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3 years ago

What is the answer to this equation?

Mathematics

1 answer:

sweet [91]3 years ago

5 0

Step 1. Factor x^2 - 2x - 15

(x - 5)(x + 3)/x^2 + 4x + 3

Step 2. Factor x^2 + 4x + 3

(x - 5)(x + 3)/(x + 1)(x + 3)

Step 3. Cancel x + 3

x - 5/x + 1

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Carla makes a scale drawing of her garden that is 30 feet long and 24 feet wide. If the garden in her drawing is 20 inches long.

patriot [66]

Answer:

Sorry you will have to clarify more on the width I do not under stand :/

Step-by-step explanation:

5 0

3 years ago

(7 + 7i)(2 − 2i)

Ostrovityanka [42]

The complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

<h3>What is a complex number?</h3>

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number shown in the picture:

-7i(3 + 3i)

= -7i

In trigonometric form:

z = 7 (cos (90) + sin (90) i)

= 3 + 3i

z = 4.2426 (cos (45) + sin (45) i)

$\rm 7\:\left(cos\:\left(90\right)\:+\:sin\:\left(90\right)\:i\right)4.2426\:\left(cos\:\left(45\right)\:+\:sin\:\left(45\right)\:i\right)$

$\rm =7\left(\cos \left(\dfrac{\pi }{2}\right)+\sin \left(\dfrac{\pi }{2}\right)i\right)\cdot \:4.2426\left(\cos \left(\dfrac{\pi }{4}\right)+\sin \left(\dfrac{\pi }{4}\right)i\right)$

$\rm 7\cdot \dfrac{21213}{5000}e^{i\dfrac{\pi }{2}}e^{i\dfrac{\pi }{4}}$

$\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}$

=21-21i

After converting into the exponential form:

$\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}$

From part (b) and part (c) both results are the same.

Thus, the complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

Learn more about the complex number here:

brainly.com/question/10251853

#SPJ1

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2 years ago

A random survey of 1000 students nationwide showed a mean ACT score of 21.1. Ohio was not used. A survey of 500 randomly selecte

vodka [1.7K]

Answer:

We conclude that the mean Ohio score is below the national average.

Step-by-step explanation:

We are given that a random survey of 1000 students nationwide showed a mean ACT score of 21.1. Ohio was not used.

A survey of 500 randomly selected Ohio scores showed a mean of 20.8. The population standard deviation is 3.

Let $\mu$ = mean Ohio scores.

So, Null Hypothesis, $H_0$ : $\mu$ $\geq$ 21.1 {means that the mean Ohio score is above or equal the national average}

Alternate Hypothesis, $H_A$ : $\mu$ < 21.1 {means that the mean Ohio score is below the national average}

The test statistics that would be used here One-sample z test statistics as we know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n}}}$ ~ N(0,1)

where, $\bar X$ = sample mean Ohio score = 20.8

$\sigma$ = population standard deviation = 3

n = sample of Ohio = 500

So, test statistics = $\frac{20.8-21.1}{\frac{3}{\sqrt{500}}}$

= -2.24

The value of z test statistics is -2.24.

Now, at 0.1 significance level the z table gives critical value of -1.2816 for left-tailed test. Since our test statistics is less than the critical values of z as -2.24 < 1.2816, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean Ohio score is below the national average.

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4 years ago

Two fair spinners are divided into quarters as shown.

UkoKoshka [18]

Answer:

bro this is confusing

Step-by-step explanation:

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3 years ago

Hewwo!

ella [17]

Answer:

See Below.

Step-by-step explanation:

Please refer to the diagram below.

We are given that O is the center of the circle, and chords MN and RS are intersected a P. OP is the bisector of ∠MPR. And we want to prove that MN = RS.

We will construct segments OK and OJ such that it perpendicularly bisects MN and RS.

Since OP bisects ∠MPR, it follows that:

$\displaystyle \angle JPO\cong \angle KPO$