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ad-work [718]
2 years ago
10

Need help with this one NO LINKS!!! Special Right Triangles (Radical Answers)

Mathematics
2 answers:
Natalka [10]2 years ago
5 0

Answer:

x = 5\sqrt{2} (or \frac{5\sqrt{2}}{1} if it has to have a rational denominator)

Step-by-step explanation:

We know;

1.) This triangle is isosceles (two of the sides are congruent).

2.) Hypotenuse is the biggest side in a right triangle. Therefore, that un-labeled side can't be 10, it has to be x as well.

So;

A² + B² = C²

x² + x² = 10²

2x² = 100

x² = 100/2

x² = 50

x = \sqrt{50}

Simplifying this would result in;

\sqrt{50} = \sqrt{25} * \sqrt{2}

\sqrt{50} = 5\sqrt{2} (or \frac{5\sqrt{2}}{1} if it has to have a rational denominator)

Hope this helps!

AURORKA [14]2 years ago
4 0

Answer:

x = 5*sqrt(2)

Step-by-step explanation:

Equation

Use the Pythagorean Theorem to get the value of x. If the triangle is isosceles, it means that both lets are equal to x.

x^2 + x^2 = 10^2

2x^2 = 100

x^2 = 50

x^2 = 5 * 5 * 2

sqrt(x^2) = sqrt(5*5*2)

x = 5*sqrt(2)

There is no denominator to rationalize. The answer is given as a irrational root.  The only other way to present it is in an approximate decimal form.

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A phone manufacturer wants to compete in the touch screen phone market. He understands that the lead product has a battery life
alisha [4.7K]

Answer:

a)

The null hypothesis is H_0: \mu \leq 10

The alternative hypothesis is H_1: \mu > 10

b-1) The value of the test statistic is t = 1.86.

b-2) The p-value is of 0.0348.

Step-by-step explanation:

Question a:

Test if the battery life is more than twice of 5 hours:

Twice of 5 hours = 5*2 = 10 hours.

At the null hypothesis, we test if the battery life is of 10 hours or less, than is:

H_0: \mu \leq 10

At the alternative hypothesis, we test if the battery life is of more than 10 hours, that is:

H_1: \mu > 10

b-1. Calculate the value of the test statistic.

The test statistic is:

We have the standard deviation for the sample, so the t-distribution is used to solve this question

t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}

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

10 is tested at the null hypothesis:

This means that \mu = 10

In order to test the claim, a researcher samples 45 units of the new phone and finds that the sample battery life averages 10.5 hours with a sample standard deviation of 1.8 hours.

This means that n = 45, X = 10.5, s = 1.8

Then

t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}

t = \frac{10.5 - 10}{\frac{1.8}{\sqrt{45}}}

t = 1.86

The value of the test statistic is t = 1.86.

b-2. Find the p-value.

Testing if the mean is more than a value, so a right-tailed test.

Sample of 45, so 45 - 1 = 44 degrees of freedom.

Test statistic t = 1.86.

Using a t-distribution calculator, the p-value is of 0.0348.

5 0
2 years ago
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