Triangle LMN has vertices at L(-1,5),M(-1,0),N(-2,5), then the vertices are L'(-5, -1), M'(0, -1), N'(-5, -2).
To rotate a point counterclockwise:
For a point (x, y):
x' = x*cos(theta) - y*sin(theta)
y' = x*sin(theta) + y*cos(theta)
In this situation, rotate the triangle 90° counterclockwise about the origin.
The transformation equations to each vertex of the triangle states that:
For vertex L(-1, 5):
x' = -1*cos(90°) - 5*sin(90°) = -1*0 - 5*1 = -5
y' = -1*sin(90°) + 5*cos(90°) = -1*1 + 5*0 = -1
Therefore, vertex L' is (-5, -1).
For vertex M(-1, 0):
x' = -1*cos(90°) - 0*sin(90°) = -1*0 - 0*1 = 0
y' = -1*sin(90°) + 0*cos(90°) = -1*1 + 0*0 = -1
Therefore, vertex M' is (0, -1).
For vertex N(-2, 5):
x' = -2*cos(90°) - 5*sin(90°) = -2*0 - 5*1 = -5
y' = -2*sin(90°) + 5*cos(90°) = -2*1 + 5*0 = -2
Therefore, vertex N' is (-5, -2).
Thus, the vertices of the image triangle L'M'N' after rotating the original triangle 90° counterclockwise about the origin are: L'(-5, -1), M'(0, -1), N'(-5, -2).
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NO LINKS!! URGENT HELP PLEASE!!!
Solve each continuous exponential growth problem.
24. A savings account balance is compounded continuously. If the interest rate is 3% per year and the current balance is $1727.00, what will the balance be 6 years from now?
Answer:
$2,067.59
Step-by-step explanation:
To calculate the balance of the savings account, we can use the continuous compounding interest formula:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Interest Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]
Given values:
P = $1,727.00r = 3% = 0.03t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\begin{aligned}A&=1727 \cdot e^{0.03 \cdot 6}\\&=1727 \cdot e^{0.18}\\&=1727 \cdot 1.19721736...\\&=2067.59438...\\&=2067.59\end{aligned}[/tex]
Therefore, the balance of the savings account 6 years from now is $2,067.59.
Determine the equation of the circle graphed below. 100pts
The equation of the circle graphed below is (x + 2)² + (y - 3)² = 16.
To determine the equation of the circle graphed below, we need to use the standard form equation of a circle.
The standard form of a circle equation is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.
Given the graph, we can see that the center is located at (-2, 3), and the radius is 4 units. Therefore, we can substitute these values into the standard form equation as follows:(x - (-2))² + (y - 3)² = 4²(x + 2)² + (y - 3)² = 16
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Answer:
[tex](x +3)^2+(y-2)^2=4[/tex]
Step-by-step explanation:
The equation of a circle in standard form is:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
To determine the equation of the graphed circle, we need to find its center and radius.
The center of the circle is a single point that lies at an equal distance from all points on the circumference of the circle.
From inspection of the graphed circle, we can see that its domain is [-5, -1] and its range is [0, 4]. The x-coordinate of the center is the midpoint of the domain, and the y-coordinate of the center is the midpoint of the range.
[tex]x_{\sf center}=\dfrac{-5+(-1)}{2}=-3[/tex]
[tex]y_{\sf center}=\dfrac{0+4}{2}=2[/tex]
Therefore, the center of the circle is (-3, 2).
The radius of the circle is the distance from the center to all points on the circumference of the circle. From observation, we can see that the radius of the circle is r = 2.
To determine the equation of the circle, substitute the center and radius into the standard formula.
[tex](x - (-3)^2+(y-2)^2=2^2[/tex]
[tex](x +3)^2+(y-2)^2=4[/tex]
Therefore, the equation of the graphed circle is:
[tex]\boxed{(x +3)^2+(y-2)^2=4}[/tex]
PLEASE HELP (60)POINTS
The points (2, 1), (1, 0), (2, 1), (4, 2), and (8, 3) will be plotted on the graph accordingly. The x-coordinate represents the value from the domain, and the y-coordinate represents the corresponding value obtained by evaluating the equation
To plot the points on the graph for the equation y = log2x, we will substitute the given values from the domain (2, 1, 2, 4, 8) into the equation and calculate the corresponding y-values.
