Let f(x) = 4x2 + x + 1 and g(x) = x2 − 2. Find g(f(x)). Show each step of your work.

Answer:

[tex]x^{7}[/tex]

Step-by-step explanation:

= [tex]x^{5} * x^{2}[/tex]

When bases are same, powers are to be added

= [tex]x^{5+2}[/tex]

= [tex]x^{7}[/tex]

Answer:

4

Step-by-step explanation:

36/9=4

Answer:

4

Step-by-step explanation: division

Answer: x = 5, y = 2

Step-by-step explanation

x = 0, x = 5

5 - 0 = 5

y = 1, y = 3

3 - 1 = 2

Answer:

Step-by-step explanation:

[tex]tan^2 \theta+1=-2 \tan \theta \\tan^2 \theta +2 tan \theta +1=0\\(tan \theta+1)^2=0\\tan \theta=-1=-tan 45=tan (360-45)=tan 315\\\theta =315 ^\circ[/tex]

Answer:

The expression is: [tex]\text{total thickness} = \text{cookie thickness} + \text{frosting thickness}[/tex]

The thickness of the cookie is: [tex]\frac{123}{100}[/tex] cm

Step-by-step explanation:

The cookie is formed by two layers, the cookie and the frosting. So if we want to know the total thickness of the cookie and frosting we need to sum the thickness of each layer as shown below:

[tex]\text{total thickness} = \text{cookie thickness} + \text{frosting thickness}\\\text{total thickness} = \frac{9}{10} + \frac{33}{100}\\\\\text{total thickness} = \frac{10*9 + 33}{100}\\\\\text{total thickness} = \frac{123}{100} \text{ cm}[/tex]

The expression is: [tex]\text{total thickness} = \text{cookie thickness} + \text{frosting thickness}[/tex]

The thickness of the cookie is: [tex]\frac{123}{100}[/tex] cm

Answer: A point

Step-by-step explanation:

To find the point of intersection algebraically, solve each equation for y, set the two expressions for y equal to each other, solve for x, and plug the value of x into either of the original equations to find the corresponding y-value. The values of x and y are the x- and y-values of the point of intersection.

Answer.

x=156

How to solve

x /6 +6=32

1 /6 x+6=32

1 /6 x+6−6=32−6

1 /6 x=26

6*( 1/ 6 x)=(6)*(26)

x=156

Answer:

type 2 in the first box,

13/4 in the second box, and

-9/8 in the third one

Step-by-step explanation:Notice that you are asked to write the following quadratic expression in vertex form, so you need to find the "x" value of the vertex, and then the "y" value of the vertex:

[tex]x_{vertex}= -b/2a[/tex]

Which in our case is: -13/4

and the value of the y for the vertex is obtained using the functional expression when x equals -13/4:

[tex]f(-13/4)= -9/8[/tex]

Then your expression for this quadratic should be:

[tex]f(x)=2\,(x+\frac{13}{4} )^2+(-\frac{9}{8})[/tex]

Then type 2 in the first box, 13/4 in the second box, and -9/8 in the third one

Answer:

[tex]\frac{9}{10}[/tex]

Step-by-step explanation:

Let the fraction be [tex]\frac{x}{y}[/tex].

That would mean:

(1)    x+y = 19

&

(2)    y+8 = 2x or 2x = y+8

In order to use substitution, we multiply equation by 2:

(3)   2x+2y = 38

Then we substitute equation (2) into (3):

y+8 + 2y = 38

3y + 8 = 38

3y = 30

y = 10

Substitute this into equation (1)

x + 10 = 19

x = 9

Therefore the fraction would be:

[tex]\frac{9}{10}[/tex]

Answer:

9/10

Step-by-step explanation:

let the fraction be x/y.

x+y=19

x/y+8=1/2

solve simultaneously

y=2x-8

y=19-x

2x-8=19-x

3x=27

x=9

y=10

Answer:

∠ABD ≅ ∠CBE

Step-by-step explanation:

So we know that ∠ABC ≅ ∠DBE. Those angles equal the same thing. Let's represent that with x.

So does ABD = CBE?

Well we can model that with our xs.

