Suppose that F(x) = x² and G(x) = 3x^2 + 8. Which statement best compares the graph of G(x) with the graph of F(x)?
A. The graph of G(x) is the graph of F(x) stretched vertically and
shifted 8 units to the left.
B. The graph of G(x) is the graph of F(x) compressed vertically and
shifted 8 units to the left.
C. The graph of G(x) is the graph of F(x) compressed vertically and
shifted 8 units up.
D. The graph of G(x) is the graph of F(x) stretched vertically and
shifted 8 units up.
Answers
Answer:
The graph of G(x) is the graph of F(x) stretched vertically and shifted 8 units up.
Related Questions
What is the length of DE?
A A
12
DXE
A. 6
B. 8
C. 5
D. 7
Answers
Answer:
A
Step-by-step explanation:
these two triangles are similar
therefore corresping sides are proportionate
12/8=9/x
12x=72
x=72/12=6
Answer:
the answer is 6
Step-by-step explanation:
i hope this is helpful
Find the general solution of the given differential equation. cos^2(x)sin(x)dy/dx+(cos^3(x))y=1 g
Answers
If the given differential equation is
[tex]\cos^2(x) \sin(x) \dfrac{dy}{dx} + \cos^3(x) y = 1[/tex]
then multiply both sides by [tex]\frac1{\cos^2(x)}[/tex] :
[tex]\sin(x) \dfrac{dy}{dx} + \cos(x) y = \sec^2(x)[/tex]
The left side is the derivative of a product,
[tex]\dfrac{d}{dx}\left[\sin(x)y\right] = \sec^2(x)[/tex]
Integrate both sides with respect to [tex]x[/tex], recalling that [tex]\frac{d}{dx}\tan(x) = \sec^2(x)[/tex] :
[tex]\displaystyle \int \frac{d}{dx}\left[\sin(x)y\right] \, dx = \int \sec^2(x) \, dx[/tex]
[tex]\sin(x) y = \tan(x) + C[/tex]
Solve for [tex]y[/tex] :
[tex]\boxed{y = \sec(x) + C \csc(x)}
which follows from [tex]\tan(x)=\frac{\sin(x)}{\cos(x)}[/tex].
what is mean by Expanded form power of 10 please answer it quickly urgent!
Answers
1,000.
Why? Well, the expanded form of 1,000 is itself because it is in a digits place notable for being able to do expanded form in. There are the ones place, tens place, hundreds place, and thousands place. Because ten to the third power is 1,000, the number itself is representative of its own expanded form. This varies for numbers that are different though. Another example would be as follows; the number 1,783. Here is the expanded form of that number:
1,000 + 700 + 80 + 3
Remember the digits places I mentioned above (ones, tens, hundreds, and thousands)? Those come in handy for these kinds of numbers. 1 is in the thousands place so the number is 1,000. 7 is in the hundreds place so the number is 700. 80 is in the tens place so the number is 80. Lastly, 3 is in the ones place so the number is 3. An easy way to remember expanded form is to just take the number by what digits place it is in, and multiply it by the corresponding digit value that it is in. For example, to get 80, we can do 8 x 10 because we are multiplying the 8 that is in the tens place by the digit place it is in, which happens to be the tens place. If you need to better understand, let me know and I will gladly assist you!
The local public pool is a rectangle with two semicircles.
The area of the rectangle is
.
Using 3.14 for π and rounding to the nearest meter, the area of each half circle is
m2.
The area of the surface of the pool is
m2.
Answers
The area of the surface of the pool is 7322.64 m².
What is Area of rectangle?The area of rectangle is product of length and its breadth.
i.e., length * breadth
Given: Length = 100 m, Width = 52 m and Diameter = 52 m
Area of rectangle,
= 100 × 52
= 5200 m²
Now,
Area of semicircle = 1/2 × πr²
=1/2 × 3.14 × 26²
= 1061.32 m²
Hence, area of the surface of the pool is
= 1061.32 + 1061.32 + 5200
= 7322.64 m²
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5200 square meters, 1061, 7322
Which of the following describe an angle with a vertex at E.
