Answer: x = 15, ∠K = 45.7°, ∠L = 45.7°, ∠M = 88.6°
<u>Step-by-step explanation:</u>
Since ∠K ≅ ∠L, then ΔKLM is an isoceles triangle with base KL
KM ≅ LM
3x + 23 = 7x - 37
23 = 4x - 37
60 = 4x
15 = x
KM = LM = 3x + 23
= 3(15) + 23
= 45 + 23
= 68
KL = 9x - 40
= 9(15) - 40
= 135 - 40
= 95
Next, draw a perpendicular bisector KN from K to KL. Thus, N is the midpoint of KL and ΔMNL is a right triangle.
- Since N is the midpoint of KL and KL = 95, then NL = 47.5
- Since ∠N is 90°, then NL is adjacent to ∠l and ML is the hypotenuse
Use trig to solve for ∠L (which equals ∠K):
cos ∠L = 
cos ∠L = 
∠L = cos⁻¹ 
∠L = 45.7
Triangle sum Theorem:
∠K + ∠L + ∠M = 180°
45.7 + 45.7 + ∠M = 180
91.4 + ∠M = 180
∠M = 88.6
Answer:

Step-by-step explanation:
For this case we can use the formula for the future value with compound interest given by:
(1)
For this case since the interest is compounded quarterly we have 3 periods each year, since we have 3 quarters in a year.
r represent the rate =0.026
t = 6 represent the number of years
P = 3200 represent the amount invested at the begin
If we apply the formula (1) we got:

So then the balance after 6 years would be approximately 50995 with the conditions provided.
Answer:
6
Step-by-step explanation:
You have 2 conditions.
1. The digits must be different.
2. The digits must add to 7.
There aren't very many
124
142
214
241
412
421
That's it. That's your answer. There are 6 of them