CalTheGreat

hint: cross multiply to get: (x+5)^2=2x(x+4)

-2/-9=x/14

2/9=x/14 (\(\frac{2}{9}=\frac{x}{14}\))

cross multiply to get: 9x=28

x=28/9

sqrt(4761) = 69.

recheck: 69*69=sqrt(4761)

hints: 

AE: sin 45 degrees = AE/1

CE: cos 45 degrees = CE/1

using the fact that:

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

easy way to remember sin, cos, & tan: sohcahtoa

hope this helped.

-c

right, thank u! :]

adding onto geno, i'm going to explain the difference

negative number raised without parenthesis: you will calculate the expression WITHOUT including the negative (for example, if it was -5^4, do 5^4 first before adding the negative) and then add the negative sign to your answer. so, you would do 5*5*5*5*-1 to get -625

negative number raised with parenthesis: you will calculate the expression using -5*-5*-5*-5 to get 625.  

apologize that the explanation is kind of messy. feel free to let me know if you have any other questions or concerns :] 

5 cos θ = 3

cos θ = 3/5

arccos 3/5 = θ

θ = 53.13 degrees

if the answer should be in radians, you can simply follow my steps but use the radians instead (for calculator use) 

24*-8=-192

right, sorry my bad.

i did that wrong, the correct answer should be (3, -1/2). please ignore my first answer

Find the distances between the x's and y's, then divide by two to find the midpoint.

(-2-8)/2=-5

(-2-1)/2=-3/2

(-5, -3/2)