For x = 2, y = log2(2) = 1. The point (2, 1) represents this on the graph.
For x = 1, y = log2(1) = 0. The point (1, 0) represents this on the graph.
For x = 2, y = log2(2) = 1. The point (2, 1) represents this on the graph.
For x = 4, y = log2(4) = 2. The point (4, 2) represents this on the graph.
For x = 8, y = log2(8) = 3. The point (8, 3) represents this on the graph.
Now, we can plot these points on the graph. The x-axis will range from 0 to 10, and the y-axis will range from -1 to 4 to accommodate the points we have calculated.
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PLEASE HELP
I need this done in 15 minutes
Triangle ABC has vertices at A(-5,2), B(1,3), and C(-3,0). Determine the coordinates of the vertices for the image of the pre image is translated 4 units right.
A. A’(-9,2),B’(-3,3), C’(-7,0)
B. A’(-4,6),B’(0,7),C’(1,0)
C. A’(-1,2),B’(5,3),C’(1,0)
D. A’ (-5,-2), B’(-1,-1), C’(-3,-4)
The coordinates of the vertices for the image of the pre image is translated 4 units right are:
C. A' = (-1,2), B' = (5, 3), C' = (1,0)
How to determine the coordinates of the vertices for the image of the pre image is translated 4 units right?A geometric transformation involves taking a geometric object as input and producing a new geometric object as output. We have different types of geometric transformations such as translation, rotation, reflection etc.
A translation moves a geometric object a certain distance in a certain direction. Translation to the right means movement in the positive x-direction.
Thus, the coordinates of the vertices for the image of the pre image if it is translated 4 units right can be obtained by adding 4 to x-coordinate values while y-coordinate values remain the same. That is:
A(-5,2) becomes A'(-5+4, 2) = (-1,2)
B(1,3)becomes B'(1+4, 3) = (5, 3)
C(-3,0) becomes C'(-3+4, 0) = (1,0)
Therefore, the coordinates of the vertices of the image of triangle ABC after it is translated 4 units right are (-1, 2), (5, 3), and (1, 0).
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A train travels 70 feet in 1/10th of a second. At this same speed, how many feet will it travel in 3 and 1/2 ( three and one half) seconds?
Answer:
the train will travel 245 feet in 3 and 1/2 seconds
Step-by-step explanation:
To determine the distance the train will travel in 3 and 1/2 seconds, we can use a proportion based on the given information.
Let's set up the proportion:
70 feet / (1/10 second) = x feet / (3 1/2 seconds)
To solve this proportion, we can first convert the mixed number 3 1/2 to an improper fraction.
3 1/2 = 7/2
Now we can rewrite the proportion:
70 / (1/10) = x / (7/2)
To simplify the proportion, we can multiply the numerator and denominator of the right side by 10/1:
70 / (1/10) = (x * 10) / (7/2)
Simplifying further, we get:
70 * (10/1) = x * (10/7/2)
700 = x * (20/7)
To find x, we can divide both sides of the equation by (20/7):
x = 700 / (20/7)
x = 700 * (7/20)
x = 245 feet
Therefore, at the same speed, the train will travel 245 feet in 3 and 1/2 seconds.
Miranda likes to have wine with her dinner on Friday and Saturday nights. She usually buys two bottles of wine for the weekend. she really needs to cut back on spending. She decides to buy only one bottle per week. on average a bottle of wine cost $15. How much does she save in one year?
We subtract the cost of wine when buying one bottle per week from the cost of wine when buying two bottles per weekend. Miranda saves $780 in one year by buying only one bottle of wine per week instead of two.
To calculate how much Miranda saves in one year by buying only one bottle of wine per week instead of two, we can follow these steps:
Determine the number of bottles of wine she buys in a year:
Miranda used to buy 2 bottles of wine per weekend, so in a week, she bought 2 bottles.
Since there are 52 weeks in a year, the number of bottles she bought in a year is 2 bottles/week * 52 weeks = 104 bottles.
Calculate the total cost of wine for the year:
Since each bottle costs $15, the total cost of wine for the year when buying 2 bottles per week would be 104 bottles * $15/bottle = $1560.
Calculate the cost of wine for one year when buying only one bottle per week:
With Miranda's decision to buy one bottle per week, the total number of bottles she buys in a year is 1 bottle/week * 52 weeks = 52 bottles.
