Answer:
D-70
Step-by-step explanation:
It is a combination C(8,4)
Answer:
x = 8
y = 21
Step-by-step explanation:
(7x + 12)° and (12x - 28)° are alternate interior angles. Alternate interior angles are congruent. Therefore:
(7x + 12)° = (12x - 28)°
Solve for x
7x + 12 = 12x - 28
Collect like terms
7x - 12x = - 12 - 28
-5x = -40
Divide both sides by -5
-5x/-5 = -40/-5
x = 8
(12x - 28)° + (9y - 77)° = 180° (linear pair)
To find y, plug in the value for x = 8.
12(8) - 28 + 9y - 77 = 180
96 - 28 + 9y - 77 = 180
Combine like terms
- 9 + 9y = 180
Add 9 to both sides
-9 + 9y + 9 = 180 + 9
9y = 189
Divide both sides by 9
9y/9 = 189/9
y = 21
Answer:
<u>The lowest height at which the two stacks will be the same height is 24 inches.</u>
Step-by-step explanation:
For answering this problem, we have to find out the lowest common multiple of 6 and 8, listing its prime factors, this way:
6 = 3 * 2
8 = 2 * 2 * 2
Now, we multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.
Therefore, we have:
2 : 3 times as prime factor of 8
3: 1 time as prime factor of 6
The lowest common multiple is:
2 * 2 * 2 * 3 = 24
<u>The lowest height at which the two stacks will be the same height is 24 inches.</u>
Answer: Area of the polygon is 43.31 cm^2 t
Step-by-step explanation:
The polygon show in the diagram is a hexagon. It has six sides, since it is a regular hexagon, all the six sides are equal.
From the information given, the apotherm = 5√3
The apotherm is the perpendicular distance from the center of one side of the polygon to the center of the polygon. To determine the area of the polygon,
Area of polygon
=area = a^2n ×tan 180/n
Area = (5√3)^2 tan(180/6)
Area = 5^2×(√3)^2 × tan30
Area = 25×3×0.5774
Area = 43.305
Approximately 43.31 cm^2 to the nearest tenth
Answer:
13
Step-by-step explanation:
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