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3 years ago

Please help! Find all the missing angles ??

Mathematics

1 answer:

Natasha2012 [34]3 years ago

5 0

Answer:

A 62°

B 118°

C 62°

D 118°

E 50°

F 58°

G 120°

H 120°

I 120°

J 60°

K 60°

L 60°

M 120°

N 120°

P 60°

Q 35.5°

R 49°

S 35.5°

T 109°

U 71°

V 109°

W 60°

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An isosceles right triangle has a hypotenuse of length e. Select all that are true for the triangle.

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<h3>2 Answers: </h3>

Choice C) Leg length = $\frac{e\sqrt{2}}{2}$
Choice E) Area = $\frac{e^2}{4}$

Note: if the formulas don't load properly, then you may need to refresh the page.

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Explanation:

For any 45-45-90 right triangle, the hypotenuse H is always sqrt(2) times the leg L

In terms of symbols, we can say

$H = L*\sqrt{2}$

We're told the hypotenuse is e, so H = e

Let's solve for L in terms of e

$H = L*\sqrt{2}\\\\e = L*\sqrt{2}\\\\L*\sqrt{2} = e\\\\L = \frac{e}{\sqrt{2}}\\\\$

Now let's multiply top and bottom by $\sqrt{2}$ to rationalize the denominator

$L = \frac{e}{\sqrt{2}}\\\\L = \frac{e\sqrt{2}}{\sqrt{2}*\sqrt{2}}\\\\L = \frac{e\sqrt{2}}{\sqrt{2*2}}\\\\L = \frac{e\sqrt{2}}{\sqrt{4}}\\\\L = \frac{e\sqrt{2}}{2}\\\\$

If the hypotenuse is e, then the length of each leg is $\frac{e\sqrt{2}}{2}$

This matches with choice C, which is one of the two answers. This allows us to rule out choices A and B, as those expressions are not equivalent to the expression for choice C.

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The two legs of any right triangle form the base and height. The order doesn't matter. The base is always perpendicular to the height. In a right triangle, the two legs are always perpendicular.

The base and height are $\frac{e\sqrt{2}}{2}$ each.

The area of the triangle is...

$\text{Area} = \frac{1}{2}*\text{base}*\text{height}\\\\\text{Area} = \frac{1}{2}*\frac{e\sqrt{2}}{2}*\frac{e\sqrt{2}}{2}\\\\\text{Area} = \frac{e\sqrt{2}*e\sqrt{2}}{2*2*2}\\\\\text{Area} = \frac{e*e\sqrt{2*2}}{2*2*2}\\\\\text{Area} = \frac{e^2\sqrt{4}}{2*2*2}\\\\\text{Area} = \frac{e^2*2}{2*2*2}\\\\\text{Area} = \frac{e^2}{2*2}\\\\\text{Area} = \frac{e^2}{4}\\\\$

This matches with choice E, which is the other answer. Choices D and F are eliminated as they are not equivalent to the expression for choice E.

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3 years ago

There are approximately 12 inches in 1 foot. If Johnny is 5 feet and 4 how tall is he in inches?

Rom4ik [11]

Answer: It's 64

Step-by-step explanation:

12x5=60

60+4=64

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3 years ago

Read 2 more answers

Commute times in the U.S. are heavily skewed to the right. We select a random sample of 45 people from the 2000 U.S. Census who

Delicious77 [7]

Answer:

The mean commute time in the U.S. is less than half an hour.

Step-by-step explanation:

In this case we need to test whether the mean commute time in the U.S. is less than half an hour.

The information provided is:

$n=45\\\bar x=25.5\\s=19.1\\\alpha =0.05$

(a)

The hypothesis for the test can be defined as follows:

<em>H</em>₀: The mean commute time in the U.S. is not less than half an hour, i.e. <em>μ</em> ≥ 30.

<em>Hₐ</em>: The mean commute time in the U.S. is less than half an hour, i.e. <em>μ</em> < 30.

(b)

As the population standard deviation is not known we will use a t-test for single mean.

Compute the test statistic value as follows:

$t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{25.2-30}{19.1/\sqrt{45}}=-1.58$

Thus, the test statistic value is -1.58.

(c)

Compute the p-value of the test as follows:

$p-value=P(t_{(n-1)}$

*Use a t-table.

The p-value of the test is 0.061.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

p-value = 0.061> α = 0.05

The null hypothesis will not be rejected at 5% level of significance.

Thus, concluding that the mean commute time in the U.S. is less than half an hour.

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4 years ago

Which situations most likely involve the use of decimals? Choose more than one answer.

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Answer:

Estimating the weight of an elephant

Step-by-step explanation:

Put an elephant onto a large boat and the marker that the water rises to Minus the starting point

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3 years ago

Write an expression for the measurement of angle L using the measurement of angle C found in part C

kap26 [50]

Answer:

180’ - 130’

Step-by-step explanation:

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3 years ago