Therefore, the cost of wine for one year when buying only one bottle per week would be 52 bottles * $15/bottle = $780.
Calculate the amount saved in one year:
To determine the amount saved, we subtract the cost of wine when buying one bottle per week from the cost of wine when buying two bottles per weekend.
Amount saved = $1560 - $780 = $780.
Therefore, Miranda saves $780 in one year by buying only one bottle of wine per week instead of two.
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QUESTION 6 1 POINT
Using the table, what is the average daily balance of the credit card for the August 1 through August 31 billing period?
Round your answer to the nearest dollar.
Provide your answer below:
Day
1
8
16
24
Activity
Payment
Purchase
Purchase
Adjustment Closing Balance
-550
4
+200
+150
850
300
500
650
Rounded to the nearest dollar, the average daily balance of the credit card for the August 1 through August 31 billing period is $74.
To find the average daily balance of the credit card for the August 1 through August 31 billing period, we need to calculate the sum of the daily balances and divide it by the number of days in the billing period.
Let's calculate the daily balances for each day:
Day 1: Closing Balance = $850
Day 8: Closing Balance = $300
Day 16: Closing Balance = $500
Day 24: Closing Balance = $650
To calculate the daily balances, we need to consider the activities that occurred on each day.
On Day 1, there was no activity recorded, so the closing balance remains at $850.
On Day 8, a payment of $550 was made. Therefore, the closing balance is $850 - $550 = $300.
On Day 16, a purchase of $200 was made. Therefore, the closing balance is $300 + $200 = $500.
On Day 24, a purchase of $150 was made and an adjustment of $4 was applied. Therefore, the closing balance is $500 + $150 - $4 = $650.
Now, let's calculate the average daily balance:
Sum of daily balances = $850 + $300 + $500 + $650 = $2300
Number of days in the billing period = 31
Average daily balance = Sum of daily balances / Number of days = $2300 / 31 ≈ $74.19
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What is the magnitude of -3 + 4i?
The magnitude of the complex number -3 + 4i is 5.
To find the magnitude of a complex number, we use the formula:
Magnitude = √(real^2 + imaginary^2)
In this case, the complex number is -3 + 4i.
The real part is -3, and the imaginary part is 4.
Using the formula, we can calculate the magnitude:
Magnitude = √((-3)^2 + 4^2)
= √(9 + 16)
= √25
= 5
Therefore, the magnitude of the complex number -3 + 4i is 5.
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write the inequality shown -4x+y=-3
The inequality corresponding to the equation -4x + y = -3 is either y > 4x - 3 or y < 4x - 3, depending on the relationship between 4x - 3 and 0.
To write the inequality represented by the equation -4x + y = -3, we first need to manipulate the equation to express y in terms of x.
Starting with -4x + y = -3, we isolate y by adding 4x to both sides:
y = 4x - 3
Now we have y expressed in terms of x. To form the inequality, we consider the relationship between x and y. The inequality depends on whether the expression 4x - 3 is greater than or less than 0.
If 4x - 3 is greater than 0, then y is greater than 0, and we can write the inequality as:
y > 4x - 3
If 4x - 3 is less than 0, then y is less than 0, and we can write the inequality as:
y < 4x - 3
The inequality represents a region in the coordinate plane where the y-values are either greater than or less than the expression 4x - 3, depending on the direction of the inequality sign.
For example, if we choose a point (x, y) in the region above the line y = 4x - 3, where y is greater than 4x - 3, the inequality y > 4x - 3 will hold true. On the other hand, if we choose a point below the line, where y is less than 4x - 3, the inequality y < 4x - 3 will be satisfied.
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You just completed your math course and you want to calculate your overall grade. You know that tests are weighted 15%, quizzes 10%. projects 35%, participation 35%, and the final exam 5%. What is your overall grade if you scored the following in each category?
Your overall grade, rounded to the nearest hundredth, is approximately 86.35%.
To calculate your overall grade, we need to assign weights to each category and then calculate the weighted average based on your scores.
