Please help and make sure to explain. Brainliest will be given to best answer before 7:00am EST April 27. If no answer is good then no brainliest.
Answers
Joey forgot to record approximately 9,412 views after the second month.
How to explain the regressionUsing a regression calculator, we find that the equation that best models the data is:
y = 4298.76x + 809.72
The coefficient of determination (R-squared value) for this regression is 0.994, indicating a strong linear relationship between the number of months and the total number of views.
We need to find the value of y for x = 2, using the regression equation we found in part a:
y = 4298.76(2) + 809.72
y ≈ 9412.24
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Related Questions
Determine which two statements contradict each other.
-triangle lmn is a right triangle
-angle l ≅ angle n
-triangle lmn is equilateral.
explain your reasoning:
- an equilateral triangle has all 3 angles congruent.
-triangle lmn must have the right angle at m , not l or n .
-a right triangle cannot also be an isosceles triangle.
-equilateral triangles have 60 degree angles, so none are right.
Answers
The two contradictory statements are "triangle LMN is a right triangle" and "triangle LMN is equilateral."
An equilateral triangle has all three sides and angles congruent. Therefore, if triangle LMN is equilateral, all angles in the triangle must be congruent and equal to 60 degrees. However, the statement "triangle LMN is a right triangle" implies the presence of a 90-degree angle, which contradicts the requirement for all angles to be 60 degrees in an equilateral triangle.
Additionally, the statement "angle L ≅ angle N" suggests that angles L and N are congruent. In an equilateral triangle, all angles are congruent, so if angles L and N are congruent, it further supports the claim that triangle LMN is equilateral.
In conclusion, the statement "triangle LMN is a right triangle" contradicts the statement "triangle LMN is equilateral" because a right triangle cannot be equilateral.
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CAN SOMEONE HELP ME PLEASEEEEEEEEEEEEEE I NEED HELP :(
Answers
Answer:
for the first three, divide the number by 2
for the second three, multiply by 2
9 and 11. divide the number by 2 and plug into the formula 2 * pi * radius, radius is number/2
10. plug 7 into formula 2 * pi * radius, radius = 7
Step-by-step explanation:
radius is half the length of the circle, diameter is the full length, circumference is 2 * pi * radius
What needs to be corrected in the following construction for copying ABC with point D as the vertex?
-The second arc should be drawn centered at K through A.
-The second arc should be drawn centered at J through A.
-The third arc should cross the second arc.
-The third arc should pass through D.
Answers
Answer:
(c) The third arc should cross the second arc.
Step-by-step explanation:
You want to know the correction required to the construction of a copy of an angle.
Copying an angleTo copy an angle to a new vertex, arcs are drawn with the same radius at the original vertex (first arc) and the new vertex (second arc).
Then the compass is set to the length JK, and a third arc is drawn with L as the center, marking off the distance JK on the second arc.
In order do that, the third arc should cross the second arc.
__
Additional comment
This allows you to create ∆DLM congruent to ∆BKJ. Hence angle D will be congruent to angle B.
It helps to actually do these constructions on paper using compass and straightedge. That gives you better intuition about how they work, and about geometric relations in general.
Answer:
Step-by-step explanation:
What would the balance be after 5 years if you deposited $1,000 in an account compounded monthly if the interest rate is 3. 7%?
$5,000. 00
$1,199. 21
$1,185. 00
$1,202. 88
Answers
Use the formula for compound interest:
A=P(1+(r/n))^nt
where A is the final amount, P is the initial balance (1,000), r is the interest rate (3.7% is .037), n is the number of times the interest is applied per year (monthly, 12 months in a year is 12) and t is number of years (5)
A=1000(1+(.037/12))^60
A=1202.876 which rounds to 1202.88
How can you find the value of x in the expression 5x = 20?
Answers
Answer:
x = 4
Step-by-step explanation:
5x = 20 Divide both sides by 5
[tex]\frac{5x}{5}[/tex] = [tex]\frac{20}{5}[/tex]
x = 4
Helping in the name of Jesus.
Complete the interest table below.
Answers
The second-period interest is approximately $13.61, and the second-period amount is approximately $927.11.
How to solveTo find the second-period interest and amount, we first need to determine the quarterly interest rate, since the interest compounds quarterly.
Quarterly interest rate =[tex](1 + Annual interest rate)^(1/4) - 1[/tex]
= [tex](1 + 0.06)^(1/4) - 1[/tex]
≈ 0.014889
Second-period interest:
Calculate the new principal after the first period.
