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3 years ago

P=2a+2b , solve for b

Mathematics

1 answer:

sashaice [31]3 years ago

3 0

P = 2A + 2B (subtract 2A on both sides)

P - 2A = 2B (divide by 2 on both sides)

P/2 - 2A/2 = B

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

Tema [17]

Answer:

See Below.

Step-by-step explanation:

By definition, if two functions, f and g, are inverses, then:

$\displaystyle f(g(x)) = g(f(x)) = x$

We are given the two functions:

$\displaystyle g(x) = \sqrt{x + 8} -4 \text{ and } f(x) = x^2 + 8x + 8$

Find f(g(x)) and g(f(x)):

$\displaystyle \begin{aligned} f(g(x)) &= (\sqrt{x + 8} -4)^2 + 8(\sqrt{ x+ 8}-4) + 8 \\ \\ &= ((x+8) -8\sqrt{x + 8} +16) + 8\sqrt{x + 8} - 32 + 8 \\ \\ &= x + (-8\sqrt{x+8} + 8\sqrt{x + 8}) +(16 - 32 + 8 + 8) \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}$

And:

$\displaystyle \begin{aligned}g(f(x)) &= \sqrt{(x^2 + 8x + 8) + 8} - 4 \\ \\ &= \sqrt{x^2 + 8x+16 } - 4 \\ \\ &=\sqrt{(x+ 4)^2} - 4 \\ \\ &= (x +4) - 4 \\ \\ &= x \stackrel{\checkmark}{=} x \end{aligned}$

Hence, f and g are indeed inverses of each other.

8 0

2 years ago

Read 2 more answers

Bethany is working her way through school. She works two part-time jobs for a total of 23 hours a week. Job A pays $5.70 per hou

Lady bird [3.3K]

Step-by-step explanation:

x = number of hours A

y = number of hours B

x + y = 23

5.7x + 7.1y = 143.7

from the first equation we get

x = 23 - y

this we use in the second

5.7×(23 - y) + 7.1y = 143.7

131.1 - 5.7y + 7.1y = 143.7

1.4y = 12.6

y = 12.6/1.4 = 9

x = 23 - y = 23 - 9 = 14

she worked 14 hours on job A and 9 hours on job B.

8 0

2 years ago

For the function f defined b f(x)=x^2+2x+3 find f(-x), -f(x), and -f(-x).

Rom4ik [11]

Answer:

see explanation

Step-by-step explanation:

To evaluate f(- x) substitute x = - x into f(x)

f(- x) = (- x)² + 2(- x) + 3 = x² - 2x + 3

-----------------------------------------------------

- f(x) = - (x² + 2x + 3) ← distribute parenthesis by - 1

= - x² - 2x - 3

-----------------------------------------------------------

- f(- x) ← substitute f(- x) from above

= - (x² - 2x + 3) ← distribute parenthesis by - 1

= - x² + 2x - 3

5 0

3 years ago

What is the missing length?

OlgaM077 [116]

Answer:

12.1

Step-by-step explanation:

to doublecheck times it 8 to see if you get 96.8

7 0

2 years ago

Read 2 more answers

1,2,3 or 4? Look at the picture. Thank u!

Georgia [21]

Answer:

option 2

4/7

Step-by-step explanation:

Multiply 4/3x3/7 = 12/21

now simplify 12/21 = 4/7

7 0

2 years ago