Answer:
Step-by-step explanation:
Let s represent the son's age now. Then s+32 is the father's age. In 4 years, we have ...
5(s+4) = (s+32)+4
5s +20 = s +36 . . . . . eliminate parentheses
4s = 16 . . . . . . . . . . . . subtract s+20
s = 4
The son is now 4 years old; the father, 36.
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<em>Alternate solution</em>
In 4 years, the ratio of ages is ...
father : son = 5 : 1
The difference of their ages at that time is 5-1 = 4 "ratio units". Since the difference in ages is 32 years, each ratio unit must stand for 32/4 = 8 years. That is, the future age ratio is ...
father : son = 40 : 8
So, now (4 years earlier), the ages must be ...
father: 36; son: 4.
Answer:
x = 12
Step-by-step explanation:
First you figure out which function your going to use. I notice that from the angle we have 5 which is the opposite side and 23 which is the adjacent side. This means we have to use tangent.
Then set up your equation: tan(x)=5/23. This is because the opposite side is 5 and the adjacent is 23 and it must be set up in that order.
Next get x alone by making the equation: x=tan^-1(5/23).
Then put it into the calculator and round to get 12.
Answer:
9 and 4/5
Step-by-step explanation:
Isosceles triangle: two equal sides.
We have the following relationship:
root (32) = root (L ^ 2 + L ^ 2)
root (32) = root (2L ^ 2)
root (32) = Lraiz (2)
root (32) / root (2) = L
The surface area is:
Area of the base and top:
A1 = (1/2) * (root (32) / root (2)) * (root (32) / root (2))
A1 = (1/2) * (32/2)
A1 = (1/2) * (16)
A1 = 8
Area of the rectangles of equal sides:
A2 = (root (32) / root (2)) * (6)
A2 = 24
Rectangle area of different side:
A3 = (root (32)) * (6)
A3 = 33.9411255
The area is:
A = 2 * A1 + 2 * A2 + A3
A = 2 * (8) + 2 * (24) + (33.9411255)
A = 97.9411255
Round to the nearest tenth:
A = 97.9 cm
Answer:
The surface area of the triangular prism is:
A = 97.9 cm
