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2 years ago

13

Graph the function y=

x} -2-5" align="absmiddle" class="latex-formula">. Which point lies on the graph?
(1, 4)

(3, –4)

(–5, 2)

(–2, 5)

1 answer:

Rashid [163]2 years ago

5 0

Answer:

(3, -4)

Step-by-step explanation:

The correct equation is:

$y=\sqrt{x-2}-5$

From the list of given points, we have to identify which point lies on the graph. This can be done by using the value of x-coordinates from the given points and see if they result in the corresponding y-coordinate:

For point (1, 4)

$y=\sqrt{1-2}-5=\sqrt{-1}-5$ , This is not equal to 4, so it does not lie on the graph of given function.

For point (3, -4)

$y=\sqrt{3-2}-5=\sqrt{1}-5=-4$ , The answer ans corresponding y-coordinate are the same. This means, (3, -4) point lies on the graph of given function.

Likewise, checking for 3rd and 4th point we find out that they do not lie on the graph.

So the correct answer is (3, -4)

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2 years ago

What is the value of x g^x-1 -2 = 25

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<h2>Answer: </h2>

Third choice, option C

x = 5/2

To solve for the value of x<em> </em>if <em>9^(x-1) - 2 = 25</em>, we can substitute each of the options into a simplified equation.

<h2>Simplify the equation</h2>

We <em>could </em>substitute each option into the given equation, but then we would have to simplify it four more times. It's easier to simplify once first.

$9^{x-1} -2=25$ Start with the given equation

$9^{x-1} -2+2=25+2$ Add 2 to both sides

$9^{x-1} =25+2$ –2 + 2 on the left side cancels out

$9^{x-1} =27$ Add on the right side

We found a simplified equation.

<h2>Substitute</h2>

Now, let's substitute each option choice for 'x' in the simplified equation. We only have to substitute choices until we find the choice that makes the left and right sides of the equation equal, but let's try all of the choices today.

<h3>Option A: x = 1/2</h3>

$9^{x-1} =27$ Start with the simplified equation

$\displaystyle{9^{\frac{1}{2}-1} =27}$ Substitute x = 1/2

$\displaystyle{9^{\frac{1}{2}-\frac{2}{2}} =27}$ Find a common denominator within the exponent

$\displaystyle{9^{\frac{1-2}{2}} =27}$ Combine numerators and subtract

$\displaystyle{9^{-\frac{1}{2}} =27}$

$\displaystyle{(3^{2})^{-\frac{1}{2}} =27}$ Convert 9 into a base and exponent

$\displaystyle{ 3^{ 2*-\frac{1}{2} } =27 }$ Multiply exponents

$\displaystyle{ 3^{ -\frac{2*1}{2} } =27 }$ Combine into numerator

$\displaystyle{ 3^{ -\frac{2}{2} } =27 }$ Simplify the fraction

$\displaystyle{ 3^{ -1 } =27 }$ Use negative exponent rule to simplify

$\displaystyle{ \frac{1}{3^{1}} =27 }$ Simplify the denominator

$\displaystyle{ \frac{1}{3} \neq 27 }$ Left and right sides are <u>not equal</u>

So, <em>x</em> is not equal to 1/2.

<h3>Option B: x = 2</h3>

$9^{x-1} =27$ Start with the simplified equation

$9^{2-1} =27$ Substitute x = 2

$9^{1} =27$ Subtract within the exponent

$9 \neq 27$ Left and right sides are <u>not equal</u>

So, <em>x</em> is not equal to 2.

<h3>Option C: x = 5/2</h3>

$9^{x-1} =27$ Start with the simplified equation

$\displaystyle{9^{\frac{5}{2}-1} =27}$ Substitute x = 5/2

$\displaystyle{9^{\frac{5}{2}-\frac{2}{2}} =27}$ Find a common denominator within the exponent

$\displaystyle{9^{\frac{5-2}{2}} =27}$ Combine numerators and subtract

$\displaystyle{9^{\frac{3}{2}} =27}$ Use fractional exponent rule to simplify

$\displaystyle{\sqrt[2]{9^{3}} =27}$

$\displaystyle{\sqrt{9^{3}} =27}$

$\displaystyle{\sqrt{9 * 9 * 9} =27}$ Solve the exponent by multiplying bases

$\displaystyle{\sqrt{729} =27}$ Solve the root

$\displaystyle{27 =27}$ Left and right sides are <u>equal</u>

So, <em>x</em> is equal to 5/2.

<h3>Option D: x = 4</h3>

$9^{x-1} =27$ Start with the simplified equation

$9^{4-1} =27$ Substitute x = 4

$9^{3} =27$ Subtract within the exponent

$9*9*9 =27$ Solve the exponent by multiplying bases

$729 \neq 27$ Left and right sides are <u>not equal</u>

So, <em>x</em> is not equal to 4.

∴ in $9^{x-1} -2=25$ , <em>x</em> is equal to $\displatestyle{\frac{5}{2}}$ , making option C correct.

Learn more about exponent rules here:

brainly.com/question/84608

brainly.com/question/12173411

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