Answers
Answer:
A and B are correct
Step-by-step explanation:
The middle letter represents the vertex of an angle. For instance, angle ABC has a vertex at B. Because the letter "e" is in the middle of angle FED and angle DEF, it represents the vertex of those angles. Hope this helps
ASAP!!! What is the least common denominator of the expression below?
Answers
Answer:
D
Step-by-step explanation:
factor the denominators of both fractions
x² - 16 ← is a difference of squares
= (x - 4)(x + 4)
8x + 2x² ← factor out 2x from each term
= 2x(4 + x) = 2x(x + 4)
then expression is
[tex]\frac{x^2}{(x-4)(x+4)}[/tex] + [tex]\frac{9x}{2x(x+4)}[/tex]
with LCD of 2x(x + 4)(x - 4)
What is the value of 3 in this number? 728. 36
Answers
Answer:
The place value of 3 is tens
the 3 is in the value of tens
4
Which equation represents a linear function that has a slope of 5 and a y-intercept of -6?
4
O y=-6x+²/
O y=x-6
Oy=x+6
Oy=6x+
k
Answers
Answer:
y = 5x - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = 5 and c = - 6 , then
y = 5x - 6 ← equation of line
The equation represents a linear function with a slope of 5 and a y-intercept of -6 is y = 5x - 6.
The equation of a linear function is typically written in the form "y = mx + b," where "m" represents the slope and "b" represents the y-intercept.
Given that the slope is 5 and the y-intercept is -6, the equation becomes:
y = 5x - 6
Here's the calculation:
The slope (m) is 5, and the y-intercept (b) is -6. Therefore, the equation becomes:
y = 5x - 6
This equation represents a linear function with a slope of 5 and a y-intercept of -6.
Hence the equation represents a linear function with a slope of 5 and a y-intercept of -6 is y = 5x - 6.
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Laurel has an area in her yard that is in the shape of a parallelogram. It has a base of 30 feet and a height of 22 feet. She wants to cover this area with wildflower seeds. She finds out that 1 ounce of seeds covers 125 square feet of ground. How many ounces of seeds does she need to cover this area?
Answers
Answer:
Laurel has to cover this area with 2.64 ounces of seeds.
Step-by-step explanation:
Given
Base of Parallelogram = 30ft
Height of Parallelogram = 22ft
Area of Parallelogram = 1/2*base*height
Therefore, Area of Parallelogram = 1/2*30*22
= 330sq. ft
Given
One ounce of seed covers 125 sq. ft
Hence, No. of ounces needed to cover 330 sq. ft= 330/125
= 2.64
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6,000+50+5 standard form
Answers
The expression 6000 + 50 + 5 in standard form is 6.055 * 10^3
How to express in standard form?The expression is given as:
6000 + 50 + 5
Evaluate the sum
6055
A number in standard form is represented as
a * 10^b
Where:
0 < a < 1
b is an integer
So, we have:
6055
Multiply by 1
6055 * 1
Express 1 as 1000/1000
6055 * 1000/1000
This gives
6.055 * 1000
Express 1000 as 10^3
6.055 * 10^3
Hence, 6000 + 50 + 5 in standard form is 6.055 * 10^3
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If f(x)=7^x and g(x)=15x/x+9, find a simplified formula for: g(f(x))=
Answers
Answer:
[tex]\frac{15*7^{x} }{7^{x} +9}[/tex]
Step-by-step explanation:
→ Substitute f(x) into g(x)
[tex]\frac{15*7^{x} }{7^{x} +9}[/tex]
is about and DC are parallel, which angles are congruent to D 3?
Answers
Answer:
A
Step-by-step explanation:
Angles 1 and 3 are congruent since they are vertical angles.
Angle 7 is congruent to angle 3 since they are corresponding angles.
Angle 5 is congruent to angle 1 since they are corresponding angles.
Answer: A
Howard drew a square in Quadrant IV and correctly reflected it across the y-axis.Which statement explains one method Howard could have used to determine the coordinates of the vertices of the image?
Answers
Using translation concepts, the method that Howard could have used to determine the coordinates of the vertices of the image is:
(x,y) -> (-x,y).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
A reflection over the y-axis can be described according to the following rule:
(x,y) -> (-x,y).