Let's assume your scores in each category are as follows:
Tests: 85%
Quizzes: 90%
Projects: 92%
Participation: 80%
Final Exam: 88%
Now, let's calculate the weighted average:
Tests: 15% weight × 85% score = 12.75
Quizzes: 10% weight × 90% score = 9.00
Projects: 35% weight × 92% score = 32.20
Participation: 35% weight × 80% score = 28.00
Final Exam: 5% weight × 88% score = 4.40
Overall Grade = Sum of weighted scores / Total weight
Overall Grade = (12.75 + 9.00 + 32.20 + 28.00 + 4.40) / 100
Overall Grade ≈ 86.35%
Therefore, your overall grade, rounded to the nearest hundredth, is approximately 86.35%.
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Five less than twice the sum of a number n and twelve
PLEASE HELP 50 POINTS!!
The sum of two consecutive numbers is 157. This equation, where n is the first number, represents the situation:
2n + 1 = 157.
What is the first number?
A. 77
B. 78
C. 79
D. 80
Marianna finds an annuity that pays 8% annual interest, compounded quarterly. She invests in this annuity and contributes $10,000 each quarter for 6 years. How much money will be in her annuity after 6 years? Enter your answer rounded to the nearest hundred dollars.
The amount of money in Marianna's annuity after 6 years will be approximately $300,516.
To calculate the amount of money in Marianna's annuity after 6 years, we can use the formula for compound interest on an annuity:
A = P * ((1 + r/n)^(n*t) - 1) / (r/n)
Where:
A = the final amount in the annuity
P = the regular contribution (each quarter) = $10,000
r = annual interest rate = 8% = 0.08
n = number of compounding periods per year = 4 (since it's compounded quarterly)
t = number of years = 6
Plugging in the values:
A = 10000 * ((1 + 0.08/4)^(4*6) - 1) / (0.08/4)
Calculating this expression:
A ≈ 10000 * ((1.02)^24 - 1) / 0.02
A ≈ 10000 * (1.601032449136241 - 1) / 0.02
A ≈ 10000 * 0.601032449136241 / 0.02
A ≈ 10000 * 30.05162245681205
A ≈ 300,516.22
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Answer:
304200
Step-by-step explanation:
To find the value of P6, use the savings annuity formula
PN=d((1+r/k)N k−1)r/k.
From the question, we know that r=0.08, d=$10,000, k=4 compounding periods per year, and N=6 years. Substitute these values into the formula gives
P6=$10,000 ((1+0.08/4)6⋅4−1)/(0.08/4).
Simplifying further gives P6=$10,000 ((1.02)24−1)/(0.02) and thus P6=$304,218.62.
Rounding as requested, our answer is 304200.
a system of equations is shown below
y = 3x - 1
y = - 2x + 4
what is the sum of X and Y in the solution to the system
Answer:
3
Step-by-step explanation:
You want the value of (x+y) as determined by the system of equations ...
y = 3x -1y = -2x +4SolutionWe can subtract the second equation from the first to get ...
(y) -(y) = (3x -1) -(-2x +4)
0 = 5x -5
0 = x -1
1 = x
Using the first equation to find y, we have ...
y = 3(1) -1 = 2
The sum of x and y is (x +y) = (1 +2) = 3.
Alternate solutionLet t = x+y. This means y = t -x.
Now, the equations become ...
t -x = 3x -1t -x = -2x +4Adding 4 times the second equation to the first gives ...
(t -x) +4(t -x) = (3x -1) +4(-2x +4)
5t -5x = -5x +15
Adding 5x and dividing by 5 gives ...
t = 3
The sum of x and y is 3.
__
Additional comment
Sometimes you can find the value of the objective function directly, as in the second solution here.
The reason we chose 4 as a multiplier in the alternate solution is that we observed the equations could be written as ...
t -4x = -1
t +x = 4
where the variable x has coefficients with a ratio of -4. Using 4 as the multiplier eliminates the x-variable, leaving t — the variable whose value we want.
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Mark’s cost does not vary directly with time spent talking because
Mark's cost does not vary directly with time spent talking, it indicates the presence of other factors, such as pricing structure, additional services, peak hours, bundled packages, or promotions, that influence the overall cost. These factors can lead to non-linear cost variations and a lack of direct proportionality between the cost and time spent talking.
If Mark's cost does not vary directly with the time spent talking, it means that there is not a simple proportional relationship between the two variables. In other words, doubling the time spent talking does not necessarily result in doubling the cost. This indicates that there are other factors influencing Mark's cost besides just the time spent talking.
