the graph of f(x), shown below, has the same shape as the graph of G(x)=x^4-x^2, which contains the point (0,0) Which of the following is the equation of F(x)

The Graph Of F(x), Shown Below, Has The Same Shape As The Graph Of G(x)=x^4-x^2, Which Contains The Point

Answers

Answer 1

Answer:  Option B

[tex]F (x) = x ^ 4-x ^ 2 + 4[/tex]

Step-by-step explanation:

We have the function [tex]G (x) = x ^ 4-x ^ 2[/tex] and we know that it contains the point (0,0). That is, it cuts the y axis and y = 0

Then the graph of F(x) is shown in the image and we know that it is a transformation of F(x).

The function F(x) cuts the y axis and y = 4.

For this reason we can conclude that the function F(x) is the function G(x) displaced 4 units upwards.

The transformation that shifts the graph of a function k units upwards is:

[tex]F (x) = G (x) + k[/tex]

Where [tex]k> 0[/tex].

In this case k = 4. Therefore:

[tex]F (x) = G (x) +4\\\\F (x) = x ^ 4-x ^ 2 + 4[/tex]

The answer is Option B


Related Questions

Drag each tile to the correct box. Arrange these bank balances from highest debt to lowest debt. Liz -$22 Kevin -$42 Paul -$10 Henry -$32 Jenny -$28 Sean -$20 Kelly -$3

Answers

Answer:

Kevin-$42, Henry-$32,Jenny -$28,  Liz -$22, Sean -$20, Paul -$10, Kelly -$3

Answer:

kevin, henry,  jenny, liz, sean, paul, kelly

Step-by-step explanation:

i did the pretest and got it right!

Angles T and U are a linear pair. Angle U measure (9x+6) and Angle T measures(6x+9). What is the value of x, in degrees?

Answers

Answer:

11 degrees.

Step-by-step explanation:

"Angles T and U are a linear pair. Angle U measure (9x+6) and Angle T measures(6x+9). What is the value of x, in degrees?"

We know that a linear pair MUST add up to 180 degrees, therefore (9x+6)+(6x+9)= 180

Now for some algebra-

(9x+6)+(6x+9)= 180

6 and nine can both be divided by 3, so we will do that for simplicity:

((9x+6)+(6x+9)= 180)/3=

(3x+2)+(2x+3)=60

We will now separate the parenthesis, as they serve no purpose anymore.

(3x+2)+(2x+3)=60

3x+2+2x+3=60

Combine terms

5x+5=60

Take away the 5 to isolate the variables

5x+5=60

-5

5x=55

Divide by 5

5x=55

/5

x=11

The value of x is 11 degrees.

imagine you pour some hot soup into a bowl, and you place your hands on the outside of the bowl and the outside is warm, how did the heat from the soup through the bowl to your hands?

Answers

Answer:

conduction

Step-by-step explanation:

the process by which heat or electricity is directly transmitted through a substance when there is a difference of temperature or of electrical potential between adjoining regions, without movement of the material.

PLEASE HELP!

What is AD?

A. 15

B. 12

C. 3

D. 20

Answers

Answer:

A. 15

Step-by-step explanation:

To solve this you need to compare the lengths given to you in the question statement.

Because the lines originate from a single point, they're like triangles.  We can easily see a triangle AGF and a triangle ADE, right?

Both triangles are similar triangles, so we can see triangle ADE as a larger version of angle AGF.

They give you the dimension of A F and A E (through A F + F E) to establish a ratio... and they give you A G, asking for A D.

So, A F = 16, A E = 20 (16 + 4), A G = 12.

Since A D is to A G what A E is to A F, we can easily make the following cross-multiplication:

[tex]\frac{A D}{A G} = \frac{A E}{A F}[/tex]

So, A D = (A G * A E)/A F

A D = (12 * 20) / 16 = 15

9 inches of ribbons are needed for wrapping each present. How many presents can be wrapped with 6 yards of ribbons?

Answers

Answer:

24 presents.

Step-by-step explanation:

First I did 36 multiplied by 6 and got 216. Then i divided 216 by 9 and got 24.

Answer: with 6 yards of ribbons we can wrap 24 presents.

