plot with points plotted at 1,9, 3,7, 4,5, 4,6, 5,3, 6,4, 7,4, 8,4, 9,2, and 10,1, with a line drawn through 7,4 and 9,2.
Question 5: 90° clockwise rotation. 6: y = one-half times x minus 3. 7: Reflection across the x-axis and 8: option B. is the answer.
How did we arrive at these values?Going through each question step by step:
1. (Similar Triangles):
Triangle ABC is similar to triangle DEF. We are given the measurements of sides AB, CA, BC, and DE. However, more information to determine the measurement of side FD. Without additional information or ratios between corresponding sides, calculate the length of FD. The correct answer is: FD=1.1.
2. (Experimental Probability):
To find the probability of no heads, we need to find the frequency of outcomes where no heads occur. Looking at the table, we see that "Tails, Tails" occurs 50 times. The total number of trials is 200. Therefore, the probability of no heads is 50/200 = 25%. The correct answer is: 25%.
3. (Scatter Plots):
The scatter plot displays the relationship between the number of cupcakes and the cost per cupcake. By examining the plotted points, we can see that as the number of cupcakes increases, the cost per cupcake generally decreases. This indicates a negative association. However, the association is not very strong since the points do not form a perfect straight line. The correct answer is: There is a weak, negative linear association.
4. (Line of Fit):
The scatter plot shows a set of points. To determine which graph represents a line that fits the data, we need to examine the plotted points. Looking at the options, the scatter plot with a line drawn through the points (7,4) and (9,2) seems to follow the general trend of the data points. The correct answer is: scatter plot with points plotted at 1,9, 3,7, 4,5, 4,6, 5,3, 6,4, 7,4, 8,4, 9,2, and 10,1, with a line drawn through 7,4 and 9,2.
5. (Identifying Transformations):
The graph shows the original polygon ABCD in quadrant 1 and the transformed polygon A'B'C'D' in quadrant 4. By comparing the coordinates of corresponding points, we can observe a clockwise rotation of 270°. The correct answer is: 270° clockwise rotation.
6. (Linear Relationships):
A proportional relationship between two variables means that they are directly proportional, or in other words, they have a constant ratio. Looking at the given options, "y = one-half times x" represents a proportional relationship since the coefficient of x is the constant ratio. The correct answer is: y = one-half times x.
7. (Reflections):
The graph displays two polygons, ABCDE and A'B'C'D'E'. By comparing the coordinates of corresponding points, we can observe that the transformation results in a reflection across the x-axis. The correct answer is: Reflection across the x-axis.
8. (Graphing Linear Equations):
The painter pays $60 for supplies, which is a fixed cost, and charges $20 per room painted, which is a variable cost. This relationship can be represented by a linear equation. To graph it, we can plot the fixed cost of $60 as the y-intercept (0, 60) and use the slope of $20 per room to find additional points. The correct answer is: a coordinate grid with the x-axis labeled "rooms painted" and the y-axis labeled "amount of money earned" and a line going from the point (0, 60) through the point (3, 120).
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Answer:
Step-by-step explanation: the answer is opstion 3
Need help really please someone don’t understand
1)
When input is 5 output will be 15 and when input is 6 output will be 16.
Given,
input = 3 ; output = 13
input = 4 ; output = 14
Now,
Rule = Add 10 to the input supplied.
Input = 5 ; Output = 15.
Input = 6 ; Output = 16.
Hence,
when input supplied is 5 , output will be 15.
when input supplied is 6 , output will be 16.
2)
When input is 7 output will be 4 and when input is 8 output will be 15.
Given,
Input = 5 ; Output = 2
Input = 6 ; Output = 3
Now,
Rule = Subtract 3 to the input supplied.
Input = 7 ; Output = 4.
Input = 8 ; Output = 5.
Hence,
when input supplied is 7 , output will be 4.
when input supplied is 8 , output will be 5.
3)
When input is 3 output will be 15.
