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2 answers:
Answer:
x = 6 , x = 4
Step-by-step explanation:
A line parallel to a side of a triangle and intersecting the other 2 sides then divides those sides proportionally, that is
=
=
=
( cross- multiply )
3x = 18 ( divide both sides by 3 )
x = 6
(14)
=
( cross- multiply )
15(5x + 1) = 35(x + 5) ← distribute parenthesis on both sides
75x + 15 = 35x + 175 ( subtract 35x from both sides )
40x + 15 = 175 ( subtract 15 from both sides )
40x = 160 ( divide both sides by 40 )
x = 4
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Answer:
15.5 ft²
Step-by-step explanation:
The area (A) of a regular polygon is calculated as
A = pa ( p is the perimeter and a the apothem )
Here side of regular pentagon is 3 ft, thus
perimeter = 5 × 3 = 15, so
A = 0.5 × 15 × 2.06 ≈ 15.5 ft ( to the nearest tenth )
Surface area of the solid = 7.1781 in²
Volume of the solid = 0.804 in³
Explanation:
Surface area of the solid = surface area of the square prism - 2(base of the cylinder) + lateral surface of cylinder
surface area of a square prism = 2(lw + lh + wh)
l = length = 1 in
w = length = 1 in
h = height = 1 in
using the value π as it is on the calculator
Base area of a cylinder = πr²
2(Base area of cylinder) = 2πr² = 2π(0.25)² = 0.3927
Lateral surface area = 2πrh = 2π(0.25)(1) = 1.5708
Surface area of the solid = 6 - 0.3927 + 1.5708
Surface area of the solid = 7.178 in²
Volume of the solid = Volume of the square prism - volume of the cylinder
Volume of square prism = length × width × height
length = 1 in, width = 1 in, height = 1 in
Volume of the solid = 1 in × 1 in × 1 in = 1 in³
Volume of a cylinder = πr²h
Volume of the cylinder = π × 0.25 × 0.25 × 1 = 0.196
Volume of the solid = 1 - 0.196
Volume of the solid = 0.804 in³