ABD = ABC + CBD

so ABD = x + CBD

CBE = DBE + CBD

so CBE = x + CBD

Look at what we have!

x + CBD = x + CBD.

You can tell that ∠ABD ≅ ∠CBE because those given angles are equal to each other.

Or for an easier (but lazier) method, you can just look at the diagram, which is actually drawn to a reasonable scale. You can tell right off the bat that none of the other options work.

Answer:

[tex]\fbox{\begin{minipage}{4em}36 ways\end{minipage}}[/tex]

Step-by-step explanation:

Step 1: Re-state the problem in an easier way to set up a permutation problem

"The numbers 1,6,8,13,15,20 can be placed in the circle below, each exactly once, so that the sum of each pair of numbers adjacent in the circle is a multiple of seven"

The series above can be represented again, in form of:

7a + 1, 7b - 1, 7c + 1, 7d - 1, 7e + 1, 7f - 1

with a, b, c, d, e, f are non-negative integers.

=> 3 numbers are multiply of 7 plus 1

=> 3 numbers are multiple of 7 minus 1

Step 2: Perform the counting:

For the 1st number, there are 6 ways to select

To satisfy that each pair of numbers creates a multiple of 7, then:

For the 2nd number, there are 3 ways left to select

For the 3rd number, there are 2 ways left to select

For the 4rd number, there are 2 ways left to select

For the 5th number, there are 1 way left to select

For the 6th number, there are 1 way left to select

=> In total, the number of possible ways to select:

N = 6 x 3 x 2 x 2 x 1 x 1 = 72

However, these numbers are located around a circle, each option is counted twice.

=> The final number of possible ways:

N = 72/2 = 36

Hope this helps!

:)

Answer:

-8

Step-by-step explanation:

Answer:

Let's do this step by step

Step-by-step explanation:

I hope this helps

Answer:

The correct options are (1), (2) and (4).

Step-by-step explanation:

If the cross-section of a right rectangular prism parallel to its base then the cross section is a rectangle.

If the cross section of a right rectangular prism perpendicular to its base then the cross section is a rectangle.

It is provided that a right rectangular prism has a rectangular base measuring 15 inches by 8 inches.

Then the right rectangular prism could have:

Thus, the correct options are (1), (2) and (4).

Answer:

to solve an equation you do PEMDAS in reverse.

Step-by-step explanation:

Add 1 to both sides.

multiply both sides by 4

square root both sides

now solve what's inside the parentheses by subtracting 5 from both sides.

Answer:

see below

Step-by-step explanation:

Add 1 to both sides

multiply both sides  by 4

take the square root of both sides

subtract 5 from both sides

Answer:

2/9

Step-by-step explanation:

If the bakery sold 4 brownies and 14 other desserts, then they sold a total of +14=18 desserts. This means that the experimental probability that the next dessert is a brownie is 4/18=2/9. Hope this helps!

Answer:

(0,-2)(-2,-8)

Step-by-step explanation:

Answer:

(0,-2) (-2,-8)

Hope this helps

Answer:

72.8%

Step-by-step explanation:

1729 / 2375 = 0.728 -> 72.8%

Answer:

72.8 %

Step-by-step explanation:

£2375 ............ 100%

£1729 ...................x%

x = £1729×100%/£2375 = £172900/£2375 = 72.8 %

al3xis

Step-by-step explanation:

It might be easier thinking of "rate of change" as the slope. Since you'll be finding a slope, then, use the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and substitute the values.

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{20-12}{8-6}\\m=\frac{8}{2} \\m=4[/tex]

Answer:

[tex]m=\frac{4}{1}[/tex] or [tex]m=4[/tex]

Answer:

The answer is :

[tex] \cos(51) = 0.63[/tex]

[tex] \sin(63) = 0.89[/tex]

[tex] \tan(12) = 0.21[/tex]

Answer:

Left side simplifies to (-2/3)^1 and the right side simplifies to (-2/3)^(-n) which means 1 = -n so n = -1.

Answer:

No it isn't a function one of the x values, -3, repeats

Step-by-step explanation:

Answer:

She needs  cups of flour for each batch of cookies.

