All categories

3 years ago

Simplify (-5x^3)^-2 using only positive exponents

Mathematics

2 answers:

mihalych1998 [28]3 years ago

5 0

Hope you know that x^(-1) = 1/x used this you get

(-5x^3)^-2 = 1/(-5x^3)^2 = 1/{(-5^2)(x^6)} = 1/(25x^6)

hope helped

Alona [7]3 years ago

4 0

$a^{-n}=\dfrac{1}{a^n}\\\\(a^n)^m=a^{n\cdot m}\\\\(a\cdot b)^n=a^n\cdot b^n\\------------------\\\\\left(-5x^3\right)^{-2}=\dfrac{1}{\left(-5x^3\right)^2}=\dfrac{1}{(-5)^2(x^3)^2}=\dfrac{1}{25x^{3\cdot2}}=\boxed{\dfrac{1}{25x^6}}$

You might be interested in

The sum of Alex's height and Ben's height is 130 inches. Subtracting Alex's height from Ben's height yields one-third of Ben's h

In-s [12.5K]

Ben is 97.5 inches tall.

Alex is 32.5 inches tall.

5 0

3 years ago

Read 2 more answers

Draw 2 lines to cut each triangle into the given shapes. 1 pentagon and 2 triangles

vlada-n [284]

Answer:

cut the two lines at the corner, don't let the lines touch

Step-by-step explanation:

8 0

3 years ago

Select all the numbers that are equivalent.

xz_007 [3.2K]

B,C,D are all equivalent.

5 0

3 years ago

Read 2 more answers

A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is

insens350 [35]

Answer:

The value of the test statistic and its associated p-value at the 5% significance level are -1.54 and 0.9382, respectively.

Step-by-step explanation:

A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.16.

This means that the null hypothesis is:

$H_{0}: p \geq 0.16$

Testing this hypothesis, means that the alternate hypothesis is:

$H_{a}: p > 0.16$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.16 is tested at the null hypothesis:

This means that $\mu = 0.16, \sigma = \sqrt{0.16*0.84}$

In a sample of 200 graduates, 24 students have a GPA of 3.00 or below.

This means that $n = 200, X = \frac{24}{200} = 0.12$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.12 - 0.16}{\frac{\sqrt{0.16*0.84}}{\sqrt{200}}}$

$z = -1.54$

Pvalue:

The pvalue is the probability of finding a sample mean above 0.12, which is 1 subtracted by the pvalue of z = -1.54.

Looking at the z-table, z = -1.54 has a pvalue of 0.0618

1 - 0.0618 = 0.9382

The value of the test statistic and its associated p-value at the 5% significance level are -1.54 and 0.9382, respectively.

6 0

3 years ago

HELPPPP ME PLZZZZ!!!!!!

mihalych1998 [28]

<h3>Answers:</h3>

14. Each leg is $21\sqrt{2}$ units long.

15 (a). The longer leg is $7\sqrt{3}$ units long

15 (b). The hypotenuse is $14$ units long

=====================================================

Explanations:

For a 45 degree right triangle, aka 45-45-90 triangle, the hypotenuse is equal to sqrt(2) times the short leg. Algebraically we can say

$y = x\sqrt{2}$ where x is the leg and y is the hypotenuse

Let's solve for x

$y = x\sqrt{2}\\\\x\sqrt{2} = y\\\\x = \frac{y}{\sqrt{2}}\\\\x = \frac{y\sqrt{2}}{\sqrt{2}*\sqrt{2}} \ \text{rationalizing denominator}\\\\x = \frac{y\sqrt{2}}{2}\\\\$

Now plug in the given hypotenuse y = 42, this leads to,

$x = \frac{y\sqrt{2}}{2}\\\\x = \frac{42\sqrt{2}}{2}\\\\x = \frac{42}{2}\sqrt{2}\\\\x = 21\sqrt{2}\\\\$

---------------------------

For a 30-60-90 triangle, the hypotenuse is double that of the short leg. So the hypotenuse is 2*7 = 14.

The longer leg is equal to sqrt(3) times the short leg. The longer leg is $7\sqrt{3}$

5 0

3 years ago