Show algebraically that f and g are inverse functions:
g = sqrt(x+8)-4
f=x^2+8x+8

9514 1404 393

Explanation:

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

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  [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:

m = -1

Step-by-step explanation:

Find the equation in slope intercept form [ y = mx + b ] for line AB. Find the slope using the formula [ y2-y1/x2-x1 ].

8-5/7-4

3/3

1

Find the y-intercept.

5 = 1(4) + b

5 = 4 + b

1 = b

So the equation of the line AB is y = x + 1.

The slope of a perpendicular line is the opposite reciprocal of the original line.

1 -> -1/1 -> -1

Best of Luck!

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:

answer: 9

Step-by-step explanation:

x = - 4; y = 3; z = 2;2 x² - 2 z^4 + y² - x² + z^4 = = 2 * (-4)² - 2 * 2^4 + 3² - ( -4)² + 2^4 == 2 * 16 - 2 * 16 + 9 - 16 + 16 = = 32 - 32 + 9 - 16 + 16 = 9

Answer:

-19

Step-by-step explanation:

-13-25-24-14

= -76/4

= -19

Answer:

1360

Step-by-step explanation:

there are 1200 seconds in 20 minutes. if Ella can do 17 jumps in 15 seconds, you would divide 1200 by 15 (which equals 80) because that would be the number of 15 seconds in 20 minutes. then you would divide 80 by 17, which gives you your final answer of 1360 jumps in 20 minutes.

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]

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:

point C

Step-by-step explanation:

both planes include point C so that is where they intersect

Answer:

Point C

Step-by-step explanation:

As you can see in the picture below, Point C is where both planes intersect. Point C is what both planes have in common.

Answer:

2456

Step-by-step explanation:

Answer:

3=g/-4  -5

3+5=g/-4

8= g/-4

8x(-4)=g

g=-32

Step-by-step explanation:

Answer:

=fx+5f

Step-by-step explanation:

=fx+5f

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:

I belive I might be c not completely sure but pretty positive

Answer:

(7n-2p)(7n−2p) + (2n+4q)(2n+4q) + (q-5p)(q−5p) OR

53n² +29p² +17q² -14np +8nq -10pq

Step-by-step explanation:

The perimeter is found by adding all the side lengths.

P = (7n-2p)(7n−2p) + (2n+4q)(2n+4q) + (q-5p)(q−5p)

We know that (a+b)(a+b) = (a+b)², and (a-b)(a-b) = (a-b)²

P = (7n-2p)² + (2n+4q)² +  (q-5p)²

We know that (a+b)² = a²+b²+2ab, and (a-b)² = a²+b²-2ab

P = 49n² + 4p² - 14np +4n² +16q² + 8nq +q²+25p² -10pq

Combine like terms

Lets do

[tex]\\ \sf\longmapsto g(x)=5\sqrt{x}+2[/tex]

Lets take an example

[tex]\\ \sf\longmapsto g(4)=5\sqrt{4}+2[/tex]

[tex]\\ \sf\longmapsto 5(2)+2[/tex]

[tex]\\ \sf\longmapsto 10+2[/tex]

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

Answer:

the answer is "B"

the "a" (as in ax^2) is negative thus the parabola "goes downward"

Step-by-step explanation:

The equation of parabola is,

y = - 1/2x²

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line, which is known as the directrix.

We have to given that;

In a parabola,

Vertex = (0, 0)

Since, We know that;

Standard form of equation of parabola is,

y = a (x - h)² + k

Where, (h, k) = (0, 0) = vertex

Hence, We get;

y = a (x - 0)² + 0

y = ax²

Here, A point on parabola is, (2, - 2)

- 2 = a (2)²

a = - 2 / 4

a = - 1/2

Hence, The equation of parabola is,

y = - 1/2x²

Learn more about parabola visit:

https://brainly.com/question/29635857

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Answer:

l think it's consumer spending

Answer:

5 more matches was won by yu-na kim

Answer:

C) [tex]y = \frac{1}{2}[/tex] × [tex]4^x[/tex]

Answer:

C.    y= 1/2*4^x

Step-by-step explanation:

Recall that density = mass / volume.

Let's plug our known values into the equation.

15 g/cm^3 = 360g / volume

First, let's multiply both sides by volume

Volume * 15 g/cm^3 = 360g

Divide both sides by 15 g/cm^3

Volume = 24 cm^3

Density is defined as the mass per unit of volume. The volume of the ball is 24 cm³.

Density is defined as the mass per unit of volume. It is given by the formula,

Density = Mass / Volume

Given that You have a lead ball with a mass of 360 g. The density of lead is 15 g/cm³.

Now, since density is the ratio of mass and volume. Therefore, we can write the volume of the ball as,

Density = Mass / Volume

Volume = Mass / Density

Volume of the ball = 360g / 15g/cm³

                               = 24 cm³

Hence, the volume of the ball is 24 cm³.

Learn more about Density here:

https://brainly.com/question/952755

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Answer:

c= 13

Step-by-step explanation:

The complementary angles add up to 90° so we use some basic algebra to solve this question. like in the step by step explaination I have provided on paper

Answer:

sq rt of 66 is 8.12 so 8.1 closest

Answer:

8.1

I hope it will help you a lot.

HOPE your day goes great.

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

Answer:

D . p = 50

Step-by-step explanation:

To find the value of p we first need to find the values of inner angles

180 - 140 (linear pair)

= 40

180 -90 (linear pair)

= 90

now use angle sum property of triangle

40 + 90 + p = 180

130 + p = 180

p = 180 - 130

p = 50

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

Hello :D

The answer is 0.08

I hope this helps :)