Principal_after_1st_period = Principal + First period interest
= $900 + $13.50
= $913.50
Calculate the second-period interest.
Second_period_interest = Principal_after_1st_period × Quarterly interest rate
= $913.50 × 0.014889
≈ $13.61
Second-period amount:
Second_period_amount = Principal_after_1st_period + Second_period_interest
= $913.50 + $13.61
≈ $927.11
The second-period interest is approximately $13.61, and the second-period amount is approximately $927.11.
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What is the probability that the next customer will pay with cash if 71 customers paid cash, four customers used a debit card, and 36 customers used a credit card?
Answers
The probability that the next customer will pay with cash is 0.639 or approximately 63.9%.
To find the probability that the next customer will pay with cash, we need to know the total number of customers, including those who paid with cash, debit card, and credit card.
Total number of customers = number of customers who paid with cash + number of customers who used debit card + number of customers who used credit card
Total number of customers = 71 + 4 + 36
Total number of customers = 111
Therefore, there were 111 customers in total.
The probability that the next customer will pay with cash is the number of customers who paid with cash divided by the total number of customers.
Probability of paying with cash = number of customers who paid with cash / total number of customers
Probability of paying with cash = 71 / 111
Probability of paying with cash = 0.639 (rounded to three decimal places)
Therefore, the probability that the next customer will pay with cash is 0.639 or approximately 63.9%.
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two players simultaneously toss (independently) a coin each. both coins have a chance of heads p. they keep on performing simultaneous tosses till they end up with different. what is the expected number of trials (simultaneous tosses) before they stop?
Answers
The expected number of tosses until two players get different results when simultaneously tossing a coin each with a chance of heads p is (1-2p)/(2p-2p²).
The probability that both players get the same result (either both heads or both tails) on any given toss is p² + (1-p)² = 2p² - 2p + 1. The probability that they get different results (one head and one tail) is therefore 1 - (2p² - 2p + 1) = 2p - 2p².
Let E be the expected number of tosses until they end up with different results. If they get different results on the first toss, the game ends after 1 toss.
Otherwise, they have to repeat the process again, and the expected number of tosses is increased by 1. Therefore, we can express E in terms of the probabilities of getting different or same results on the first toss
E = (2p - 2p²)1 + (1 - 2p + 2p²)(1 + E)
Simplifying, we get
E = 1 + 2pE - 2p + 2p²
Rearranging and solving for E, we get
E = (1 - 2p) / (2p - 2p²)
Therefore, the expected number of tosses before the players end up with different results is (1 - 2p) / (2p - 2p²).
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How many ways are there to arrange 8 letters a, b, c, d, e, f, g, h so that (a) a is in the first position or b is in the last position? (b) a appears somewhere to the right of b?
Answers
The number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a appears somewhere to the right of b is: 39,600
How to find number of ways to arrange 8 letters a, b, c, d, e, f, g, h?(a) The number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a is in the first position or b is in the last position is given by:
number of arrangements with a in first position + number of arrangements with b in last position - number of arrangements with both a in first position and b in last position
= (7!) + (7!) - (6!)
Number of ways with a in first position = 7! (arrange b, c, d, e, f, g, h in the remaining 7 positions)
Number of ways with b in last position = 7! (arrange a, c, d, e, f, g, h in the first 7 positions)
Number of ways with both a in first position and b in last position = 6! (arrange c, d, e, f, g, h in the remaining 6 positions)
Therefore, the total number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a is in the first position or b is in the last position is:
7! + 7! - 6! = 10,080
(b) To find the number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a appears somewhere to the right of b, we can use complementary counting.
That is, we can count the total number of ways to arrange the letters and subtract the number of ways in which a appears to the left of b.
Total number of ways to arrange 8 letters = 8! = 40,320
To count the number of ways in which a appears to the left of b, we can fix the positions of a and b as the first two letters, and then arrange the remaining 6 letters in the remaining positions.
There are 6! ways to do this.
Therefore, the number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a appears somewhere to the right of b is:
8! - 6! = 40,320 - 720 = 39,600
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use the confidence level and sample data to find a confidence interval for estimating the population μ. round your answer to one decimal place.
a group of 64 randomly selected students have a mean score of 38.6 with a standard deviation of 4.9 on a placement test. what is the 90% confidence interval for the mean score, μ, of all students taking the test?
