Given the following functions:

f(x)=x^2

g(x)=x−3

Find the composition of the two functions and show your process:

f(g(x))

We have to find derivative of t

[tex]\\ \sf\longmapsto \dfrac{d}{dx}3t^2-12t+4[/tex]

[tex]\boxed{\sf \dfrac{d(x^n)}{dx}=nx^{n-1}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{d}{dx}3t^2-\dfrac{d}{dx}12t+\dfrac{d}{dx}40[/tex]

[tex]\\ \sf\longmapsto 6t-12[/tex]

Now

[tex]\\ \sf\longmapsto 6(8)-12[/tex]

[tex]\\ \sf\longmapsto 48-12[/tex]

[tex]\\ \sf\longmapsto 36[/tex]

Answer:

0.33333333

0.9375

0.125

7/8

7/16

5/8

3/100

4/10 or 40/100

Step-by-step explanation:

Answer:

70 feet above the water will it begin to stretch.

Step-by-step explanation:

200 - 130 = 70

Answer:

The choose C. 24x+6y

Step-by-step explanation:

[tex]3(8x + 2y) = 24x + 6y[/tex]

I hope I helped you^_^

Answer 61

Step-by-step explanation:

The answer is 61 bc the pattern is +5

Answer:

26, 31, 36, 41, 46, 51, 56, 61

the eighth number is 61.

Step-by-step expanation:

Answer:

23.8 years

Step-by-step explanation:

Assuming this is compound interest, we'll use the compound interest formula

A = P(1 + r)ⁿ

A = Final amount (2000)

P = Initial amount (500)

r = Annual interest rate (.06)

n = ?

Our equation will look like this

2000 = 500(1.06)ⁿ

First, divide both sides by 500

2000/500 = (500(1.06)ⁿ)/500

(1.06)ⁿ = 4

Then we have to take the log₁.₀₆ out of both sides

n = log₁.₀₆(4)

n = 23.79132

Step-by-step explanation:

please subscribe to my mom channel please

Answer:

y²z²-x²

3*3*4*4-2*2

3*16-4

48-4

44

Step-by-step explanation:

* means multiply

Answer:

[tex]here \: we \: want \: to \: find \: {x}^{2} {y}^{2} {z}^{2} \\ x = 2 \\ y = 3 \\ z = 4 \\ then \: {2}^{2} \times {3}^{2} \times {4}^{2} \\ = 4 \times 9 \times 16 \\ = 36 \times 16 \\ = 576 \\ thank \: you[/tex]

a) The x-coordinates of the points A and B are [tex]x_{A} = 11[/tex] and [tex]x_{B} = -7[/tex].

b) The point of intersection of the tangents to the circle at A and B is [tex](x,y) = (2, 27)[/tex].

a) In this part we simplify the equation of the circle and solve for [tex]x[/tex] to determine the coordinates associated to the required points:

The coordinates of the two points so that circle intersects the x-axis, occurs when the following condition is met:

[tex]f(x, 0) = 0[/tex] (1)

Where [tex]f(x,y)[/tex] is in implicit form.

If we know that the equation of the circle is [tex]x^{2} + y^{2} - 4\cdot x + 6\cdot y - 77 = 0[/tex] and [tex]y = 0[/tex], then the reduced equation is:

[tex]x^{2} - 4\cdot x - 77 = 0[/tex] (2)

And we obtain the x-coordinates of the points by factoring (2):

[tex](x-11) \cdot (x + 7) = 0[/tex]

The x-coordinates of the points A and B are [tex]x_{A} = 11[/tex] and [tex]x_{B} = -7[/tex].

b) Lines are defined by both slope and intercept. Slope is defined by implicit differentiation and intercept is found by equation of the line.

Given that [tex]A(x,y) = (11, 0)[/tex] and [tex]B(x,y) = (-7, 0)[/tex], we determine line equations corresponding to each tangent line:

Slope

[tex]2\cdot x + 2\cdot y \cdot \dot y - 4 + 6\cdot \dot y = 0[/tex]

[tex](2\cdot y + 6)\cdot \dot y = 4 - 2\cdot x[/tex]

[tex]\dot y = \frac{2 - x}{y + 3}[/tex]

Point A

[tex]\dot y = \frac{2-11}{0 + 3}[/tex]

[tex]\dot y = -3[/tex]

Point B

[tex]\dot y = \frac{2-(-7)}{0 + 3}[/tex]

[tex]\dot y = 3[/tex]

Intercept

Point A ([tex]A(x,y) = (11, 0)[/tex], [tex]\dot y = -3[/tex])

[tex]b = y - m\cdot x[/tex]

[tex]b = 0 - (-3)\cdot (11)[/tex]

[tex]b = 33[/tex]

Point B ([tex]B(x,y) = (-7, 0)[/tex], [tex]\dot y = 3[/tex])

[tex]b = y - m\cdot x[/tex]

[tex]b = 0 - 3\cdot (-7)[/tex]

[tex]b = 21[/tex]

The equations of the lines tangent to the circle are:

[tex]y = -3\cdot x +33[/tex] (3)

[tex]y = 3\cdot x +21[/tex] (4)

The point of intersection is the solution of this system of linear equations:

[tex](x,y) = (2, 27)[/tex]

The point of intersection of the tangents to the circle at A and B is [tex](x,y) = (2, 27)[/tex].