There can be several reasons why Mark's cost does not vary directly with time spent talking:
Pricing structure: Mark's cost may be determined by a pricing structure that includes fixed fees or additional charges based on certain conditions. For example, there might be a base rate for a certain duration of talk time, and any additional time may be billed at a different rate.
Additional services: Mark's cost might include additional services or features that are not solely dependent on talk time. For instance, there could be charges for international calling, call forwarding, or other value-added services.
Peak hours or special rates: Mark's cost might be affected by peak hours or special rates. Some service providers offer different pricing during certain times of the day or specific days of the week. This could result in non-linear cost variations with respect to time spent talking.
Bundled packages: Mark's cost might be part of a bundled package that includes other services like internet or television. In such cases, the overall cost may be influenced by factors other than talk time.
Promotions or discounts: Mark's cost may be subject to promotional offers or discounts that are not directly related to the time spent talking.
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Using the image below, find the missing part indicated by the question mark.
(3 separate questions)
The missing part indicated in the figures are ? = 12, TX = 9 and x = 20
How to find the missing part indicated in the figuresFigure a
The missing part can be calculated using the following equation
?/(11 - 5) = 22/11
Evaluate the difference
?/6 = 22/11
So, we have
? = 6 * 22/11
Evaluate the expression
? = 12
Figure b
The missing part can be calculated using the following equation
TX/3 = 6/2
So, we have
TX = 3 * 6/2
Evaluate
TX = 9
Figure c
The value of x can be calculated using the following equation
1/4x + 6 = 2x - 29
So, we have
x + 24 = 8x - 116
Evaluate
-7x = -140
Divide
x = 20
Hence, the value of x is 20
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How many 20kobo make up #20
Answer:
100
Step-by-step explanation:
#20 naira - 20 * 100
= 2000kobo
2000/20
100
QED✅✅
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Please answer the following question on linear algebra.
T satisfies the homogeneity property.
To prove that T is a linear transformation, we need to show that it satisfies two properties: additivity and homogeneity.
Additivity:
Let's consider two arbitrary vectors z₁ = [x₁, y₁] and z₂ = [x₂, y₂] in R².
T(z₁ + z₂) = T([x₁ + x₂, y₁ + y₂])
= [-2(x₁ + x₂) - 1, -2(x₁ + x₂) + 2(y₁ + y₂)]
= [-2x₁ - 2x₂ - 1, -2x₁ - 2x₂ + 2y₁ + 2y₂]
= (-2x₁ - 1, -2x₁ + 2y₁) + (-2x₂ - 1, -2x₂ + 2y₂)
= T(z₁) + T(z₂)
Therefore, T satisfies the additivity property.
Homogeneity:
Let's consider an arbitrary vector z = [x, y] in R² and a scalar k.
T(kz) = T([kx, ky])
= [-2(kx) - 1, -2(kx) + 2(ky)]
= (-2kx - 1, -2kx + 2ky)
= k(-2x - 1, -2x + 2y)
= kT(z)
Since T satisfies both additivity and homogeneity, we can conclude that T is a linear transformation.
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1. A company has $6582 to give out in bonuses. An amount is to be given out equally to each of the 32 employees.
(a) A manager, Jake, reasoned that since 32 goes into 64 twice, each employee will get about $2000. Is his estimate correct? Why or why not?
(b) How much will each employee receive, rounded to the nearest whole dollar? Leave the remainder undivided. Show your work.
Answer:
Answer:
A) His estimate is incorrect, since he has increased a figure to the amount that each employee would receive.
B) Rounded to the nearest dollar, each employee would receive $ 209.
Step-by-step explanation:
Since a company has $ 6582 to give out in bonuses, and an amount is to be given out equally to each of the 32 employees, and A) a manager, Jake reasoned that since 32 goes into 64 twice, each employee will get about $ 2000 , to determine if his estimate is correct, and B) determine how much will each employee receive, rounded to the nearest whole dollar, the following calculations must be performed:
A)
2000 x 32 = 64000
200 x 32 = 6400
Therefore, his estimate is incorrect, since he has increased a figure to the amount that each employee would receive.
B)
6582/32 = X
208.68 = X
Therefore, rounded to the nearest dollar, each employee would receive $ 209.
tion
The graph shows a linear function and an exponential function. Compare and contrast the
two functions. Make sure to use vocabulary words.