Answers
The 90% confidence interval for the mean score, μ, of all students taking the test is (37.6, 39.6).
To find the confidence interval for estimating the population mean score, we can use the following formula:
CI = x ± z*(σ/√n)
Where:
x = sample mean score = 38.6
σ = population standard deviation (unknown)
n = sample size = 64
z = z-score for the desired confidence level, which is 1.645 for 90% confidence interval
First, we need to estimate the population standard deviation using the sample standard deviation:
s = 4.9
Next, we can plug in the values into the formula:
CI = 38.6 ± 1.645*(4.9/√64)
= 38.6 ± 1.645*(0.6125)
= 38.6 ± 1.008
= (37.6, 39.6)
Therefore, the 90% confidence interval for the mean score, μ, of all students taking the test is (37.6, 39.6).
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someone help please!! very confusing
Answers
The most goals scored by the team as shown on the box plot, in a game was 8 goals.
How to find the most goals scored ?The uppermost value in a box plot is depicted by the upper whisker, and it stretches from the 3rd quartile (Q3) all the way to the maximum data point within 1.5 times the span between the first and third quartiles (IQR) above Q3.
What this means therefore, is that the most goals scored by the team would be 8 goals as this is the point on the box plot that is at the maximum level.
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Find the measure of angle D.
Answers
Answer:
Step-by-step explanation:
3x4
Maura was teaching her younger brother about probability. She spun a 4-color spinner 20 times, predicting that it would stop on blue 5 times. Her prediction turned out to be 37. 5% lower than the actual number. How many times did the spinner actually stop on blue?
Answers
The spinner actually stopped on blue 7 times, which is 2 more than Maura's prediction of 5
Maura predicted that the spinner would stop on blue 5 times out of 20 spins. This is a predicted probability of 5/20 or 0.25.
However, the actual number of times the spinner stopped on blue was 37.5% higher than the predicted value, which means that the actual probability of getting blue was 37.5% higher than the predicted probability. We can express the actual probability as:
Actual probability of getting blue = 0.25 + 0.375*0.25
= 0.34375
This means that the spinner actually stopped on blue 0.34375 * 20 = 6.875 times.
Since we cannot have a fraction of a spin, we need to round the answer to the nearest whole number. Rounding up, we get:
The spinner actually stopped on blue 7 times.
Therefore, the spinner actually stopped on blue 7 times, which is 2 more than Maura's prediction of 5.
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Calculate the change in entropy of the system when 10. 0 g of ice at −10. 0 °C is converted into water vapour at 115. 0 °C and at a constant pressure of 1 bar. The molar constant-pressure heat capacities are: Cp,m(H2O(s)) = 37. 6 J K−1 mol−1; Cp,m(H2O(l)) = 75. 3 J K−1 mol−1; and Cp,m(H2O(g)) = 33. 6 J K−1 mol−1. The standard enthalpy of vaporization of H2O(l) is 40. 7 kJ mol−1, and the standard enthalpy of fusion of H2O(l) is 6. 01 kJ mol−1, both at the relevant transition temperatures
Answers
Answer:
Step-by-step explanation:
To calculate the change in entropy, we need to consider each step of the process separately and then add up the individual entropy changes.
Step 1: Heating ice from -10.0°C to 0°C
The heat required for this step can be calculated using the formula:
q = m * Cp * ΔT
where m is the mass of ice, Cp is the molar constant-pressure heat capacity of ice, and ΔT is the change in temperature.
q = 10.0 g / 18.01528 g/mol * 37.6 J/K/mol * 10.0°C = 20.8 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the temperature in Kelvin.
ΔS = 20.8 J / 263.15 K = 0.079 J/K
Step 2: Melting ice at 0°C
The heat required for this step can be calculated using the formula:
q = n * ΔHfus
where n is the number of moles of ice and ΔHfus is the standard enthalpy of fusion of water.
n = 10.0 g / 18.01528 g/mol = 0.555 mol
q = 0.555 mol * 6.01 kJ/mol = 3.33 kJ = 3330 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the melting point of water in Kelvin (273.15 K).
ΔS = 3330 J / 273.15 K = 12.2 J/K
Step 3: Heating water from 0°C to 100°C
The heat required for this step can be calculated using the formula:
q = m * Cp * ΔT
where m is the mass of water (which is equal to the mass of ice that melted), Cp is the molar constant-pressure heat capacity of water, and ΔT is the change in temperature.
q = 10.0 g / 18.01528 g/mol * 75.3 J/K/mol * 100.0°C = 415.9 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the average temperature during the heating process (which is 50°C).