Step-by-step explanation:

Step-by-step explanation:

A baker needs a total  cups of flour to make four batches of cookies.

We have to calculate how much flour she needs for each batch of cookies.

Let the flour needed for one batch be f, so the expression would be

f × 4 =

First we convert mixed fraction to proper fraction.

f × 4 =

f =

=  ×  =

Now we convert this proper fraction to mixed fraction.

=

She needs  cups of flour for each batch of cookies.

Answer:

she needs 3 1/3 of a cup

Step-by-step explanation:

I have finished the test

EDGE 2021

Answer:

He bough 1.25 lbs of shrimp and 3.75 lbs of potato.

Step-by-step explanation:

Since the stew is composed of shrimps and potatoes, then the sum of the weighs of these ingredients must be equal to the weigh of the stew, so we have:

[tex]shrimp + potato = 5[/tex]

We also know that he bought three times more potatoes than shrimps, therefore:

[tex]potato = 3*shrimp[/tex]

Using the second equation on the first one, we have:

[tex]shrimp + 3*shrimp = 5\\4*shrimp = 5\\shrimp = \frac{5}{4} = 1.25[/tex]

[tex]potato = 3*shrimp = 3*1.25 = 3.75[/tex]

He bough 1.25 lbs of shrimp and 3.75 lbs of potato.

Answer:

                          A,C,D

                             or

Line WZ has the same slope as line XY.

Line XW has a lesser slope than line YZ.

Line ZW has the same y-intercept as line YZ.

Step-by-step explanation:

did it on edge 2020

Answer:

A C D

Step-by-step explanation:

BOYYYYYYYYYYYYYYYYYY

Answer:

Step-by-step explanation:

y - 1 = 3(x - 4)

y - 1 = 3x - 12

y = 3x - 11

Answer:c

Step-by-step explanation:

Answer:

Problem 2) : the gradient is "-2", and the y-intercept is "3"

Problem 3)

A is  [tex]y=2x+2[/tex]

B is [tex]y=x+2[/tex]  

Step-by-step explanation:

Problem 2)

In the line given by the equation:   [tex]y=-2x+3[/tex]

the "gradient" (also known as "slope") is the numerical coefficient that multiplies the variable "x". So in this case the gradient is "-2"

the y-intercept is the numerical term "+3" because that is the y-value result of evaluating the expression for x = 0

[tex]y=-2x+3\\y=-2\,(0)+3\\y=3[/tex]

Problem 3)

Consider the two lines :

[tex]y=x+2[/tex]  and  [tex]y=2x+2[/tex]

notice that both have the same y-intercept (that is the numerical term "2" at the end of both expressions. That means that both lines cross the y-axis at the point y=2.

Now notice that the gradient of one of them is "1"  (for [tex]y=x+2[/tex] ) that is the coefficient that multiplies the variable "x". While for the other line ( [tex]y=2x+2[/tex])  the gradient is "2" and therefore steeper than the previous one.

Then, the line identified as "A" which is the one with steeper gradient, corresponds to the equation   [tex]y=2x+2[/tex], and the line identified with "B" is the one with smaller gradient  [tex]y=x+2[/tex]  .

Answer:

4 units

Step-by-step explanation:

Length would be 6 units and width would be 4 units

6*4 = 24 proving my claim to be true

Answer:

Width = 4 units

Step-by-step explanation:

Let us pose the width as w, and the length as l. If the length is 2 units greater than the width, consider the following;

[tex]l = 2 + w,\\\\w = width,\\l = length[/tex]

The area of this rectangle can be determined through length * width / l * w, and is given to be 24 square units. We can say l = 2 + w instead, solving for the width ( w );

[tex]( 2 + w ) * w = 24,\\2w+w^2=24,\\\left(w-4\right)\left(w+6\right)=0,\\w = 4, w = - 6\\\\Solution - width = 4 units[/tex]

As the width couldn't be a negative value, we had to take the positive of 4 and - 6, which was 4 units.

Answer:

B

Step-by-step explanation:

Answer: the answer is 77 degrees

Step-by-step explanation: a triangle's angles all add up to 180, so all you need to do is 180-(59+44)