Given the definitions of f(x) and g(x) below, find the value of (fog)(-8).
f(x) = x2 – 3x – 12
g(x) = -x - 12

(4 – 5) – (13 – 18 + 2).

= -1-(13+2-18).

= -1-(15-18).

= -1-(-3).

= -1+3.

= 2.

Answer:

the answer is 3

Step-by-step explanation: ik

Answer:

The answer is 36 or c all you need to do is multiply 12 by 3

C-36 because your multiplying all of them by 3

Answer:

-27 or 1/27 ( both are same)

Step-by-step explanation:

-[tex]3^{3}[/tex]

-3 * -3 * -3

=-27 or 1/27

Answer:

The average rate of change over the interval is 120

Step-by-step explanation:

For a function f(x) the average rate of change over an interval [a,b] is given as;

f(b)-f(a)/b-a

in this case, a is 2 and b is 4

f(b) is 256 and f(a) is 16

Substituting these values in the equation for rate of change, we have;

(256-16)/(4-2) = 240/2 = 120

Answer:

B. $180

Step-by-step explanation:

3/2 × $120 = $180

______

Answer:

The percentage markdown is approximately 19%

Step-by-step explanation:

The cost at which the computer store bought the program = $40

The selling price at which the store sold the program = $32.5

The percentage markdown is given as follows;

Let CP represent the cost at which the computer store bought the program, and let SP represent the selling price of the program, we can find the percentage markdown as follows;

[tex]Percentage \ markdown = \dfrac{CP- SP}{CP } \times 100[/tex]

CP = $40, SP = 32.5

Therefore, we get;

[tex]Percentage \ markdown = \dfrac{40- 32.5}{40} \times 100 = 18.75\% \approx 19\%[/tex]

The percentage markdown ≈ 19%.

Answer:

3×2-2x + 6 + 3x - 4

-2x +3x + 3 × 2 +6-4

Answer:

W ≈ 5.2 cm

Step-by-step explanation:

Represent the length and width by L and W respectively.

Then L * W = 81 cm^2, and L = 3W.

Substituting 3W for L in the first equation, we get:

3W * W - 81 = 0, or 3W^2 - 81 = 0.

To make it easier to find the final answer, rewrite 3W^2 - 81 = 0 as

            81

W^2 = ------- = 27

              3

Then W (the width) is the positive square root of 27, or W ≈ 5.2 cm

Answer:

60.75 ≈ 60.8

Step-by-step explanation:

4u-> 81

1u -> 20.25 (width)

3u-> 60.75 (length)

Answer:

10 litres

Step-by-step explanation:

50 litres - 100%

x litres - 30%

x=(50*30)/100=15 litres - that's 30% of the tank (this amount of water is already added)

50 litres - 100%

x litres - 50%

x=(50*50)/100=25 litres - that's 50% of the tank (this amount of water will be in the tank)

To find what amount of water should be added we must subtract the amount of water that is already added from the amount of water that will be in the tank.

25 - 15=10 litres should be added

Answer:

[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex] --- General polynomial

The degree is 6

[tex]p(x) = -\frac{1}{3}(x -1)^{3} * (x -4)^{2} * (x +3)[/tex] --- The polynomial precisely

Step-by-step explanation:

Given

[tex](a,b,c)= (1,4,-3)[/tex] --- zeros

[tex](m_1,m_2,m_3) =(3,2,1)[/tex] --- multiplicities

Solving (a): The polynomial

The polynomial is represented as:

[tex]p(x) = (x -a)^{m_1} * (x -b)^{m_2} * (x -c)^{m_3}[/tex]

So, we have:

[tex]p(x) = (x -1)^{3} * (x -4)^{2} * (x +3)^{1}[/tex]

[tex]p(x) = (x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

Include constant k; So, the polynomial becomes

[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

Solving (b): The degree (d)

To do this, add up the multiplicities

[tex]d = m_1 +m_2 +m_3[/tex]

[tex]d = 3+2+1[/tex]

[tex]d = 6[/tex]

The degree is 6

Solving (c): The actual polynomial

In (a), we have:

[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

[tex]p(0)=16[/tex] means:

[tex](x,p(x)) = (0,16)[/tex]

This gives:

[tex]16 = k(0 -1)^{3} * (0 -4)^{2} * (0 +3)[/tex]

[tex]16 = k(-1)^{3} * (-4)^{2} * (3)[/tex]

[tex]16 = k*-48[/tex]

Solve for k

[tex]k = \frac{16}{-48}[/tex]

[tex]k = -\frac{1}{3}[/tex]

So:

[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

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

Answer:

w equal to 9z

or z equals to w/9

Answer: 3

Step-by-step explanation:

Distribute the 5: 15x-5=40

Add 5 from both sides: 15x=45

Divide 15 by both sides: 3

Answer:

a-3

Step-by-step explanation:

5(3x-1)=40

15x-5=40

15x=40+5

15x=45

x=45/15

x=3

Answer:

28[tex]\pi[/tex] in

Step-by-step explanation:

The circumference of a circle is [tex]2\pi r[/tex] in which [tex]r[/tex] represents radius.