Step-by-step explanation:

For each 9 inches of ribbons, we can wrap one present, then if we have 6 yards we have:

1 yard = 36 inches

then 6 yards is equal to 6*36 inches = 216 inches

now, in how many pieces of 9 inches we can divide the 216 inches?

this is:

N = 216/9 = 24

for each one of those 24 pieces of 9 inches we can wrap a present, this means that with 6 yards of ribbons we can wrap 24 presents.

Will the graph of the equation above intersect the x-axis in zero, one, or two points?

Answers

Answer: Option D

Step-by-step explanation:

Add 4x² to both sides  of the equation:

[tex]16x+8+4x^2=-4x^2+4x^2\\4x^2+16x+8=0[/tex]

The Quadratic formula is:

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

You can identify that in this case:

[tex]a=4\\b=16\\c=8[/tex]

Substitute into the Quadratic formula:

[tex]x=\frac{-16\±\sqrt{(16)^2-4(4)(8)}}{2(4)}[/tex]

 [tex]x_1=-0.58\\x_2=-3.41[/tex]

Therefore, the graph of the equation above intersect the x-axis in two points.

Hello!

The answer is:

D. The parabola intercepts the x-axis in two points.

[tex]x_{1}=-0.59\\\\x_{2}=-3.41[/tex]

Why?

To find the parabola intercepts, we need to use the quadratic formula. The parabola intercepts with the x-axis, are also called roots or zeroes.

The quadratic formula states that:

[tex]x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]

We are given the parabola:

[tex]16x+8=-4x^{2} \\[/tex]

Which is also equal to:

[tex]4x^{2}+16x+8=0[/tex]

Where,

[tex]a=4\\b=16\\c=8\\[/tex]

Then, substituting into the quadratic formula to find the roots of the parabola, we have:

[tex]x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}\\\\x=\frac{-16+-\sqrt{(16)^{2}-4*4*8 } }{2*4}=\frac{-16+-\sqrt{(256-128) } }{8}\\\\x==\frac{-16+-\sqrt{(256-128) } }{8}=\frac{-16+-\sqrt{(28 } }{8}\\\\x=\frac{-16+-\sqrt{128 } }{8}=\frac{-16+-(11.31) }{8}\\\\\\x_{1}=\frac{-16+(11.31) }{8}=-0.59\\\\x_{1}=\frac{-16-(11.31) }{8}=-3.41[/tex]

Hence,the parabola intercepts the x-axis in two points.

[tex]x_{1}=-0.59\\\\x_{2}=-3.41[/tex]

Have a nice day!

Please help and thank you

Answers

Through my understanding of the question I think the correct answers would be A and D.

hope this helps

A price increases from $82 to $89.38. What is the percent change?

Answers

Answer:

9%

Step-by-step explanation:

89.38/82 = 1.09

.09% increase

or 9%

The answer is 9% I think

In the equation 4x+5y=20 what is the y value that solves the equation when x=5? Show your work

Answers

Answer:

4(5)+5y=20          20+5y=20 then subtract the 20 with other 20= 0

5y/5=0/5                               y=0

Step-by-step explanation:

ANSWER

y=0

EXPLANATION

The given equation is

4x+5y=20

We want to find the y value that solves the equation when x=5.

We substitute x=5 into the given equation and solve for y.

4(5)+5y=20

20+5y=20

5y=20-20

5y=0

y=0

Please help this is confusing!!!!!

Answers

Do 5^2 first

25+ 7*3+4

Multiply 7*3=21

25+21+4

= 46+4

= 50

Answer:50 ( the second choice)

Answer:

Step-by-step explanation:

use BIDMAS to answer

5 squared is 25

7 x 3 = 21

25 + 21 + 4  = 50

your welcome

the population of Linton is 12 times as great as the population of Ellmore. the combined population of both towns is 9,646 people. what is the population of Linton?​

Answers

Answer:

8904

Step-y-step explanation:

Answer:

The population of Linton is 8,904.

Step-by-step explanation:

To start out, they give you a ratio of 12:1, adding all the parts to get a whole would make this ratio 13:1.

Now, since the whole is 13, this means that 13 = 9,646 people.

Next we want to divide 9,646 by 13, this gives us 742.

