The length of each side of the square is 3 ft.
<u>Step-by-step explanation:</u>
We have , A composite figure is formed by combining a square and a triangle. Its total area is 52.5 ft. The area of the triangle is 43.5 ft . We know that area of a square = . According to question:
area of square =
area of triangle = 43.5 ft
total area = 52.5 ft.
Total area = area(square+triangle)
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Therefore, the length of each side of the square is 3 ft.
Answer:
a) a +8a +3a = 180°
b) 15°, 45°, 120°
c) see attached
Step-by-step explanation:
<h3>a)</h3>Let 'a' represent the measure of the smallest angle. The largest angle is 8a, and the middle angle is 3a. The sum of angles, as always, is 180°.
a +8a +3a = 180° . . . . . . equation modeling the relationship
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<h3>b)</h3>12a = 180° . . . . . . collect terms
a = 15° . . . . . . . divide by 12
3a = 3×15° = 45°
8a = 8×15° = 120°
The angle measures are 15°, 45°, and 120°.
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<h3>c)</h3>see attached. We have arbitrarily let the shortest side be 10 units.
Answer: nickels = 13, dimes = 7, quarters = 14
<u>Step-by-step explanation:</u>
First, set up the equations for each coin:
Next, the sum of the coins is $4.85 so substitute and solve for the variable:
Nickels + Dimes + Quarters = Sum
(0.30 + 0.05d) + 0.10d + 0.50d = 4.85
0.30 + 0.65d = 4.85
0.65d = 4.55
d = 7
Lastly, plug the d-value into the quantity equation for the nickels and quarters to find their quantity.
nickels: 6 + d = 6 + (7) = 13
quarters: 2d = 2(7) = 14