Acute angles are angles that measure below 90°, meaning below a right angle.
Initially, Charlotte owes $7680. She finishes her payments after a total of 6 + 36 = 42 months. Using a simple compounding formula, the amount she owes is worth P at the end of 42 months, where P is:
P = 7680 * (1 + .2045/12)^42 = 15616.67379
Now, the first installment she pays (at the end of six months) is paid 35 months in advance of the end, so it is worth x * (1 + .2375/12)^35 at the end of her loan period.
Similarly, the second installment is worth x * (1 + .2375/12)^34 at the end of the loan period.
Continuing, this way, the last installment is worth exactly x at the end of the loan period.
So, the total amount she paid equals:
x [(1 + .2375/12)^35 + (1 + .2375/12)^34 + ... + (1 + .2375/12)^0]
To calculate this, assume that 1+.2045/12 = a. Then the amount Charlotte pays is:
x (a^35 + a^34 + ... + a^0) = x (a^36 - 1)/(a - 1)
Clearly, this value must equal P, so we have:
x (a^36 - 1)/(a - 1) = P = 15616.67379
Substituting, a = 1 + .2045/12 and solving, we get
x = 317.82
There are many ways to solve this. I think the easiest way for this one is to add the equations up.
The you solve that, now that y is gone. You get x=2.
Now plug in x into one of the original equations.
Finish solving, and you get y=8.
The answer is (2,8)
Answer:
Step-by-step explanation:
angle 4 is congruent to angle 4 because they are alternate interior angles.
angle 5 is congruent to angle 3 because they are alternate interior angles.
angle 1+angle 2+angle 3 is equal to (=) angle 1+angle 2+angle 3
angle 1+angle 2+angle 3=180 degree(being sum of interior angles of a trianngle)