X = 742

12x = 12 * 742 = 8,904

please help........​

Answers

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=36\pi \end{cases}\implies 36\pi =\cfrac{4\pi r^3}{3}\implies 108\pi =4\pi r^3 \\\\\\ \cfrac{108\pi }{4\pi }=r^3\implies 27=r^3\implies \sqrt[3]{27}=r\implies \boxed{3=r} \\\\[-0.35em] ~\dotfill\\\\ \textit{surface area of a sphere}\\\\ SA=4\pi r^2\qquad \qquad \implies SA=4\pi \left( \boxed{3} \right)^2\implies SA=4\pi (9)\implies SA=36\pi[/tex]

A, B and C are the vertices of a triangle.
A has coordinates (4, 6)
B has coordinates (2,-2)
C has coordinates (-2,-4)
D is the midpoint of AB.
E is the midpoint of AC.
Prove that DE is parallel to BC.
You must show each stage of your working.

Answers

Answer:

Step-by-step explanation:

2/4=0.5

BC gradient is 2

AB (3,2)

AC (1,1)

DE gradient is 1/2=0.5

same gradients

parallel line have the same gradients

DE=0.5

BC=0.5

D has coordinate (3,2) and E has coordinate (1,1)

Gradient of DE = (2 - 1)/(3 - 1) = 0.5

Gradient of BC = (-2 - -4)/(3 - 1) = 0.5

BC and DE have the same gradient so they are parallel.  

To prove that DE is parallel to BC, we need to show that their slopes are equal. Let's start with finding the midpoints D and E:

Midpoint D: The coordinates of D are the averages of the coordinates of A and B.A = (4, 6)B = (2, -2)D = ((4+2)/2 ,  (6+(-2))/2) => (3, 2)Midpoint E: The coordinates of E are the averages of the coordinates of A and C.A = (4, 6)C = (-2, -4)E = ( ( 4 + (-2) )/2 =  ( 6 + (-4) ) /2) = (1, 1)Step-by-step explanation:Slope of BC: The slope of line BC is calculated as follows:(y2 - y1) / (x2 - x1) = (-4 - (-2)) / (-2 - 2) = (-4 + 2) / (-4) = -2 / -4 = 1/2Slope of DE: The slope of line DE is calculated as follows:(y2 - y1) / (x2 - x1) = (1 - 2) / (1 - 3) =  (-1) / (-2) = 1/2Since the slope of DE is equal to the slope of BC (both are 1/2), we can conclude that DE is parallel to BC.

Find the values for a and b that would make the equality true. 4(ax^2 -5x+3)=8x^2 +bx+12

Answers

Answer:

a 2 and b -20

Step-by-step explanation:

Answer:

a = 2 and b = -20

Step-by-step explanation:

4(ax^2 -5x+3)=8x^2 +bx+12 should be multiplied out.  Next, we equate the coefficients of the several powers of x:

4ax² - 20x + 12 = 8x² + bx + 12

Then 4a = 8, so a = 2

and   -20 = b

3. In a set of points that Milton scored in basketball games, there is an outlier.
Before one game, Milton injured his knee. Do you think the outlier is greater
or less than the rest of the numbers of points? Explain.

Answers

Answer:

Less - He wouldn't be able to score as many points.

Hope this helps you out!

the dot plot shows the mass, in grams, of several substances in an experiment. How many substances has their mass recorded during the experiment?

Answers

Answer:

the answer would be 13

Step-by-step explanation:

The dot plot showed that 13 substances had their mass recorded during the experiment

What is a graph?

A graph is used to provide a pictorial representation or diagram so as to represents data in an orderly way. Examples of graphs are histogram, box plot, pie chart, dot plot.

A Dot Plot is used to provide a graphical display of data using dots.

From the dot plot:

Number of substances = 4 + 1 + 2 + 2 + 4 = 13

The dot plot showed that 13 substances had their mass recorded during the experiment

Find out more on graph at: https://brainly.com/question/14323743

HELP ME WITH THIS 60 POINTS,5-STAR RATING, AN THANKS AND MARKED AS BRANLIEST.

Answers

Step-by-step explanation:

Step 1: Additive inverse

Step 2: Additive identity

Step 3: Addition property of equality

22 is D

Answer:

21)

step 1 = Additive inverse Step 2 = Additive identityStep 3 = Addition property of equality

22)

D)  h > 48

~batmans wife dun dun dun....

1/2x+3/2(x+1)-1/4=5​

Answers

Answer:

x= 15/8

Step-by-step explanation:

we need to solve the equation to find the value of x by adding like terms and then finding the value of x.

