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3 years ago

15

A:Alternate interior angles

2 answers:

Liono4ka [1.6K]3 years ago

8 0

Answer:

A, Alternate interior angles.

Step-by-step explanation:

There interior angles because there inside the parallel lines and they alternate/are positioned at the inner corners of the intersection line, they lie on opposite sides of the transversal line.

PilotLPTM [1.2K]3 years ago

7 0

Answer:

Vertically angles

Step-by-step explanation:

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What is the volume of the composite figure? Explain your work. A complete answer should include how you broke up the figure, whi

Sphinxa [80]

Answer:

$15,000\:\mathrm{mm^3}$

Step-by-step explanation:

The composite figure consists of a square prism and a trapezoidal prism. By adding the volume of each, we obtain the volume of the composite figure.

The volume of the square prism is given by $V=s^2\cdot h$ , where $s$ is the base length and $h$ is the height. Substituting given values, we have: $V=14^2\cdot 30=196\cdot 30=5,880\:\mathrm{mm^3}$

The volume of a trapezoidal prism is given by $V=\frac{b_1+b_2}{2}\cdot l\cdot h$ , where $b_1$ and $b_2$ are bases of the trapezoid, $l$ is the length of the height of the trapezoid and $h$ is the height. This may look very confusing, but to break it down, we're finding the area of the trapezoid (base) and multiplying it by the height. The area of a trapezoid is given by the average of the bases ( $\frac{b_1+b_2}{2}$ ) multiplied by the trapezoid's height ( $l$ ).

Substituting given values, we get:

$V=\frac{14+24}{2}\cdot (30-14)\cdot 30,\\V=19\cdot 16\cdot 30=9,120\:\mathrm{mm^3}}$

Therefore, the total volume of the composite figure is $5,880+9,120=\boxed{15,000\:\mathrm{mm^3}}$ (ah, perfect)

Alternatively, we can break the figure into a larger square prism and a triangular prism to verify the same answer:

$V=30^2\cdot 14+\frac{1}{2}\cdot10\cdot 16\cdot 30=\boxed{15,000\:\mathrm{mm^3}}\checkmark$

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2 years ago

In how many ways can 4 boys and 4 girls be arranged in a row such that no two boys and no two girls are next to each other?(A) 1

nirvana33 [79]

Answer:

1152

Step-by-step explanation:

4 boys and 4 girls be arranged in a row such that no two boys and no two girls are next to each other.

Two boys and two girls are not next to each other. so one boy and one girl are next to each other in two ways.

BGBGBGBG, GBGBGBGB

4 boys are arranged in 4! ways and 4 girls are arranged in 4! ways

So number of ways = $2 \cdot 4! \cdot 4!=2 \cdot 24 \cdot 24=1152$

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3 years ago

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JulsSmile [24]

Answer:

C

Step-by-step explanation:

U just gotta learn the definitions

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3 years ago

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List all of the quadrilaterals with exactly one pair of parallel sides.

Leno4ka [110]

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3 years ago

70 POINTS Given the function, f (x) = 1/x-1 - 5 , choose the correct transformation.

matrenka [14]

Answer:

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Step-by-step explanation:

We are given function as

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3 years ago

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