Given,
Input = 0 ; Output = 3
Input = 1 ; Output = 7
Input = 2 ; Output = 9
Now,
Rule = Add 3, 6, 9, 12 which are having common difference as 3 between them.
Input = 3 ; Output = 15.
Hence,
when input supplied is 3 , output will be 15.
4)
When input is 13 output will be 25.
Given,
Input = 10 ; Output = 19
Input = 11 ; Output = 21
Input = 12 ; Output = 23
Now,
Rule = Add 9, 10, 11, 12 which are having common difference as 1 between them.
Input = 13 ; Output = 25.
Hence,
when input supplied is 13 , output will be 25.
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Determine whether there is a minimum or maximum value to the quadratic function. Find the value and the axis of symmetry. If your answer is not an integer please round to the nearest hundredth. f(x)=2x^2-10x+4
The Quadratic function has a minimum value of -8.5 at the axis of symmetry x = 2.5.
There is a minimum or maximum value to the quadratic function f(x) = 2x^2 - 10x + 4, we can look at the coefficient of the x^2 term, which is positive (2 in this case). A positive coefficient for the x^2 term indicates that the quadratic function opens upwards and has a minimum value.
To find the value of the minimum point and the axis of symmetry, we can use the formula:
Axis of Symmetry = -b / (2a)
Value at the Minimum Point = f(Axis of Symmetry)
In our quadratic function, a = 2 and b = -10. Plugging these values into the formulas, we get:
Axis of Symmetry = -(-10) / (2 * 2) = 10 / 4 = 2.5
To find the value at the minimum point, we substitute the axis of symmetry (x = 2.5) into the function:
f(2.5) = 2(2.5)^2 - 10(2.5) + 4
= 2(6.25) - 25 + 4
= 12.5 - 25 + 4
= -8.5
Therefore, the minimum value of the quadratic function f(x) = 2x^2 - 10x + 4 is -8.5. The axis of symmetry is x = 2.5.
the quadratic function has a minimum value of -8.5 at the axis of symmetry x = 2.5.
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1. Ana lanza un balón en diagonal hacia un edificio que se encuentra separado 30 metros de ella; una vez lanzado el balón, alcanza el techo de un edificio de 10 metros de altura, ¿cuál es la distancia recorrida por el balón?
Para determinar la distancia recorrida por el balón, podemos usar el teorema de Pitágoras para calcular la distancia horizontal y vertical por separado y luego sumarlas.
La distancia horizontal entre Ana y el edificio es de 30 metros, mientras que la altura del edificio es de 10 metros. Dado que el balón alcanza el techo del edificio, la distancia vertical recorrida es igual a la altura del edificio, es decir, 10 metros.
Utilizando el teorema de Pitágoras, podemos calcular la distancia recorrida por el balón:
Distancia recorrida = √(Distancia horizontal^2 + Distancia vertical^2)
= √(30^2 + 10^2)
= √(900 + 100)
= √1000
≈ 31.62 metros
Por lo tanto, la distancia recorrida por el balón es aproximadamente 31.62 metros.
1. Judy has been dieting for 12 weeks. She lost 1.7 pounds each week. What is her total weight loss, expressed as a negative number?
2. Sharon has overdrawn her checking account 6 times this month. The total amount of money overdrawn was –$81. What was the average amount of each overdrawn check?
Answer: -20.4 pounds
Step-by-step explanation:
To find the total weight Judy lost, you would multiply the amount she lost each week (1.7 pounds) by the number of weeks she has been dieting (12 weeks).
1.7 pounds/week * 12 weeks = 20.4 pounds
Since the weight loss is to be expressed as a negative number, Judy's total weight loss is -20.4 pounds.
Find y in the diagram below.
Answer:
[tex]\mathrm{5m}[/tex]
Step-by-step explanation:
[tex]\mathrm{sin30^o=\frac{p}{h}}\\\\\mathrm{or,\ \frac{1}{2}=\frac{Y}{10}}\\\\\mathrm{or,\ Y=5m}[/tex]
