Compute the inverse of the following matrix with steps.

Triangle GCH is similar to triangle DCE. Find CH

soldier1979 [14.2K]

Answer:

x = 65

Step-by-step explanation:

if two triangles are similar then we can use the similarity ratio to find the length of CH

60/156 = x/169 cross multiply expressions

156x = 10140 divide both sides by 156

x = 65

5 0

3 years ago

You're standing on the ground 7777 meters away from the bottom of a tall tower. The tower itself is 346346 meters tall. What is

lys-0071 [83]

Answer:

88.7°

Step-by-step explanation:

First, visualize. Assuming that the tower is at a perfectly 90° angle to the ground, you have a right triangle. We will call this triangle ΔABC where A is where you are, B is the top of the tower, and C is the base of the tower. Now we know the following:

∠A = ?

∠B = ?

∠C = 90

a = 346346

b = 7777

c = ?

Note: Triangles are labeled with three pairs of letters: a, b and c and A, B and C. The lower case letters, a, b and c represent the sides, and the upper case letters are the angles that are directly opposite of those sides. (see attached reference)

c is easy, c is the hypotenuse, so you can use the following equation to find the hypotenuse:

a² + b² = c²

Rearranged:

c = ± $\sqrt{a^{2} +b^{2} }$

Substitute a and b:

c = ± $\sqrt{346346^{2} +7777^{2} }$

Comes out to ~346433.3 meters.

Now if we use the Law of Sines:

$\frac{a}{sinA}$ = $\frac{b}{sinB}$ = $\frac{c}{sinC}$

We can use c and a, since we're trying to find what angle A is, so the ratio is set up as:

$\frac{346346}{sinA}$ = $\frac{346433.3}{sinC}$

Well we know that C = 90, and so sin(90) in degrees (as opposed to radians) is 1. So then the set of equations is now:

$\frac{346346}{sinA}$ = $\frac{346433.3}{1}$

Cross Multiply to get rid of the fractions:

346346 = 346433.3 * sin(A)

Divide:

$\frac{346346}{346433.3}$ = sin(A)

Using a calculator, if you take the arcsin of that fraction, you will get what angle A is supposed to be:

arcsin( $\frac{346346}{346433.3}$ ) = ∠A = 88.7°

5 0

2 years ago

A 99% confidence interval for the difference between two proportions was estimated at 0.11, 0.39. Based on this, we can conclude

sladkih [1.3K]

Answer:

$\hat p_1 -\hat p_2 \pm z_{\alpha/2} SE$

And for this case the confidence interval is given by:

$0.11 \leq p_1 -p_2 \leq 0.39$

Since the confidenc einterval not contains the value 0 we can conclude that we have significant difference between the two population proportion of interest 1% of significance given. So then we can't conclude that the two proportions are equal

Step-by-step explanation:

Let p1 and p2 the population proportions of interest and let $\hat p_1$ and $\hat p_2$ the estimators for the proportions we know that the confidence interval for the difference of proportions is given by this formula:

$\hat p_1 -\hat p_2 \pm z_{\alpha/2} SE$

And for this case the confidence interval is given by:

$0.11 \leq p_1 -p_2 \leq 0.39$

Since the confidence interval not contains the value 0 we can conclude that we have significant difference between the two population proportion of interest 1% of significance given. So then we can't conclude that the two proportions are equal

4 0

2 years ago

Can someone help me please with this question?

lubasha [3.4K]

$\frac{10}{7}$ = $\frac{3}{x}$
so x=2.1

8 0

2 years ago

Read 2 more answers

How to solve <img src="https://tex.z-dn.net/?f=log_%7By%7D%285y%29%20%3D%202" id="TexFormula1" title="log_{y}(5y) = 2" alt="log_

Natalija [7]

Answer:

y = 5

Step-by-step explanation:

Expand the logarithm:

$\log_y{(5)}+\log_y{(y)}=2\\\\\dfrac{\log{(5)}}{\log{(y)}}+1=2 \quad\text{change of base formula}\\\\\dfrac{\log{(5)}}{\log{(y)}}=1 \quad\text{subtract 1}\\\\\log{(5)}=\log{(y)} \quad\text{multiply by log(y)}\\\\5=y \quad\text{take the anti-log}$

_____

You can also take the antilog first:

5y = y²

y(y -5) = 0 . . . . . subtract 5y, factor

y = 0 or 5 . . . . . y=0 is not a viable solution, so y=5.

5 0

3 years ago