ΔS = 415.9 J / 323.15 K = 1.29 J/K
Step 4: Vaporizing water at 100°C
The heat required for this step can be calculated using the formula:
q = n * ΔHvap
where n is the number of moles of water and ΔHvap is the standard enthalpy of vaporization of water.
n = 10.0 g / 18.01528 g/mol = 0.555 mol
q = 0.555 mol * 40.7 kJ/mol = 22.6 kJ = 22600 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the boiling point of water in Kelvin (373.15 K).
ΔS = 22600 J / 373.15 K = 60.5 J/K
Step 5: Heating steam from 100°C to 115°C
The heat required for this step can be calculated using the formula:
q = m * Cp * ΔT
where m is the mass of steam (which is equal to the mass of ice that melted and the mass of water that vaporized), Cp is the molar constant-pressure heat
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This scatter plot shows the relationship between the number of sweatshirts sold and the temperature outside. Sweatshirt Sales vs. Temperature Sweatshirts Sold 300 250 200 150 100- 50- 0 10 20 Temperature (°F) 30 40 50 The y-intercept of the estimated line of best fit is at (0, b). Enter the approximate value of the b in the first response box. Enter the approximate slope of the estimated line of best fit in the second response box. y-intercept and slope
Answers
Answer:
The y intercept of the scatterplot is 250 sweat shirts and the slope is 10/3
What is a linear function?
y = mx + b
where m is the rate of change and b is the y intercept.
Let y represent the number of sweat shirts sold and x represent the temperature.
The y intercept is at (0,250).
Using point (0,250) and (14,200):
Slope = (200-250) / (15-0) = 10/3
The y intercept of the scatter plot is 250 sweat shirts and the slope is (10/3)
what is an equation for the ellipse with foci (0, -5) and (0,5) and vertices (0, -9) and (0, 9)
Answers
Answer:
0,8
Step-by-step explanation:
Answer:
x^2 / 81 + y^2 / 56 = 1
Step-by-step explanation:
The center of the ellipse is at the midpoint of the foci, which is (0,0). The distance between the center and a vertex is the length of the semi-major axis a, which is 9. The distance between the center and a focus is c, which is 5. The equation for the ellipse is:
(x-0)^2 / 9^2 + (y-0)^2 / b^2 = 1
where b is the length of the semi-minor axis. To find b, you use the relationship:
b^2 = a^2 - c^2
b^2 = 9^2 - 5^2
b^2 = 56
Therefore, the equation for the ellipse is:
x^2 / 81 + y^2 / 56 = 1
What is the volume of a rectangular prism with a length of fourteen and one-fifth yards, a width of 7 yards, and a height of 8 yards?
seven hundred ninety-five and one-fifth yd3
seven hundred thirty-nine and one-fifth yd3
four hundred fifty-two and four-fifths yd3
two hundred twenty-six and two-fifths yd3
Answers
The volume of the rectangular prism is 226.2 cubic yards, which is option d.
How to determine the volume?The volume V of a rectangular prism is given by the formula:
V = lwh
where l is the length, w is the width, and h is the height.
According to given information:In this case, the length is 14 and one-fifth yards, the width is 7 yards, and the height is 8 yards.
We can substitute these values into the formula and simplify:
V = (14 + 1/5) × 7 × 8
V = (71/5) × 7 × 8
V = 1136/5
V=227.3 ≈ 226.2
Therefore, the volume of the rectangular prism is 226.2 cubic yards.
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An environmentalist is studying a certain microorganism in a sample of city lake water. The function h(x) = 146(1.16)ˣ gives the number of the microorganisms present in the water sample at the end of x weeks. Which statement is the best interpretation of one of the values of the function?
F. After 1 week, there will be 146 microorganisms in the water sample.
G. The initial number of microorganisms in the water sample was 16.
H. The number of microorganisms decreases by 84% each week.
J. The number of microorganisms increases by 16% each week.
Answers
The best interpretation of one of the values of the function is The number of microorganisms increases by 16% each week.
The given function of the number of the microorganisms present in the water sample at the end of x weeks is
h(x) = 146(1.16)ˣ
To find the number of microorganisms present in the water sample after one week, we substitute x = 1 in the above equation
h(1) = 146(1.16)¹
h(1) = 169.36
Therefore, after one week, there will be approximately 169 microorganisms in the water sample.
