Answer:
x = 15
Step-by-step explanation:
Assuming 3x and x-60 are in degrees, you can use:
cos(a) = sin(a+90)
To rewrite the equation as:
sin(3x) = sin(x-60+90)
sin(3x) = sin(x+30)
3x = x+30
2x = 30
x = 15
But, solving 3x = x+30 which simplifies to x=15 is not the only solution to this equation, as you can see in below picture. Finding all solutions is a bit more work, but maybe that is not required in your case.
ANSWER
10 weeks, $310
EXPLANATION
We have a system of linear equations as both equations need to be satisfied by the same ordered pair (x,y):
y = 25x + 60
y = 30x + 10
We can solve this by substitution. Since y is equal to 25x+60, we can substitute in 25x + 60 for y in the equation y=30x+10
y = 30x + 10
25x + 60 = 30x + 10
Subtract 25x from both sides
60 = 5x + 10
Subtract 10 from both sides and then divide both sides by 5
50 = 5x
x = 10
x represents time in weeks, so 10 weeks.
Find y, the amount of money, by substituting x=10 into either equation.
If we use y = 30x + 10, then
y = 30x + 10
y = 30(10) + 10
y = 300 + 10
y = 310
y = 310 implies $310 so the answer is 10 weeks, $310.
Answer:
x = 6
Step-by-step explanation:
2/(x-2) = 5/(4+x) - set up the ratios of similar sides
2(4 + x) = 5(x - 2) - cross multiply to solve
8 + 2x = 5x - 10 - simplify
18 = 3x - simplify to get x on one side of the equation
6 = x - divide both sides of the equation by 3 to isolate x
The measure of angle EAC is equivalent to 50 degrees.