Hence this rule can be applied to find the vertices.
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Helen wants to have cake for her party. She needs 1 cake for every 8 people. Which expression helps her decide how many cakes to buy if p represents the number of people?
A. 8p
B. 1/8p
C. 8 + p
D. p-8
Answers
Which explains whether or not the function represents a direct variation? This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour. This function represents a direct variation because it has a positive, constant rate of change of $10 per hour. O This function does not represent a direct variation because it does not represent the cost for 1 hour. O This function does not represent a direct variation because the function rule for the cost is to add $10, not multiply by a constant. Which explains whether or not the function represents a direct variation ? This function represents a direct variation because it passes through the origin and has a constant rate of change of $ 5 per hour . This function represents a direct variation because it has a positive , constant rate of change of $ 10 per hour . O This function does not represent a direct variation because it does not represent the cost for 1 hour . O This function does not represent a direct variation because the function rule for the cost is to add $ 10 , not multiply by a constant .
Answers
The answer choice which explains whether the function is a direct variation or not is; This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.
Which explains whether or not the function represents a direct variation?It follows from the task content that the function passes through the origin and hence, if the function was represents as a linear function, it's y-intercept would be zero.
Furthermore, the slope, otherwise termed it's rate of chage is constant and is evaluated as; $5 per hour. Hence, the aforementioned form the basis for the classification of the function as a direct variation.
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Carefully follow the steps to find the solution to the three equation system.
1.2x+y+3:= 12
2. x-2y+z=-5
3.5.x- y+ 2z = 5
a. Use equations 2 and 3 and eliminate the z by multiplication and addition, creating a new equation with only two variables.
b. Use equations 1 and 2 and eliminate the z by multiplication and addition, creating a second equation with only two variables.
c. Use the two new equations, and eliminate the x-variable by multiplication and addition, finding the value for the y-variable.
d. Substitute y-value in the second new equation and find the x-value.
e. Substitute the z-and y-values into original equation 2 to find the z-value
Answers
Answer:
This answer assumes that the first equation is meant to read:
2x + y +3z = 12, and not
1.22x+y+3:= 12
Spoiler Alert: x = 1, y=4, and z=2
Step-by-step explanation:
1. 2x + y +3z = 12
2. x - 2y + z = -5
3. 5x - y+ 2z = 5
==============
Use equations 2 and 3 to eliminate z:
2. x - 2y + z= -5
3. 5x - y+ 2z = 5
-2(x - 2y + z) = -2(-5) [Multiply equation 2 by -2]
5x - y+ 2z = 5
Now subtract this new equation from equation 3:
-2x + 4y - 2z = 10 (Eq 3)
5x - y+ 2z = 5 [
3x +3y = 15 [Equation A]
=================
Use equations 1 and 2 to eliminate z:
2x + y +3z = 12 (Eq. 1)
x - 2y + z = -5 (Eq. 2)
2x + y +3z = 12
(-3)(x - 2y + z = -5) [Multiply Eq. 2 by (-3)]
-3x + 6y -3z = 15
Now add the resulting two equations.
2x + y + 3z = 12 (Eq. 1)
-3x + 6y -3z = 15 (Eq,2 times -3)
-x +7y = 27 [Equation B]
=============
Eliminate x with the 2 resulting equations (from above)
3x +3y = 15 [Equation A]
-x +7y = 27 [Equation B]
----
3x +3y = 15
3*(-x +7y = 27) [Multiply the Equation B by 3]
-3x +21y = 81 [Aha - this equation has a -3x term, exactly what we need to eliminate the x term in Equation A]
---
Now add the two resulting equations:
3x +3y = 15
-3x +21y = 81
24y = 96 [The x term disappears. But we'll "find x" later]
y = 4 [Divide both sides by 24]
Find y and z:
Since y = 4,
-x +7y = 27 (From above, Equation B]
-x = -7y + 27
x = 7y - 27
x = 7(4)-27
x = 1 [Looking good]
=====
Find z: (Use y = 4 and x = 1)
x - 2y + z = -5 [Equation 2]
(1) -2*(4) + z = -5
1 - 8 + z = -5
z = 2
Check:
Do the original equations work when x = 1, y = 4, and z = 2?
