All categories

3 years ago

What is the value of X?

SAT

2 answers:

soldi70 [24.7K]3 years ago

7 0

Answer:

x = 7

Explanation:

To solve for x in this equation, we're going to need to get the two exponents (3x - 5 and x + 1) equal to each other, but we can't do that unless our bases are the same.

For example, in $A^{x} = B^{x + 1}$ , you cannot solve x = x + 1. In $A^{x} = A^{x + 1}$ , you can solve x = x + 1.

Just by looking at the bases, 5 and 25, you can tell that it will be simple to make them match. 25 is just 5². The tricky part is going to be figuring out where to put the 2 into x + 1.

Let's look at another example. If you have $2^{2 * 2}$ , then you can simplify it to $2^{4}$ , which is 16. Or, you could do them one at a time, so $(2^{2}) ^{2}$ . This way you'd have 4², which you'd be able to recognize as 16. Based on this example, we know that to make our bases the same, we need to change $25^{x + 1}$ to $5^{2(x + 1)}$ .

$5^{3x-5} = 25^{x+1}$ Change the right side to $5^{2(x + 1)}$

$5^{3x-5} = 5^{2(x+1)}$ Simplify that exponent using distribution

$5^{3x-5} = 5^{2x+2}$

Now that the bases match, you can get rid of them and just set the exponents equal to each other and solve for x.

3x - 5 = 2x + 2 Add 5 to both sides

3x = 2x + 7 Subtract 2x from both sides

x = 7

Now, check you work!

$5^{3x-5} = 25^{x+1}$ Plug in 7 for x

$5^{3(7)-5} = 25^{(7)+1}$ Simplify

$5^{21-5} = 25^{8}$ Simplify one more time

$5^{16} = 25^{8}$ Plug these into a calculator if you have one

152587890625 = 152587890625 So you know that x = 7 is correct.

nevsk [136]3 years ago

6 0

Answer:

Explanation:

Because 25 is a perfect square of 5, we can turn

$5^{3x - 5}$ = $25^{x + 1}$

into

$5^{3x - 5}$ = $5^{2x + 2}$

Since the bases are now both equal, we can completely ignore them, as we are only trying to find x. This leaves us with:

3x - 5 = 2x + 2

All we have to do now is solve for x:

x - 5 = 2 <em>Subtract 2x from both sides.</em>

<u>x = 7</u> <em>Add 5 to both sides.</em>

<em />

<em>Hope this helps! :)</em>

You might be interested in

Safety signs type and meaning

oksian1 [2.3K]

Stop-stop
green-go
red-stop
yellow-slow down/caution

6 0

3 years ago

Read 2 more answers

What effect did the homestead act have on westward expansion. Reward brainliest

Verdich [7]

Answer:

Read below

Explanation:

The Homestead Act of 1862 was one of the most significant and enduring events in the westward expansion of the United States. By granting 160 acres of free land to claimants, it allowed nearly any man or woman a "fair chance."

8 0

3 years ago

Read 2 more answers

Amber has been asked to identify the meter of "sonnet 18. " she is highlighting the syllables that should be stressed. And often

77julia77 [94]

Based on the provided information, syllables should Amber highlight is "of his gold".

<h3>What is syllable?</h3>

Syllable can be regarded as unit of pronunciation which posses one vowel sound.

According to this question, we were told that Amber is highlighting the syllables that should be stressed.

Then considering the statement given Amber should highlight the "of his gold" from the sentence .

Therefore, Amber should highlight is "of his gold" syllable.

Learn more about syllable at:

brainly.com/question/24858866

3 0

2 years ago

What is the following product? Assume x greater-than-or-equal-to 0 (4 x StartRoot 5 x squared EndRoot 2 x squared StartRoot 6 En

olga2289 [7]

Answer:

Explanation:

7 0

2 years ago

Use series to approximate the definite integral i to within the indicated accuracy. i = 1/2 x3 arctan(x) dx 0 (four decimal plac

Valentin [98]

The expression $\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx$ is an illustration of definite integrals

The approximated value of the definite integral is 0.0059

<h3>How to evaluate the definite integral?</h3>

The definite integral is given as:

$\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx$

For arctan(x), we have the following series equation:

$\arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 1}}{2n + 1}}$

Multiply both sides of the equation by x^3.

So, we have:

$x^3 * \arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 1}}{2n + 1}} * x^3$

Apply the law of indices

$x^3 * \arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 1 + 3}}{2n + 1}}$

$x^3 * \arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 4}}{2n + 1}}$

Evaluate the product

$x^3 \arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 4}}{2n + 1}}$

Introduce the integral sign to the equation

$\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx =\int\limits^{1/2}_{0} \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 4}}{2n + 1}}$

Integrate the right hand side

$\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx =[ \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 4}}{2n + 1}} ]\limits^{1/2}_{0}$

Expand the equation by substituting 1/2 and 0 for x

$\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx =[ \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{(1/2)^{2n + 4}}{2n + 1}} ] - [ \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{0^{2n + 4}}{2n + 1}} ]$

Evaluate the power

$\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx =[ \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{(1/2)^{2n + 4}}{2n + 1}} ] - 0$

$\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{(1/2)^{2n + 4}}{2n + 1}}$

The nth term of the series is then represented as:

$T_n = \frac{(-1)^n}{2^{2n + 5} * (2n + 4)(2n + 1)}$

Solve the series by setting n = 0, 1, 2, 3 ..........

$T_0 = \frac{(-1)^0}{2^{2(0) + 5} * (2(0) + 4)(2(0) + 1)} = \frac{1}{2^5 * 4 * 1} = 0.00625$

$T_1 = \frac{(-1)^1}{2^{2(1) + 5} * (2(1) + 4)(2(1) + 1)} = \frac{-1}{2^7 * 6 * 3} = -0.0003720238$

$T_2 = \frac{(-1)^2}{2^{2(2) + 5} * (2(2) + 4)(2(2) + 1)} = \frac{1}{2^9 * 8 * 5} = 0.00004340277$

$T_3 = \frac{(-1)^3}{2^{2(3) + 5} * (2(3) + 4)(2(3) + 1)} = \frac{-1}{2^{11} * 10 * 7} = -0.00000634131$

..............

At n = 2, we can see that the value of the series has 4 zeros before the first non-zero digit

This means that we add the terms before n = 2

This means that the value of $\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx$ to 4 decimal points is

$\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx = 0.00625 - 0.0003720238$

Evaluate the difference

$\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx = 0.0058779762$

Approximate to four decimal places

$\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx = 0.0059$

Hence, the approximated value of the definite integral is 0.0059

Read more about definite integrals at:

brainly.com/question/15127807

5 0

2 years ago