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3 years ago

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You have 4/9 of a large bottle of oil. you pour 3/5 of oil into a smaller bottle. houw much of the entire larger bottle did you

pour into th smaller bottle?

1 answer:

777dan777 [17]3 years ago

6 0

$\frac{4}{9} \times \frac{3}{5} \\ = \frac{12}{45} \\ = \frac{4}{15}$

Hope this helps. - M

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A group of 5 friends decides to rent a vacation house for a month. The monthly rent on the house is $2,250. If each friend pays

Gala2k [10]

Each friend pays $2250/5 = $450 per month as a shared resident.

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3 years ago

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yanalaym [24]

Answer:

(7.5, 1.2) and (7.5, -2.3)

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3 years ago

Consider the sequence 3, 6, 12, 24, 48, .... (a) Write a recursive rule to represent the sequence. (b) Write an explicit rule to

saveliy_v [14]

Answer:

a. a[1] = 3; a[n] = 2a[n-1]

b. a[n] = 3·2^(n-1)

c. a[15] = 49,152

Step-by-step explanation:

Each term of the given sequence is 2 times the previous term. (This description is the basis of the recursive formula.) That is, the terms of the given sequence have a common ratio of 2. This means the sequence is geometric, so the formulas for explicit and recursive rules for a geometric sequence apply.

The first term is 3, and the common ratio is 2.

<h3>(a)</h3>

The recursive rule is ...

a[1] = 3

a[n] = 2×a[n-1]

__

<h3>(b)</h3>

The explicit rule is ...

a[n] = a[1]×r^(n-1)

a[n] = 3×2^(n-1)

__

<h3>(c)</h3>

The 15th term is ...

a[15] = 3×2^(15-1) = 3×2^14

a[15] = 49,152

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3 years ago

Solve the equation<br> 42x + 7 = 16

ehidna [41]

Answer:

should get 0.2 hope this helps you!

Step-by-step explanation:

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3 years ago

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4TH TIME ASKING THIS!!! Please help me! Someone pleaseeee. I need the correct answers. I don’t want to fail

Alexeev081 [22]

Answer:

The functions are inverses; f(g(x)) = x ⇒ answer D

$h^{-1}(x)=\sqrt{\frac{x+1}{3}}$ ⇒ answer D

Step-by-step explanation:

* <em>Lets explain how to find the inverse of a function</em>

- Let f(x) = y

- Exchange x and y

- Solve to find the new y

- The new y = $f^{-1}(x)$

* <em>Lets use these steps to solve the problems</em>

∵ $f(x)=\sqrt{x-3}$

∵ f(x) = y

∴ $y=\sqrt{x-3}$

- Exchange x and y

∴ $x=\sqrt{y-3}$

- Square the two sides

∴ x² = y - 3

- Add 3 to both sides

∴ x² + 3 = y

- Change y by $f^{-1}(x)$

∴ $f^{-1}(x)=x^{2}+3$

∵ g(x) = x² + 3

∴ $f^{-1}(x)=g(x)$

∴ <u><em>The functions are inverses to each other</em></u>

* <em>Now lets find f(g(x))</em>

- To find f(g(x)) substitute x in f(x) by g(x)

∵ $f(x)=\sqrt{x-3}$

∵ g(x) = x² + 3

∴ $f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x$

∴ <u><em>f(g(x)) = x</em></u>

∴ The functions are inverses; f(g(x)) = x

* <em>Lets find the inverse of h(x)</em>

∵ h(x) = 3x² - 1 where x ≥ 0

- Let h(x) = y

∴ y = 3x² - 1

- Exchange x and y

∴ x = 3y² - 1

- Add 1 to both sides

∴ x + 1 = 3y²

- Divide both sides by 3

∴ $\frac{x + 1}{3}=y^{2}$

- Take √ for both sides

∴ ± $\sqrt{\frac{x+1}{3}}=y$

∵ x ≥ 0

∴ We will chose the positive value of the square root

∴ $\sqrt{\frac{x+1}{3}}=y$

- replace y by $h^{-1}(x)$

∴ $h^{-1}(x)=\sqrt{\frac{x+1}{3}}$

4 0

3 years ago