[tex](\frac{1}{2})x+(\frac{3}{2})(x+1)-(\frac{1}{4})=5\\(\frac{1}{2})x + (\frac{3}{2})x + (\frac{3}{2}) - (\frac{1}{4}) = 5\\Adding\,\,like\,\,terms\,\\(\frac{(1+3)x}{2}) + (\frac{6-1}{4})=5\\(\frac{4x}{2}) + (\frac{5}{4})=5\\2x= 5- \frac{5}{4}\\2x = \frac{20-5}{4}\\2x= \frac{15}{4}\\x= \frac{15}{4*2}\\x= \frac{15}{8}[/tex]

The value of X is ratio of fifteen to eight. That is, x = 15/8

ALGEBRIAC EQUATION

Algebraic equation comprises of unknown variables with equality sign.

To evaluate 1/2x+3/2(x+1)-1/4 = 5, Find the LCM in the left hand side.

[tex]\frac{x}{2}[/tex] + [tex]\frac{3(x+1)}{2}[/tex] - [tex]\frac{1}{4}[/tex] = 5

At the Left hand side, the L.C.M is 4

[tex]\frac{2x+6(x+1)-1 }{4} = 5[/tex]

Cross multiply

2x + 6x + 6 - 1 = 20

8x + 5 = 20

Collect the like terms

8x = 20 - 5

8x = 15

Make x the subject of the formula

x = 15/8

Therefore, x = 15/8 in the given algebraic equation.

Learn more about algebraic equation here: https://brainly.com/question/930208

The measures of three angles of a triangle are given by 4x-1,2x+1 and 6x. What is the measure of the largest angle

Answers

Answer:

The largest angle is 6x,and 6x=90

So, the measure of the largest angle is 90

Step-by-step explanation:

First, you create an equation by adding the three angles together and equal to 180,because a triangle has 180 degrees.

The result will be 15.If x=15 ,you need to plug it in.

the largest angle is 6x,So, 6.15=90

90 degrees

The problem states the measures of three angles of a triangle as 4x-1, 2x+1, and 6x. According to the basic theorem that the sum of the angles in a triangle is 180 degrees, if we add these angles together, and equate them to 180, we get the equation 4x - 1 + 2x + 1 + 6x = 180. Adding like terms simplifies this to 12x = 180, and dividing each side by 12 gives us x = 15. Therefore, the largest angle is 6x, which would be 6 * 15 = 90 degrees.

Which statements correctly describe the association between the variables A and B?


Select each correct answer.



no association


negative association


positive association


linear association


nonlinear association

Answers

Answer:

Negative Association

Step-by-step explanation:

Answer:

B) negative association

D) linear association

Step-by-step explanation:

We are given a scatter plot which represents the relationship between the variable A and the variable B.

As you can see the values of the variable A increase, the values of the variable B decrease.

It is clearly shows the negative trend.

Also we can see the points not deviated much, the points looks to form a linear association.

So there must be two statements which associates with this scatter plot.

B) negative association

D) linear association

A smartphone for $150.00 cash, or $25.00 down and $12.00 per month for 11 months

Answers

Answer:

150 CASH

Step-by-step explanation:

if you do 25 down and 12 dollar for 11 month you pay 7 more dollars

Final answer:

The cost of financing the smartphone with a down payment and monthly payments would be $157.00, compared to a one-time cash payment of $150.00.

Explanation:

The question posed involves comparing the cost of purchasing a smartphone either with a one-time cash payment or financing it with a down payment followed by monthly payments. To calculate the total cost of the financing option, you add the down payment to the product of the monthly payment amount and the number of months for repayment. In this case, we use the following calculation: $25.00 down payment + ($12.00 per month × 11 months) = $25.00 + $132.00 = $157.00. The total cost when financing the smartphone would be $157.00, which is $7.00 more than the upfront cash payment of $150.00.

The graph of f(x) is shown below has the same shape as the graph of g(x)= x^4 but is shifted 3 units to the left. What is the equation

Answers

A. Any horizontal transformations or reflections you make to y = x^4 must be contained within the parentheses.

Camp Ground A has an area of 300 square yards with a maximum capacity of 25 pup tents. Camp Ground B has an area of 480 square yards and requires that each of its pup tents occupies the same area as each pup tent in Camp Ground A. What is the maximum number of pup tents that can occupy Camp Ground B? In two or more sentences, explain your calculations and conclusions.