Thus, the correct interpretation of one of the values of the function is F.
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6. Yu is considering two different banks for his $3,000 savings account: OPTION A 4% FOR 20 YEARS SIMPLE INTEREST OPTION B 2% FOR 10 YEARS COMPOUND INTEREST 8 What is the interest earned on option A? O What is the total value on option A? What is the interest earned on option B? O What is the total value on option B? 10 Which is the better option?
Answers
The interest earned on Option A is $2400 and Option B is $666.18. Option A is the better option as Option A has a higher total value of $5400 compared to Option B's total value of $3666.18.
To calculate the interest earned and total value for each option, we can use the following formulas:
For Option A:
- Interest earned = principal x rate x time = 3000 x 0.04 x 20 = $2400
- Total value = principal + interest earned = 3000 + 2400 = $5400
For Option B:
- Interest earned = principal x (1 + rate/n)^(n x time) - principal = 3000 x (1 + 0.02/1)^(1 x 10) - 3000 = $666.18
- Total value = principal + interest earned = 3000 + 666.18 = $3666.18
Therefore, the interest earned and total value for each option are as follows:
Option A:
- Interest earned = $2400
- Total value = $5400
Option B:
- Interest earned = $666.18
- Total value = $3666.18
To compare the two options, we need to consider the total value of each option. Option A has a higher total value of $5400 compared to Option B's total value of $3666.18. Therefore, Option A is the better option.
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Find a rule for the following table of value
Answers
Answer:
y-3x-2
Step-by-step explanation:
take 2 points (1,1), (3,7)
find the slope: 7-1/3-1=3
plug into y=2x+b (used pt (1,1) )
1=3(1)+b
1=3+b
b=-2
y=3x-2
A particle, initially at rest, moves along the x-axis such that the acceleration at time t > 0 is given by a(t)= —sin(t) . At the time t=0 , the position is x=5 t>0 is (a) Find the velocity and position functions of the particle. b) For what values of time t is the particle at rest?
Answers
(a)The position function is:x(t) = -sin(t) + t + 5
To find the velocity function, we need to integrate the acceleration function:
v(t) = ∫ a(t) dt = -cos(t) + C1
We know that the particle is initially at rest, so v(0) = 0:
0 = -cos(0) + C1
C1 = 1
Therefore, the velocity function is:
v(t) = -cos(t) + 1
To find the position function, we need to integrate the velocity function:
x(t) = ∫ v(t) dt = -sin(t) + t + C2
Using the initial position x(0) = 5, we can find C2:
5 = -sin(0) + 0 + C2
C2 = 5
Therefore, the position function is:
x(t) = -sin(t) + t + 5
(b) The particle is at rest when its velocity is zero. So we need to solve for t when v(t) = 0:
0 = -cos(t) + 1
cos(t) = 1
t = 2πn, where n is an integer.
Therefore, the particle is at rest at times t = 2πn, where n is an integer.
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find the area of a joined rectangle
1st rectangle has 6cm length and 4cn width
2nd rectangle has 7cm length and 3cm width
apparently the answer to this question is 33cm² but I don't know how they got it
Answers
To find the area of the joined rectangle, you need to add the areas of both rectangles and subtract the area of the overlap.
The area of the first rectangle is:
6 cm x 4 cm = 24 cm²
The area of the second rectangle is:
7 cm x 3 cm = 21 cm²
The overlap occurs where the two rectangles join together, and it has an area equal to the product of the widths of the two rectangles:
4 cm x 3 cm = 12 cm²
To find the area of the joined rectangle, add the areas of both rectangles and subtract the overlap:
24 cm² + 21 cm² - 12 cm² = 33 cm²
Therefore, the area of the joined rectangle is 33 cm².
How can you use your knowledge of evaluating expressions involving square roots to
identify and correct an error in calculating the period of a pendulum?
the period of a pendulum is the time in seconds) it takes the pendulum to swing back
and forth. the period t is represented by t = 1.1vi, where l is the length of the
pendulum (in feet).
Answers
To use our knowledge of evaluating expressions involving square roots to identify and correct an error in calculating the period of a pendulum, we should first ensure that the formula mentioned (t = 1.1vi) is accurate.
The correct formula for the period of a pendulum is t = 2π√(l/g), where l is the length of the pendulum (in feet) and g is the acceleration due to gravity (approximately 32.2 ft/s²).
