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3 years ago

Let f(x)=2/3x-6 what is the inverse function?

1 answer:

4 0

Change f(x) to a y and switch places with y and x as below.
$x= \frac{2}{3} y-6$

Solve the equation for y
$x + 6 = \frac{2}{3} y$

Multiply each term by the reciprocal of $\frac{2}{3}$
$\frac{3}{2} (x+6) = y$

Distribute
$\frac{3}{2} x+9=y$

Change y to $f^{-1}(x)$
$f^{-1}(x)= \frac{3}{2} x+9$

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Free 5 points!+thanks. But you have to answer this easy question! What's your zodiac sign?

weeeeeb [17]

I am a capricorn :) wbu?

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3 years ago

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Solve for x when <img src="https://tex.z-dn.net/?f=x%5E%7Byz%7D%20%3Dy%5E%7B2%7D" id="TexFormula1" title="x^{yz} =y^{2}" alt="x^

Assoli18 [71]

The value of x in x^yz = y^2 is $x = \sqrt[yz]{y^2}$

<h3>How to solve for x?</h3>

The equation is given as:

x^yz = y^2

Rewrite the equation properly as follows

$x^{yz} = y^2$

Take the yz root of both sides

$\sqrt[yz]{x^{yz}} = \sqrt[yz]{y^2}$

Apply the law of indices

$x^{\frac{yz}{yz}} = \sqrt[yz]{y^2}$

Divide yz by yz

$x = \sqrt[yz]{y^2}$

Hence, the value of x in x^yz = y^2 is $x = \sqrt[yz]{y^2}$

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2 years ago

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If nelson invests $5000 for 4 years and earns $600, what is the simple interest rate?

klio [65]

Answer: Simple interest rate = 3%.

Step-by-step explanation: We are given invested amount = $5000.

Number of years of investment = 4 years.

Interest earned = $600.

Simple interest formula.

I = P R T.

Where I is the earned interest, P is the invested amount , R is the rate of interest and T is the time in years.

Plugging values in formula, we get

600 = 5000 × R × 4

600 = 20000R.

Dividing both sides by 20000, we get

$\frac{600}{20000} = \frac{20000R}{20000} .$

0.03 = R.

Multiplying by 100 to convert it in percentage, we get

0.03 × 100 = R

R = 3 %.

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3 years ago

Please help me with this 20 points

JulsSmile [24]

Answer:

A 4/605

Step-by-step explanation:

mathematics = 11 letters

P(m) = number of m's/total = 2/11

we replace it so we have mathematics = 11 letters

P(s) = number of s's/total = 1/11

not replacing it

we replace it so we have mathematic = 10 letters

P(vowel) = number of vowel/total = 4/10 = 2/5

P(m, replace,s, no replace, vowel) = 2/11* 1/11 * 2/5 = 4/605

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3 years ago

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Sally needs 2/3 of a pound of potatoes. This is 1/3 of a pound more than 4/3 of the potatoes Sally has in her pantry

amid [387]

Lets assume, Sally has X pound of potatoes in her pantry.

So, 4/3 of the potatoes Sally has in her pantry = $\frac{4}{3}X$

Now, Sally needs 2/3 pound of potatoes and this 2/3 pound of potatoes is 1/3 pound more than that $\frac{4}{3}X$

So the representing equation will be:

$\frac{2}{3} = \frac{1}{3}+ \frac{4}{3}X$

$\frac{2}{3} - \frac{1}{3} = \frac{4}{3} X$ (subtracting $\frac{1}{3}$ from both sides)

$\frac{1}{3}= \frac{4}{3}X$

$1= 4X$ (multiplying both sides by 3)

$X =\frac{1}{4}$

So, Sally has $\frac{1}{4}$ pound of potatoes in her pantry.

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3 years ago