Answer:
- area ≈ 59.441 in²
- lateral area ≈ 352.671 in²
- surface area ≈ 471.553 in²
Step-by-step explanation:
1. The area of the regular polygon base of the prism can be found from the formula ...
A = (nr²/2)sin(360°/n) . . . . where r is the radius and n is the number of sides
Filling in the numbers and doing the arithmetic gives ...
A = (5·5²/2)sin(72°) ≈ 59.441 . . . square inches
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2. The lateral area is the product of the height and the perimeter. The perimeter of the regular polygon can be found from ...
P = 2nr·sin(180°/n) = 50sin(36°) ≈ 29.389 . . . inches
Then the lateral area is ...
LA = Ph = (29.389 in)(12 in) = 352.671 in²
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3. The total area is the area of the two bases together with the lateral area:
S = 2·(base area) + (lateral area) = 2(59.441 in²) + 352.671 in²
S = 471.553 in²
Answer:
y<6
Step-by-step explanation:
1
/3
y + 1/4 > 3
/8y
1
/3
y + 1/4 − 3/
8
y >
3/
8
y − 3/
8
y
− 1
/24
y + 1
4 > 0
−1
/24
y + 1
/4 − 1/
4 > 0 − 1
/4
−1
/24
y > −1/
4
Multiply both sides by 24/(-1).
y<6
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Answer:
4x + 19 = -21
Step-by-step explanation:
4(-10) + 19 = -21
-40 + 19 = -21
17)
x² + 8 = -8
x² = -8 - 8
x² = 16
x = ±√-16
x = ±√16i
x = <span>±4i
</span>
18)
x² + 5 = -3
x² = -3 - 5
x² = -8
x = ±√-8
x = ±√8i
x = ±2√2i
19)
x² + 3 = 0
x² = -3
x = ±√-3
x = <span>±</span>√3i
hope this helps, God bless!