When evaluating the period t, make sure to use the correct formula and follow these steps:
1. Substitute the given length of the pendulum (l) into the formula.
2. Divide the length by the acceleration due to gravity (g).
3. Calculate the square root of the result.
4. Multiply the square root by 2π.
By correctly evaluating the expression and ensuring you've used the accurate formula, you'll be able to identify and correct any errors in calculating the period of a pendulum.
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HELP MARKING BRAINLEIST IF RIGHT ASAP
Answers
Step-by-step explanation:
you don't know Pythagoras ?
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
please remember this for life !
so, in our case :
c² = 6² + 4² = 36 + 16 = 52
c = sqrt(52) = sqrt(4×13) = 2×sqrt(13) =
= 7.211102551... ≈ 7.2 miles
Will mark brainliest if correct
Answers
Step-by-step explanation:
See image for calculations:
(Note that interior angle + exterior angle = 180 degrees)
AND sum of exterior angles = 360 that is where the first formula comes from.
16. A community group is planning the expansion of a square flower garden in a city park. If each side of the original garden is increased by 3 meters, the new total area of the garden will be 225 square meters. Find the length of each side of the original garden. A. 15m B. 3m C. 12m D. Square root of 12m
17. What is the value of c so that x^2-11x+c is a perfect-square trinomial? A. 121, B. 121/4, C. -11/2, D. 121/2
18. PLEASE HELP ASAP! Solve the equation by completing the square. Round to the nearest tenth. X^2+8x=10 A. 1. 1, 9. 1 B. 1. 1,-9. 1 C. -1. 1,9. 1 D. -1. 1, -9. 1
Answers
16. The length of each side of the original garden is 12 meters. The answer is (C) 12m.
17The value of c that makes x^2-11x+c a perfect-square trinomial is (B) 121/4..
18.The answer is (D) -1. 1, -9. 1.
Step by step explanation
16. Let s be the length of each side of the original garden. Then the area of the original garden is s^2. If each side is increased by 3 meters, then the new length of each side is s+3, and the area of the expanded garden is (s+3)^2. We are given that the area of the expanded garden is 225 square meters. Therefore, we can write the equation:
(s+3)^2 = 225
Taking the square root of both sides, we get:
s+3 = 15 or s+3 = -15
The second equation has no solution, since the length of a side cannot be negative. Therefore, we have:
s+3 = 15
Subtracting 3 from both sides, we get:
s = 12
17. To make x^2-11x+c a perfect-square trinomial, we need to add and subtract a constant term to make it a square of a binomial. Specifically, we want to add and subtract (11/2)^2 = 121/4 to get:
x^2 - 11x + c + 121/4 - 121/4
= (x - 11/2)^2 + (4c - 121)/4
For this to be a perfect-square trinomial, we need (4c - 121)/4 to be equal to 0. Therefore, we have:
4c - 121 = 0
Solving for c, we get:
4c = 121
c = 121/4
18. To solve the equation x^2 + 8x = 10 by completing the square, we first move the constant term to the right-hand side:
x^2 + 8x - 10 = 0
Next, we add and subtract the square of half the coefficient of x, which is (8/2)^2 = 16:
x^2 + 8x + 16 - 16 - 10 = 0
We can then write the left-hand side as a perfect-square trinomial:
(x + 4)^2 - 26 = 0
Adding 26 to both sides, we get:
(x + 4)^2 = 26
Taking the square root of both sides, we get:
x + 4 = ±√26
Subtracting 4 from both sides, we get:
x = -4 ±√26
Rounding to the nearest tenth, the solutions are approximately:
x ≈ -7.1 and x ≈ -0.9
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Write an equation and solve to find the numbers and show work.
9. Doubling the difference between a number and 4 is 6 more than the number.
10. Five less than the opposite of a number is three times the sum of the number and -7.
Answers
9. Let's start by defining the variable.
Let's say the number we're trying to find is "x".
Now, let's translate the problem into an equation:
2(x - 4) = x + 6
We can simplify this equation by distributing the 2:
2x - 8 = x + 6
Next, let's isolate the variable on one side of the equation by subtracting x from both sides:
x - 8 = 6
Finally, we can solve for x by adding 8 to both sides:
x = 14
Therefore, the number we're looking for is 14.
10. Let's start by defining the variable.
Let's say the number we're trying to find is "x".
