We will call:
M=Mari
J=Jen
Initial equations:
M=2J
M+J=480
(the fact that they work 20 hours a week is not needed in this problem information)
Plug in:
2J+J=480
3J=480
J=160
Jen makes $160 a week.
Therefore:
M=2J
M=2(160)
M=320
Mari makes $320 per week
Jen makes $160 per week
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<em>"Associate with people who are likely to improve you."</em>
<span>In mathematics, polygons are similar if their corresponding angles are congruent and the ratio of their corresponding sides are in proportion.</span>
<span>Once we know that triangles (or any polygons) are similar, we also know some additional facts about the figures.</span>
Answer:
n = π/6, π/4, 3π/4, 5π/6
Step-by-step explanation:
sin(3n) − sin n = cos(2n)
Use double and triple angle formulas:
(3 sin n − 4 sin³ n) − sin n = 1 − 2 sin² n
2 sin n − 4 sin³ n = 1 − 2 sin² n
4 sin³ n − 2 sin² n − 2 sin n + 1 = 0
Factor by grouping:
2 sin² n (2 sin n − 1) − (2 sin n − 1) = 0
(2 sin² n − 1) (2 sin n − 1) = 0
Solve:
2 sin² n − 1 = 0
2 sin² n = 1
sin² n = 1/2
sin n = √2/2
n = π/4, 3π/4
2 sin n − 1 = 0
2 sin n = 1
sin n = 1/2
n = π/6, 5π/6
6% of $32,345 is $1,940.70, your decimal point is off by 1 place :)