Answers

Answer:

40 pup tents

Step-by-step explanation:

Since Ground A has area 300 and maximum capacity is 25 tents, so each tent would take up area of  300/25 = 12 sq yards.

Since Ground B's tents should occupy same area as Ground A's tents (12 sq. yards), the maximum capacity of this tent (480 sq yd) would be:

480/12 = 40 pup tents

This is the maximum capacity.

What is the missing number that makes the number sentence true

20+ ( ?) x 14 )-12 =50

Answers

Answer:

Missing number is 3.

Step-by-step explanation:

20+(?)x14)-12=50

8+14?=50

14?=50-8

14?=42

?=3

Answer:

The missing number is 3

Step-by-step explanation:

Let the missing number be y

20 + (y × 14) - 12 = 50

Opening the brackets;

20 + 14y - 12 = 50

14y = 50 + 12 - 20

14y = 42

y = [tex]\frac{42}{14}[/tex] = 3

Which of the following equations fits this graph?

Answers

A. down

The -4 moves the y-intercept down from the origin to -4

Answer: Option A.

Step-by-step explanation:

The equation of the line in slope-intercept form is:

[tex]y=mx+b[/tex]

Where the slope is "m" and the intersection of the line with the y-axis is "b".

Given the function f(x) in the form [tex]f(x)=x[/tex], you can identify that:

[tex]m=1\\b=0[/tex]

This means that the line passes through the origin (0,0)

And from the function g(x) in the form [tex]g(x)=x-4[/tex], , you can identify that:

[tex]m=1\\b=-4[/tex]

This means that the line of the function g(x) and the line of the function f(x) have the same slope, but the line of g(x) passes through the point (0,-4)

Therefore, the graph of f(x) must be shifted 4 units down to produce the graph of g(x)

A bag contains eight black marbles, 16 white marbles, 14 red marbles, and 10 Green marbles. A marble is drawn at random from the bag. What is the probability that the marble drawn will not be white?

A) 1/3
B) 2/3
C) 3/4
D) 15/16

Answers

Answer:

B-2/3

There are 48 total marbles and 32 are not white, so if you reduce, you get 2/3

The Answer is B

Explanation:

A restaurant claims to have served 352,000,000 hamburgers. What is this number in scientific notation?​

Answers

Answer:

3.52 × 10⁸

Step-by-step explanation:

Scientific notation is written in: Number that is in the ones place × 10^power.

Here, the number is 3.52, since 3 has the largest placement.

The power on the 10 should be the number of 0's on 352,000,000/3.52. That is 100,000,000. That number has 8 0's, so the power is to the 8th.

Putting that together, this number in scientific notation in 3.52 × 10⁸.

Find the lateral area and surface area of a regular triangular prism with base edge 7 cm, a base height 6.1 cm and prism height of 11 cm. Round to the nearest tenth.

Answers

Lateral Area: 288 cm

Total Surface Area: 331 cm

Hi, can someone help me? I'm trying to get this all done before tomorrow. Thanks ;)

Answers

Answer:

B. 6.5 ≤ x

Step-by-step explanation:

Nathan's pay for the week, including x extra hours, will be ...

250.25 +9.50x

We want that to be at least 312, so the inequality is ...

250.25 +9.50x ≥ 312

9.50x ≥ 61.75 . . . . . . . . subtract 250.25

x ≥ 6.5 . . . . . . . . . . . . . . divide by 9.5

The graph showing a solid dot at x=6.5 and an arrow extending to the right will be the correct graph of this solution.

Samantha threw an apple out of a window from the tenth floor of her apartment building. The equation y = -16t2 + 120 can be used to represent the fruit's height above the ground, where t represents time, after she thew the apple. How long did it take the apple to hit the ground? Round your answer to the nearest hundredth.

Answers

Answer:

2.74

Step-by-step explanation:

The height of the apple when it hits the ground is zero

Equate to zero and solve for t

- 16t² + 120 = 0 ( subtract 120 from both sides )

- 16t² = - 120 ( divide both sides by - 16 )

t² = 7.5 ( take the square root of both sides )

t = [tex]\sqrt{7.5}[/tex] ≈ 2.74

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