Results:
1. 2x + y +3z = 12
(1) + (4) +3(2) YES, this equals 12
2. x - 2y + z = -5
(1) -2*(4) + (2) YES, this equals -5
3. 5x - y+ 2z = 5
5(1) - (4) + 2(2) YES, this equals 5
x = 1, y=4, and z=2
in a test out of 40,the marks of 15 students were 31,18,6,26,36,24,23,14,28,28,32,9,11,22,21.
a.calculate the mean mark for the test
b.express the mean mark as a percentage
Answers
Answer:
a. The mean mark for the test was 20.667.
b. The mean mark as a percentage is 51.6%.
Step-by-step explanation:
a. Calculate the mean mark for the test.
Add all of the scores from each student. [tex]31+18+6+26+36+24+23+14+28+28+32+9+11+22+2=310[/tex]Divide the sum by the amount of students who took the test.[tex]310/15=20.667[/tex]Therefore, the mean mark for the test was 20.667.b. Express the mean mark as a percentage.
Put mean mark and total possible marks in fraction form.[tex]\frac{20.667}{40}[/tex]Divide the numerator by the denominator (essentially changing the fraction into the decimal form). [tex]20.667/40=0.516[/tex]Multiply the quotient by 100. [tex]0.516*100=51.6[/tex]Therefore, the mean mark as a percentage is 51.6%22*90 what 2+2 3 +3 3+3
Answers
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\mathsf{ASSUMING: }\\\mathsf{22\times90}\\\mathsf{= 90 \times 22}\\\mathsf{= 1,980}[/tex]
[tex]\mathsf{ASSUMING: }\\\mathsf{2 + 2 + 3 + 3 + 3 + 3}\\\mathsf{= 2\times 2 + 3\times4}\\\mathsf{= 4 + 12}\\\mathsf{= 16}[/tex]
[tex]\huge\textsf{Answer \#1. 1,980 }\huge\checkmark\\\\\\\huge\textsf{Answer \#2. 16 }\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
how to solve this???
Answers
[tex]\large\sf{\sqrt{\frac{1+sin\theta}{1-sin\theta}}+\sqrt{\frac{1-sin\theta}{1+sin\theta}}}[/tex]
[tex]\\[/tex]
[tex]\large \sf{=\frac{\left(\sqrt{1+sin\theta}\right)^{2}+\left(\sqrt{1-sin\theta}\right)^{2}}{\sqrt{(1-sin\theta)(1+sin\theta)}}}[/tex]
[tex]\\[/tex]
[tex]\large\sf{=\frac{1-sin\theta+1+sin\theta}{\sqrt{1^{2}-sin^{2}\theta}}}[/tex]
[tex]\\[/tex]
[tex]\large \sf{=\frac{2}{\sqrt{cos^{2}\theta}}}[/tex]
[tex]\\[/tex]
[tex]\large\sf{= \frac{2}{cos\theta}}[/tex]
[tex]\\[/tex]
[tex]\large\sf{= 2sec\theta}[/tex]
[tex]\\[/tex]
[tex]\large\sf{=RHS}[/tex]
Therefore,
[tex]\large\sf\red{\sqrt{\frac{1+sin\theta}{1-sin\theta}}+\sqrt{\frac{1-sin\theta}{1+sin\theta}}=2sec\theta}[/tex]
Look at the graph below.
what is the slope of the line ?
Answers
Answer:
The slope is [tex]-\frac{1}{5}[/tex].
Step-by-step explanation:
Choose 2 points on the graph.
(7,3) and (2,2)
Use slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{2-3}{2-7}[/tex]=[tex]\frac{-1}{-5}[/tex]
The slope is [tex]-\frac{1}{5}[/tex].
Answer:
[tex]\frac{1}{5}[/tex] or [tex]0.2[/tex]
Step-by-step explanation:
The slope refers to the gradient of the line.
There is a formula to find the gradient of a line where m is the gradient:
[tex]m=\frac{y_{2}-y_{1} }{x_{2} - x_{1}}[/tex]
So, we will take two points on the line.