The comparison of the functions is
The linear function has a slope of 50 and it is proportionalThe exponential function has a growth factor of 5/3 and an initial value of 1How to compare and contrast the two functionsFrom the question, we have the following parameters that can be used in our computation:
The graph of the two functions
For the linear function, we have
y-intercept = 0
Rate = 50/1 = 50
So, the function is
y = 50x
For the exponential function, we have
y-intercept = 1
Rate = 250/150 = 5/3
So, the function is
y = (5/3)ˣ
Comparing the functions, we have
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PLEASE HELP ME
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match the expressions with their simplified forms.
(a) √2 · √8. The simplified surd expression is 4.
(b) √80. The simplified surd expression is 4√5.
(c) √5/√20. The simplified surd expression is 1/2.
(d) √20. The simplified surd expression is 2√5.
What is the simplification of the surd expression?The given surd expression is simplified as follows;
(a) √2 · √8
we can simplify it as;
√2 · √8 = √(2 x 8) = √16 = 4
(b) √80
we can simplify it as;
√80 = √ (16 x 5) = √16 x √5 = 4√5
(c) √5/√20
we can simplify it as;
√5/√20 x √20 / √20
= (√5 x √20 ) /(20)
= √100 / 20
= 10/20
= 1/2
(d) √20
we can simplify it as;
√20 = √4 x √5 = 2√5
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Determine whether 548 is greater than or less than 373. Then write the expression showing this using < or >.
Answer:
548 > 373
Step-by-step explanation:
548 is greater than 373 because when we compare the digits from left to right, we find that the first digit of 548 (5) is greater than the first digit of 373 (3). Therefore, we can conclude that 548 is greater than 373.
The ">" symbol is used to represent "greater than" in mathematical comparisons.
Hope this helps!
The functions f(x) = x^2 – 3 and g(x) = –x^2 + 2 are shown on the graph.
The graph shows f of x equals x squared minus 3, which is an upward-opening parabola with a vertex at 0 commas negative 3 and a point at negative 1 comma negative 2, and a point at 1 comma negative 2. The graph also shows g of x, which is a downward opening parabola with a vertex at 0 commas 2 and a point at negative 1 comma 1, and a point at 1 comma 1.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
y ≤ x^2 – 3
y > –x^2 + 2
The solution set to the given system of inequalities is represented by the shaded region under the curve of f(x) = x^2 – 3 (including the points on the curve) and above the curve of g(x) = –x^2 + 2 (excluding the points on the curve). The overlapping region between these shaded areas represents the solution set to the system.
To graph the solution set to the system of inequalities y ≤ x^2 – 3 and y > –x^2 + 2, we can modify the graphs of f(x) = x^2 – 3 and g(x) = –x^2 + 2 accordingly. Here's how:
For the inequality y ≤ x^2 – 3:
The original graph of f(x) = x^2 – 3 is an upward-opening parabola with a vertex at (0, -3).
To graph y ≤ x^2 – 3, we need to shade the region below or on the parabola. This includes all points on the parabola itself.
Therefore, we shade the area under the curve of the original graph of f(x) and include the points on the curve.
For the inequality y > –x^2 + 2:
The original graph of g(x) = –x^2 + 2 is a downward-opening parabola with a vertex at (0, 2).
To graph y > –x^2 + 2, we need to shade the region above the parabola. This excludes all points on the parabola itself.
Therefore, we shade the area above the curve of the original graph of g(x) but exclude the points on the curve.
By modifying the graphs of f(x) and g(x) according to these shading instructions, we can graphically represent the solution set to the system of inequalities.
The solution set can be identified by observing the overlapping region or the intersection between the shaded area under the curve of f(x) and the shaded area above the curve of g(x). The points within this overlapping region satisfy both inequalities simultaneously.
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Which graph represents the function p(x) = |x – 1|?
On a coordinate plane, an absolute value graph has a vertex at (0, 1).
On a coordinate plane, an absolute value graph has a vertex at (negative 1, 0).
On a coordinate plane, an absolute value graph has a vertex at (0, negative 1).
The correct statement is: On a coordinate plane, an absolute value graph has a vertex at (0, 1).
