Express using algebra:

Can someone help me ? Finding angle measures using triangles (veiw image)

adoni [48]

Answer:

x=52°

Step-by-step explanation:

Corresponding angles, 62° is parallel to I

so the letter I would be 62°.

In a triangle there's 180 degrees

so 180-62=118°-66=52°

that way all the angles in the triangle will add up to 180

4 0

3 years ago

A helicopter is 19 meters above the top of a canyon wall Is it goes up five meters what is the new position of the helicopter re

Orlov [11]

19 + 5 equals 23 mm 19 + 5 equals 23 m

4 0

3 years ago

Add 5/6 + 2 3/4 in the simplest form.

kogti [31]

Answer:

3 7/12

Step-by-step explanation:

3 0

4 years ago

A sanitary landfill has available space of 16.2 ha at an average depth of 10 m. Seven hundred sixty-five (765) cubic meters of s

AfilCa [17]

Answer:

16.3 years

Step-by-step explanation:

1 ha = 10,000 m^2

The total capacity of the landfill is:

$C = 16.2*10,000*10 = 1,620,000\ m^3$

If waste is compacted to twice its delivered density, its volume is half of the delivered volume. Assuming that a year has 52 weeks, the volume of compacted solid waste dumped per year is:

$V=52*(5*0.5*765)\\V=99,450\ m^3$

The expected life of the landfill is given by its capacity divided by the yearly volume:

$L=\frac{C}{V}=\frac{1,620,000}{99,450} \\L=16,3\ years$

The landfill has an expected life of 16.3 years.

6 0

3 years ago

<img src="https://tex.z-dn.net/?f=cos%20%5B%20arctan%28%5Cfrac%7B12%7D%7B5%7D%29%20-%20arcsin%20%28%5Cfrac%7B-3%7D%7B5%7D%29%5D"

qwelly [4]

Answer: -16/65

Step-by-step explanation:

Drawing the right triangle (as attached) gives us that $\arctan \left(\frac{12}{5} \right)=\arcsin \left(\frac{12}{13} \right)$

Also, $-\arcsin \left(-\frac{3}{5} \right)=\arcsin \left(\frac{3}{5} \right)$

This means our original expression is equal to:

$\cos \left[\arcsin \left(\frac{12}{13} \right)+\arcsin \left(\frac{3}{5} \right) \right]$

Using the cosine addition formula, which states $\cos(a+b)=\cos a \cos b-\sin a \sin b$ , we get this itself is equal to:

$\cos \left(\arcsin \left(\frac{12}{13} \right) \right)\cos \left(\arcsin \left(\frac{3}{5} \right)\right)-\sin \left(\arcsin \left(\frac{12}{13} \right) \right)\sin \left(\arcsin \left(\frac{3}{5} \right)\right)$

Since $\sin^{2} \theta+\cos^{2} \theta=1$ , we know that:

$\sin^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)+\cos^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)=1\\\\\frac{144}{169} +\cos^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)=1\\\\cos^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)=\frac{25}{169}\\\\cos \left(\arcsin \left(\frac{12}{13} \right)\right)=\frac{5}{13}$

Similarly, cos(arcsin(3/5))=4/5.

This means the given expression is equal to:

$\left(\frac{5}{13} \right) \left(\frac{4}{5} \right)-\left(\frac{12}{13} \right) \left(\frac{3}{5} \right)\\\\\frac{20}{65}-\frac{36}{65}=\boxed{-\frac{16}{65}}$

3 0

2 years ago