[tex]2\pi[/tex]×14 = 28[tex]\pi[/tex] in

Answer:

[tex]circumference \: of \: the \: circle = 2\pi \times radis[/tex]

[tex] = 2 \times \frac{22}{7} \times 14[/tex]

[tex] = \frac{11}{1} \times 2[/tex]

[tex] = 11 \times 2[/tex]

[tex]22cm[/tex]

Answer:

go left 2 and up 6

Step-by-step explanation:

(x,y)

(x,y) --> (-2,6)

0 = x      0 = y

0 - 2 = -2 = x

0 + 6 = 6 = y

(-2,6)

When making the X negative, you want to go left on the grid. When making Y positive, you want to go up on the grid.

Answer: you would go to the left side horizontally (aka quadrant 3), then go down until 6 vertically

Step-by-step explanation: if you don't get it, here's a visual explanation

Answer:

37

Step-by-step explanation:

Answer:

24+18 is 42.

Step-by-step explanation:

1

24

+18

____

 42

Answer:

76°

Step-by-step explanation:

Applying trigonometry :

Angle x ;

Tan x = opposite / adjacent

Tan x = (30/20)

x = tan^-1(30/20)

x = 56.31°

Angle y;

Tan y = opposite / adjacent

Tan y = (22/20)

x = tan^-1(22/20)

x = 47.73°

The angle θ ;

Sum of angles in a straight line = 180

56.31 + 47.73 + θ = 180°

θ = 75.96°

Answer:

[tex]9+4^2\div 2^3\tems*3[/tex]

[tex]9+2^4\div8*3[/tex]

[tex]9+2*3[/tex]

[tex]9+2*3[/tex]

[tex]9+6[/tex]

[tex]15[/tex]

Answer:

108

Step-by-step explanation:

Jesicca wants to make tarts

She uses 3/4 cup of flour per batch

Jessica has 9 cups of flour hence the number of batches she will make can be calculated as follows

= 9÷ 3/4

= 9÷ 0.75

= 12

= 12×9

= 108

Hence Jessica will make 108 batches of tart

Answer:

f'(x)=2

Step-by-step explanation:

[tex]if~y=ax^n\\where~a~is~constant.\\\frac{dy}{dx} =a nx^{n-1}\\f(x)=2x-1\\f'(x)=2*1x^{1-1}-0\\=2x^0\\=2*1\\=2[/tex]

Answer:

3.2 , Edgar , Liam

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

4.55

Step-by-step explanation:

step 1.     6.5 / 500 =  .013

step 2.    .013 X 350  = 4.55

Hope this helps

Answer:

They are all squares similar to the base.

Step-by-step explanation:

They are not congruent to the base but are similar.

Answer:

[tex]\text{(C) }300\pi\:\mathrm{cm^3}[/tex]

Step-by-step explanation:

The volume of a cylinder with radius [tex]r[/tex] and height [tex]h[/tex] is given by [tex]V=r^2\pi \cdot h[/tex].

What we're given:

Substituting given values, we get:

[tex]V=5^2\pi \cdot 12 =\boxed{300\pi\:\mathrm{cm^3}}[/tex]

Answer:

c

Step-by-step explanation:

The formula for the volume of a cylinder is [tex]V=\pi r^2h[/tex]

We know r is 5, and h is 12.

Then we can just plug the values into the formula.

[tex]V=\pi (5)^2(12)\\ V=\pi (25)(12)\\\V=\pi (300)[/tex]

So the answer is c, 300pi

Answer:

-10

Step-by-step explanation:

[tex]\frac{9^{2} -21}{-6} \\=-\frac{81-21}{6} \\=-\frac{60}{6} \\=-10[/tex]

Answer:

Ans:C

Step-by-step explanation:

4x^2+10x-2=6

4x^2+10x=6+2y

4x^2+10x-6=2y

(4x^2+10x-6)÷2=y

y=2x^2+5-3

Hope this is useful :)

Answer:

Step-by-step explanation:

x = 7

Symbolically, this equation is:

 x        7

----- = -----

90       9

Cross multiplying yields 9x = 9(7), and so x must be 7.

Answer:

its b!!

Step-by-step explanation:

Answer:

slope = -3/4

Step-by-step explanation:

y(1)-y(2)/x(1)-x(2)

Plug in coordinates (0,4) and (4,1)

1-4/4-0

-3/4 is the slope

Answer:

Nope, this is because the angles in a triangle add up to 180, whereas these values added are equal to 200 degrees

No, the angles with measures 80°, 55°, and 65° cannot form angles on a line.

In geometry, angles on a line are also known as "linear angles" or "straight angles." A straight angle measures 180°, and it is formed by two rays that point in opposite directions and share a common endpoint, creating a straight line. To determine if the given angles can form a straight angle, we need to add their measures.

Let's calculate the sum of the given angles:

Sum = 80° + 55° + 65°

       = 200°

Since the sum of the given angles (200°) is not equal to 180°, it means that the angles cannot form a straight line. Instead, they form a shape that is not a straight angle, such as a triangle or a polygon.

In this case, the given angles form a triangle since they satisfy the triangle inequality theorem. The sum of any two sides of a triangle is always greater than the third side. Mathematically, for a triangle with sides of lengths a, b, and c, the inequality holds: a + b > c, b + c > a, and c + a > b.

Therefore, the angles with measures 80°, 55°, and 65° cannot form angles on a line but rather form a triangle with a sum of 180°, satisfying the triangle inequality.

To know more about Linear Angles here

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