We kindly invite you to see this question on circles: https://brainly.com/question/23988015

To find the perimeter of a rectangle, you add up 2 times the length and 2 times the width. Here's the expression: [tex]2l+2w[/tex]. In this case l=22 or l=27.7 and w=27.7 or w=22. In the end, you get: [tex]2l+2w=99.4[/tex]. [tex]22*2=44. \\27.7*2=55.4[/tex].

To find the area of a rectangle, you multiply the length by the width. Here's the expression: [tex]lw[/tex].  In this case l=22 or l=27.7 and w=27.7 or w=22. In the end, you get: [tex]22*27.7=609.4[/tex].

Side note:

It doesn't matter what l or w equal because There's a property in addition that says it doesn't matter which order the values go in. There's also a property in multiplication that it doesn't matter which order the values go in (same as addition).

Answer:

D

Step-by-step explanation:

multiply each number by 40

ex:

.10x40=40

Answer:d

Step-by-step explanation:

9514 1404 393

Explanation:

If you can't operate a calculator, perhaps you can do long division. The attachment shows the work for that.

__

  [tex]\dfrac{20}{8}=\dfrac{5\cdot4}{2\cdot4}=\dfrac{5}{2}\\\\=\dfrac{5\cdot5}{2\cdot5}=\dfrac{25}{10}=2.5[/tex]

We assume that you know dividing by 10 moves the decimal point one place left.

Answer:

460 sq ft

Step-by-step explanation:

Assuming the room is a perfect rectangle and not accounting for doors and windows:

14 ft x 10 ft = 140 sq ft X 2 = 280 sq ft

9 ft x 10 ft = 90 sq ft x 2 = 180 sq ft

280 sq ft + 180 sq ft = 460 sq ft

Work Shown:

L = d+9 = length along the horizontal

W = 10 feet = width along the vertical

P = 2(L+W) = perimeter of rectangle = 70 feet

70 = 2(d+9+10)

70/2 = d+19

35 = d+19

d+19 = 35

d = 35-19

d = 16

The deep end is 16 feet wide

Answer:

Slope intercept is y = mx+b.

SLOPE is m

and Y-INTERCEPt, where the thing touches the y axis is b.

The line touches the y axis at -6.

The slope is 2/3

y=2/3x-6

Step-by-step explanation:

Answer:

[tex]4g^{2}h-12gh^{2}-9gh[/tex]

Copy and paste version:

4g^2h-12gh^2-9gh

Step-by-step explanation:

[tex](4g^{2}h-gh-9gh^{2})+(8gh-3gh^{2})=\\4g^{2}h-gh-9gh^{2}+8gh-3gh^{2}=\\4g^{2}h-9gh-12gh^{2}=\\4g^{2}h-12gh^{2}-9gh[/tex]

Answer:

4g^2h-12gh^2-9gh

Step-by-step explanation:

Hello :D

The answer is 0.08

I hope this helps :)

Answers:

The value of x is exact. The y value is approximate.

==================================================

Explanation:

Let's subtract the equations straight down.

After doing those three sets of subtractions, we have the new equation -22x = 0. This solves to x = 0 after dividing both sides by -22.

Plug this x value into any of the two original equations to solve for y

9x + 7y = 48

9(0) + 7y = 48

7y = 48

y = 48/7

y = 6.857 approximately

y = 6.9

Answer:

$7.20

Step-by-step explanation:

First, we would have to find out how much to subtract from $62.

We need to multiply 90% and 62 or 0.9 x 62

When we finish this equation we get 54.8, which is what we need to subtract from 62 to see what 90% off is.

62 - 54.8 = 7.2, so therefore our answer is $7.20

Answer:

5 more matches was won by yu-na kim

Answer:

6s-36 is the answer . Hope this helps you.

Answer:

6(x-6) = 6x-36

Step-by-step explanation:

Answer:

So coming back to the question; No, there is no rational number that is not an integer but is a whole number. The number is called as a rational number if it can be expressed as p/q where p & q are integers & q is not 0. All negative integers are rational numbers but those are not whole numbers.Jan 1, 2020

Step-by-step explanation:

Answer:

x = 6

y = - 3

Step-by-step explanation:

x * y = - 18

x - y = 9. 3-y-y = 9. 3 -2y = 9.

-2y = 9-3

y = 6/-2

y = -3

x + y = 3. x = 3-y

x * -3 = - 18

x = -18/-3

x = 6

Step-by-step explanation:

$334,654 ×14,5% = $34,024.83

therefore that is your answer

Answer:

-31+(-42)= -31-42 = -73

38+(-43)= 38-43 = -5

(-) - (-) = +

(-)+(-) = +

(-)+(+) = -

The height of the window is 9-x feet.

Given that, a window is 9 ft long. It is x feet longer than it is high.

We need to find what is the height of the window.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Here, the length of the window = 9 ft

Then, the height of the window = x feet smaller than the length = 9-x feet

Therefore, the height of the window is 9-x feet.

To learn more about an expression visit:

https://brainly.com/question/28170201.

#SPJ2

Answer:

the area!!!

Step-by-step explanation:

2(a+b)h

to find b you have to know the base of the triangle. you may use pythagoras' theorem for that. you will then get 5ft as the base.

5ft + 48ft = 53ft.

put in the formula, the area is then

2(48+53)*13

am not with a calculator.... so sort it out....

I think you can get the rest with this...