Let's take our first point as (-3, 1) and our second as (7, 3).
Let's work with the [tex]y[/tex] values.
The first [tex]y[/tex] value is 1 and the second [tex]y[/tex] value is 3.
So, in the numerator, they would look like [tex]3 - 1[/tex].
Let's work with the [tex]x[/tex] values.
The first [tex]x[/tex] value is -3 and the second [tex]x[/tex] value is 7.
So, in the denominator, this would look like [tex]7--3[/tex].
Let's use these in the fraction and work out our answer:
[tex]m = \frac{3-1}{7--3} = \frac{2}{10} = \frac{1}{5} = 0.2[/tex]
Therefore, our final answer is [tex]\frac{1}{5}[/tex] or [tex]0.2[/tex].
Please solve it. It will help me for my exam preparation.
Answers
The solution of the given expression is [tex][p^{2}(p-y)^{y-1} (p-y)^{y-2} -2p(p-y)^{y} (p-y)^{y-2} +7(p-y)^{y} (p-y)^{y-1}]/ (p-y)^{y} (p-y)^{y-1}(p-y)^{y-2}[/tex]
Given [tex]p^{2} /(p-y)^{y} -2p/(p-y)^{y-1} +7/(p-y)^{y-2}[/tex]
We have to solve the above expression.
We know that expression is a combination of numbers, symbols, variables and coefficients, indeterminants. Expression shows relationship between variables. LCM is the smallest number that is divisible by both the numbers whose LCM has been taken. Coefficients are present in the beginning of variables. Symbols are arithmetic signs like addition, subtraction, multiplication and division, etc.
We have to take LCM of the expression and solve accordingly so that the expression can be solved =
[tex]p^{2} /(p-y)^{y} -2p/(p-y)^{y-1} +7/(p-y)^{y-2}[/tex]= [tex][p^{2}(p-y)^{y-1} (p-y)^{y-2} -2p(p-y)^{y} (p-y)^{y-2} +7(p-y)^{y} (p-y)^{y-1}]/ (p-y)^{y} (p-y)^{y-1}(p-y)^{y-2}[/tex]
Hence the expression [tex]p^{2} /(p-y)^{y} -2p/(p-y)^{y-1} +7/(p-y)^{y-2}[/tex] is equal to = [tex][p^{2}(p-y)^{y-1} (p-y)^{y-2} -2p(p-y)^{y} (p-y)^{y-2} +7(p-y)^{y} (p-y)^{y-1}]/ (p-y)^{y} (p-y)^{y-1}(p-y)^{y-2}[/tex]
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Line I has a slope of -The line through which of the following pair of
13
points is perpendicular to l?
Answers
The points (2,6) (-4,-7) have a slope of 13/6 which satisfies the perpendicular condition option (B) is correct.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The question is incomplete.
The complete question is:
Line L has a slope of -6/13. The line through which of the following pair of points is perpendicular to L?
A) (6,-4) (-7,2)
B) (2,6) (-4,-7)
C) (6,9) (-4,-4)
D) (13,-4) (-7,2)
Line L slope m = -6/13
If two lines are perpendicular:
(m)(m') = -1
(-6/13)(m') = -1
m' = 13/6
From the points given finding the slope of every point:
A) (6,-4) (-7,2)
[tex]\rm m' =\dfrac{2+4}{-7-6}[/tex]
m' = -6/13
B) (2,6) (-4,-7)
[tex]\rm m' =\dfrac{-7-6}{-4-2}[/tex]
m' = 13/6
Thus, the points (2,6) (-4,-7) have a slope of 13/6 which satisfy the perpendicular condition option (B) is correct.
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marcus needs to paint a large wall with a window centered in the middle of the wall (shown below).what is the area (in square feet)that marcus will need to paint.
A 336ft
B 256ft
C 300ft
D 264ft
Answers
To calculate the area that Marcus needs to paint we must calculate the area of the window and subtract it from the total area of the wall.
How to calculate the area of a wall?To calculate the area of a rectangular wall we must use the following formula:
area = a × bWhere a is the length of the height, and b is the length of the width.
Next, we need to calculate the area of the window. If it is a square or rectangular window we use the same formula "area = a × b".
