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kirill115 [55]
3 years ago
13

Let f(x) = (7x^3 + 18)2 and h(x) = x^2.Given that f(x) = (hºg)(x), find g(x).​

Mathematics
1 answer:
evablogger [386]3 years ago
4 0

\bf \begin{cases} f(x)=(7x^3+18)^2\\ f(x) = (h\circ g)(x)\\ h(x)=x^2 \end{cases}~\hspace{5em}(h\circ g)(x) = \stackrel{f(x)}{(7x^3+18)^2} \\\\\\ h(x) = x^2\implies \stackrel{(h\circ g)(x)}{h(~~g(x)~~)}=[g(x)]^2\implies h(~~g(x)~~)=\stackrel{f(x)}{(7x^3+18)^2} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill g(x)=7x^3+18~\hfill

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6 0
3 years ago
2. If y varies inversely as x and<br> y = 3 when x = 5, find x when y = 2.5
4vir4ik [10]

Answer:

Step-by-step explanation:

From the law of variation,

y <> 1/x, where <> is the constant of proportionality. Therefore

y = k/x where k is a constant

3 = k/5 and k = 15

To find x when y = 2.5(5/2)

Go back to the second equation

y = k/x

5/2 = 15/x

When you cross multiply

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Divide through by 5,

x = 6.

8 0
3 years ago
Write the integer represented by H. List its opposite and absolute value.
musickatia [10]

Answer:

The integer represented by H is -2

Its opposite is 2 and the absolute value is also 2

4 0
3 years ago
June bought three books. For the first book, she paid one half of her allowance plus $1 more. For the second book, she paid one
inysia [295]

Answer:

$34

Step-by-step explanation:

I'd work backwards.

For the third book, she paid all her remaining money. The problem says she paid "1/2 her leftover money + $3". This means that: (let m = money used to buy book 3)

m = 1/2m + 3

1/2m = 3

m = 6

For the second book: (let n = money before book 2)

n - m (money left after book 2) = 1/2n + 2

1/2n +2 is money used up for book, which is the same as n-m.

n = 1/2n + 2 + m

1/2n = 2 + m = 2 + 6

1/2n =8

n = 16

For the first book, she spent 1/2 her money + 1. If o = money before book 1 (or the whole allowance):

o - n = 1/2o + 1

o = 1/2o + n + 1 = 1/2o + 16 + 1

1/2o = 17

o = 34

Check!

Spent 17 (half 34) + 1 on book 1

16 left

Spent 8 (half 16) +2 on book 2

6 left

Spent 3 (half 6) + 3 on book 3

0 left

4 0
3 years ago
Last year, Gena’s food cart business was $225 in debt. This year, the debt has tripled. Which expressions show how much Gena’s b
NeX [460]

Answer:

B and E

Step-by-step explanation:

5 0
3 years ago
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