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3 years ago

Use special right triangles to solve for the value of x.

Mathematics

2 answers:

snow_lady [41]3 years ago

8 0

<u>Answer </u>

<u>Explanation. </u>

The triangle shown is a right triangle. One of the acute angles is given as 45°. Angles in a triangle add up to 180°

So we can get the third angle of the triangle as follows:

180 - (90+45) = 45.

From this we can conclude that, apart from the triangle being an right triangle, it is also isosceles triangle. This means that the two shorter sides of the triangle are equal.

So, the value of x is 7.

Verizon [17]3 years ago

3 0

Answer: x = 7

Explanation:

1) This special right triangle is the isosceles right triangle: 45°-45°-90°.

It is an isosceles right triangle, then x = 7.

2) For these the isosceles right triangle you have: hypotenuse = leg length × √2.

You can prove that using Pythagoras: hypotenuse² = side² + side² = 2×side² ⇒ hypotenuse.

3) Therefore: x = 7 and y = 7√2

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What number equals 100 when squared?

vfiekz [6]

Answer: 10

Step-by-step explanation: Remember that squaring a number is multiplying a number by itself. 100 = 10² because 10 x 10 = 100.

8 0

3 years ago

Read 2 more answers

What is the LCM of 5 and 12

Virty [35]

60. The answer is 60

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3 years ago

-9(m+3) +14=-49 please show work

yKpoI14uk [10]

Answer:

m=4

Step-by-step explanation:

−9(m+3)+14=−49

Step 1: Simplify both sides of the equation.

−9(m+3)+14=−49

(−9)(m)+(−9)(3)+14=−49(Distribute)

−9m+−27+14=−49

(−9m)+(−27+14)=−49(Combine Like Terms)

−9m+−13=−49

−9m−13=−49

Step 2: Add 13 to both sides.

−9m−13+13=−49+13

−9m=−36

Step 3: Divide both sides by -9.

−9m

−9

−36

−9

m=4

8 0

3 years ago

Consider a chemical company that wishes to determine whether a new catalyst, catalyst XA-100, changes the mean hourly yield of i

kolezko [41]

Answer:

Null hypothesis: $\mu = 750$

Alternative hypothesis: $\mu \neq 750$

$t=\frac{811-750}{\frac{19.647}{\sqrt{5}}}=6.943$

$p_v =2*P(t_{4}>6.943)=0.00226$

If we compare the p value and a significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we reject the null hypothesis, and the actual true mean is significantly different from 750 pounds per hour.

Step-by-step explanation:

Data given and notation

Data: 801, 814, 784, 836,820

We can calculate the sample mean and sample deviation with the following formulas:

$\bar X =\frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=811$ represent the sample mean

$s=19.647$ represent the standard deviation for the sample

$n=5$ sample size

$\mu_o =750$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses to be tested

We need to conduct a hypothesis in order to determine if the mean is different from 750 pounds per hour, the system of hypothesis would be:

Null hypothesis: $\mu = 750$

Alternative hypothesis: $\mu \neq 750$

Compute the test statistic

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

We can replace in formula (1) the info given like this:

$t=\frac{811-750}{\frac{19.647}{\sqrt{5}}}=6.943$

Now we need to find the degrees of freedom for the t distirbution given by:

$df=n-1=5-1=4$

What do you conclude?

Compute the p-value

Since is a two tailed test the p value would be:

$p_v =2*P(t_{4}>6.943)=0.00226$

4 0

3 years ago

What is 100/ 5 i need help asap

zepelin [54]

Answer:

Step-by-step explanation:

You can take a 0 off of 100.

10/5=2

Add the 0 back to the end

20 is your answer.

3 0

3 years ago