The function p(x) = |x - 1| represents an absolute value function. The vertex of an absolute value function in the form f(x) = |x - h| + k is given by the point (h, k). In this case, the function p(x) = |x - 1| has a vertex at (1, 0).
Therefore, none of the provided options accurately represents the vertex of the function p(x) = |x - 1|. The correct vertex for this function is (1, 0), which means the vertex is at x = 1 and y = 0 on the coordinate plane. It is important to note that the vertex is located at (h, k) where h represents the x-coordinate and k represents the y-coordinate.
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write inequality shown y=-11/7x-4
Answer:The inequality represented by the equation y = -11/7x - 4 can be written as:
y ≤ -11/7x - 4
This represents a less than or equal to inequality, indicating that the values of y are less than or equal to the expression -11/7x - 4.
Step-by-step explanation: .
Which table matches the equation for y = 3/2x-3
Answer: I think it's H, if it isn't and you get a second try it should be N
Step-by-step explanation: Both H and N start with 0/-3 except F which means F is wrong. Maybe you should wait for a better answer...but it shouldn't be F
pls help and draw it so it's more easier
In this rectangle, there are two lines of symmetry.
A line of symmetry is a line that divides a shape into two equal halves, such that each half is a mirror image of the other. The lines of symmetry in a rectangle are vertical and horizontal.
Vertical Line of Symmetry:
A vertical line of symmetry runs from the top to the bottom of the rectangle, dividing it into two equal halves. Each half is a mirror image of the other. To identify the vertical line of symmetry in a rectangle, you can visualize folding the rectangle along a line from top to bottom. The left and right sides of the folded rectangle will match perfectly.
Horizontal Line of Symmetry:
A horizontal line of symmetry runs from one side of the rectangle to the other, dividing it into two equal halves. Each half is a mirror image of the other. To identify the horizontal line of symmetry in a rectangle, imagine folding the rectangle along a line from left to right. The top and bottom sides of the folded rectangle will align perfectly.
I find the lines of symmetry in a rectangle, you can also observe its properties. In a rectangle, opposite sides are parallel and equal in length, and all interior angles are right angles (90 degrees). By considering these characteristics, you can determine that the vertical and horizontal lines passing through the center of the rectangle will be the lines of symmetry.
Understanding the lines of symmetry in a rectangle is essential in various applications, such as geometry, design, and architecture. These lines allow for balanced and symmetrical arrangements, providing aesthetic appeal and structural stability.
Final answer:
In following rectangle, there are two lines of symmetry.
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HELP PLEASEEE I NEED IMMEDIATELY
There are like 4 people watching this question...
Answer:
1335.6
Step-by-step explanation:
volume = pir^2 h = (3.14)(6)^2(15) = (3.14)(36)(15) = (47.1)(36) = 1,335.6
The volume of the tank is 1695.60 ft³.
What is the volume of the tank?A cylinder is a three-dimensional object. It is a prism with a circular base. The volume is the amount of space in an object.
Volume of a cylinder = πr²h
Where:
π = 3.14 h = height = 15r = radius = 6= 3.14 x 6² x 15 = 1695.60 ft³
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algebra 2 equality’s
The algebra 2 is a vast field that deals with various mathematical concepts, such as equations and inequalities.
Algebra 2 is a branch of mathematics that mainly deals with equations and inequalities. An equation is a mathematical statement that implies that two expressions are equal.
Similarly, an inequality implies that two expressions are not equal but are related by a certain operation.There are different types of equations that one may encounter in Algebra 2.
A linear equation is an equation that can be represented by a straight line on the coordinate plane. A quadratic equation is one that can be written in the form ax² + bx + c = 0.
There are also exponential, logarithmic, and trigonometric equations that one may come across.Inequalities are statements that two expressions are not equal. Inequalities can be represented graphically on a coordinate plane, just like equations.
There are different types of inequalities such as linear, quadratic, exponential, and logarithmic inequalities.In conclusion, These concepts help in solving real-world problems by providing a framework to analyze them mathematically.
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Find the length of side X in simple radical form with a rational denominator
The length of side X in simple radical form with a rational denominator is 25/√3.
What is a 30-60-90 triangle?In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.
This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):
Adjacent side = 5/√3
Hypotenuse, x = 5 × 5/√3
Hypotenuse, x = 25/√3.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
