If cos(2/3(x) + 20) ° = sin(2x – 10)”, find the acute angles of the corresponding right triangle.

recall that

sin(x) = cos(90-x)

therefore

cos((2/3)x + 20) = cos(90 - [2x - 10])

(2/3)x + 20 = 100 - 2x

2x + (2/3)x = 120

x + (1/3)x = 60

(4/3)x =60

4x = 60*3

4x = 180

x = 45

since it is a right angled triangle, the angles are 45, 45 and 90

A=40 B=50

I just took the test

shell's the art director at her local community center. she paid $10 and for each child that attends she earns $4.

for each child she ears $4 that is the slope m = 4

she paid $10, that is the initial amount paid. so 10 is the y intercept b

m =4   and b = 10

y intercept is 10 so the point is (0,10)

we start graph from y intercept (0,10)

slope = 4 . we know slope = rise / run

slope = 4   or 4/1   are same

rise = 4   and run = 1

for rise we move 4 units up and for run we move 1 unit to the right

the graph is attached below

x axis is the number of child she attends

y axis is the amount   she earns