If the window is circular we use this formula:
Area of the circle = π r²Once we know the area of the wall and the area of the window, we subtract the area of the window from the area of the wall and we will know what is the total area that Marcus must paint.
Note: This question is incomplete because some information is missing. However I can answer it based on my general prior knowledge.
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What’s the answer? I don’t know how I got it wrong
Answers
Answer:
C. Line PQ
Step-by-step explanation:
Tangent means touching, not crossing.
PLEASE HELP!!
1.17−0.07a+(−3.92a) = ?
Simplify the equation.
Answers
Answer:
I think it's 1.17 - -3.85
A father is 28 years older than his son. in 8 years time he will be 3 times as old as his son. how old is the father now?
Answers
Answer:
34 years
Step-by-step explanation:
f = s + 28 Eq. 1
f+8 = 3(s+8) Eq. 2
f = father age
s = son age
replacing Eq. 1 on Eq. 2
(s+28) + 8 = 3(s+8)
s + 36 = 3*s + 3*8
s + 36 = 3s + 24
36 - 24 = 3s - s
12 = 2s
12/2 = s
s = 6
from the Eq. 1
f = 6 + 28
f = 34
Check
from the Eq. 2
34+8 = 3(6+8)
42 = 3*14
can someone look at this image?
Answers
Answer:
image doesn't showing up ........The following data show the scores of some students in a competition:
12 points
21 points
29 points
17 points
24 points
23 points
28 points
Which box plot represents the data?
A box plot titled Scores of Participants and labeled Scores uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 21 to 28 on the number line. A line in the box is at 23 The whiskers end at 17 and 29.
A box plot titled Scores of Participants and labeled Scores uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 17 to 24 on the number line. A line in the box is at 23 The whiskers end at 12 and 28.
A box plot titled Scores of Participants and labeled Scores uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 17 to 28 on the number line. A line in the box is at 21 The whiskers end at 12 and 29.
A box plot titled Scores of Participants and labeled Scores uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 17 to 28 on the number line. A line in the box is at 23 The whiskers end at 12 and 29.
Answers
The plot represent the data A box plot titled Scores of Participants and labeled Scores uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35.
The box extends from 17 to 24 on the number line.
A line in the box is at 23 The whiskers end at 12 and 28.
What is box- plot?A box plot is a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.
Given:
12 points
21 points
29 points
17 points
24 points
23 points
28 points
According to the given data,
A box plot titled Scores of Participants and labeled Scores uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35.
The box extends from 17 to 24 on the number line.
A line in the box is at 23 The whiskers end at 12 and 28.
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Solve the system. 2x y = −3 −2y = 6 4x write each equation in slope-intercept form. y = x y = x
Answers
The system of equation has an infinitely many solutions
How to solve the system of equations?The equations are given as:
2x + y = -3
-2y = 6 + 4x
Express 2x + y = -3 in slope-intercept form
y = - 3 -2x
Divide through by -2 in -2y = 6 + 4x
y = -3 - 2x
So, we have:
y = - 3 -2x and y = -3 - 2x
Both equations are the same.
This means that the system of equation has an infinitely many solutions
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annalise makes rectangular patchworks quilts out of leftover fabric scraps. the first scrap she is using to make a quilt has a width of 2x feet and a length of 5x feet. when finished, the entire quilt will be 5 feet wider and 3 feet longer than the first scrap used. which of the following functions will give the area, f(x), of the quilt in square feet ?
Answers
The area is given by f(x) = 10x² + 31x + 15.
The function is a rectangle's area function. We know that a rectangle is a flat, four-sided shape with straight sides and right-angled interior angles. Additionally, the opposing sides are parallel and of the same length.
Rectangle Area = Length * Width
The length of fabric scrap is 5x. So, the rectangular patchwork's length will be 5x + 3.
Since the width of the fabric scrap will be 2x, the rectangular patchwork's width will be 2x + 5.
Then area = f(x) = (5x + 3)(2x + 5) = 10x² + 25x + 6x + 15 = 10x² + 31x + 15
Therefore the area is given by f(x) = 10x² + 31x + 15.
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