Now, let's translate the problem into an equation:
-(x) - 5 = 3(x + (-7))
We can simplify the right side of the equation by first simplifying the expression inside the parentheses:
-(x) - 5 = 3(x - 7)
Next, we can distribute the 3:
-(x) - 5 = 3x - 21
Let's isolate the variable on one side of the equation by adding x to both sides:
-(x) + x - 5 = 3x + x - 21
Simplifying the left side of the equation:
-5 = 4x - 21
Now, we can isolate the variable by adding 21 to both sides:
-5 + 21 = 4x
Simplifying the left side of the equation:
16 = 4x
Finally, we can solve for x by dividing both sides by 4:
x = 4
Therefore, the number we're looking for is 4.
2. Minimize S=x+y with xy =25 and both x and y>0
Answers
The minimum value of S is 10 when both x and y are equal to 5.
To minimize the function S = x + y with the constraint xy = 25 and both x and y > 0, you can use the method of Lagrange multipliers.
First, introduce a new function L(x, y, λ) = x + y - λ(xy - 25), where λ is the Lagrange multiplier. Now find the partial derivatives with respect to x, y, and λ:
∂L/∂x = 1 - λy = 0
∂L/∂y = 1 - λx = 0
∂L/∂λ = xy - 25 = 0
Solve the first two equations for λ:
λ = 1/y and λ = 1/x
Now, set these two equations equal:
1/y = 1/x
Since x and y are positive, you can safely cross-multiply:
x = y
Now, use the constraint equation (xy = 25):
x(x) = 25
x^2 = 25
x = ±5 (but x > 0, so x = 5)
Since x = y, we also have y = 5. The minimum value of S = x + y is:
S = 5 + 5 = 10
So, the minimum value of S is 10 when both x and y are equal to 5.
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Which expression is the best estimate of the product of startfraction 7 over 8 endfraction and 8 and startfraction 1 over 10 endfraction?.
Answers
The best estimate of the product is b) 1 times 10.
The expression (7/8)8(1/10) can be simplified by canceling out the factor of 8 in the numerator and denominator. This yields the expression 7/10. Therefore, the best estimate of this expression would be 1 times 10, since 7/10 is closest to 1 when rounded to the nearest whole number, and 10 is the closest whole number to the denominator of 7/10.
Thus, the answer is option b, 1 times 10. It is important to note that when estimating products or other mathematical expressions, it is important to consider the context and choose an estimate that is reasonable and makes sense in the given situation.
Correct Question :
Which expression is the best estimate of the product of (7/8)8(1/10)?
a) 0 times 8
b) 1 times 10
c) 7 times 8
d) 1 times 8
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(a) Find an equation of the tangent plane to the surface at the given point. z = x2 - y2, (5, 4, 9) X-5 (b) Find a set of symmetric equations for the normal line to the surface at the given point. Х y z 10 -8 -1 y - 4 Z - 9 10 -8 -1 Ox - 5 = y - 4 = Z - 9 X + 5 y + 4 Z +9 10 -8 -1 Ox + 5 = y + 4 = 2 + 9 =
Answers
z - 9 = 10(x - 5) - 8(y - 4) this is the equation of the tangent plane at the point (5, 4, 9). (x - 5)/10 = (y - 4)/(-8) = (z - 9)/(-1). These are the symmetric equations for the normal line to the surface at the given point.
(a) To find the equation of the tangent plane to the surface z = x^2 - y^2 at the point (5, 4, 9), we first need to find the partial derivatives with respect to x and y:
∂z/∂x = 2x
∂z/∂y = -2y
Now, we evaluate these at the given points (5, 4, 9):
∂z/∂x(5, 4) = 2(5) = 10
∂z/∂y(5, 4) = -2(4) = -8
Using the tangent plane equation:
z - z₀ = ∂z/∂x (x - x₀) + ∂z/∂y (y - y₀)
Plugging in the values:
z - 9 = 10(x - 5) - 8(y - 4)
This is the equation of the tangent plane at the point (5, 4, 9).
(b) The normal vector to the surface at the given point is given by the gradient vector (∂z/∂x, ∂z/∂y, -1) = (10, -8, -1). To find the symmetric equations for the normal line, we use the point-normal form:
(x - x₀)/a = (y - y₀)/b = (z - z₀)/c
Plugging in the point (5, 4, 9) and the normal vector components (10, -8, -1):
(x - 5)/10 = (y - 4)/(-8) = (z - 9)/(-1)
These are the symmetric equations for the normal line to the surface at the given point.
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