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Mathematics

1 answer:

Arlecino [84]2 years ago

7 0

Answer = 504 m2
Proof is below

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If line t is a transversal of lines l and m, name the angle relationship of the given angle pairs.

Ghella [55]

Answer:

$\angle 1\ and\ \angle 3$ are corresponding angles and are congruent to each other.

$\angle 8\ and\ \angle 4$ are alternate exterior angles and thus congruent to each other.

$\angle 2\ and\ \angle 3$ are interior angles on the same side, and they are supplementary(sum=180°).

Step-by-step explanation:

Given:

Line $l\parallel m$

Line $t$ is traversal.

By angle properties we can name the angle relationship of given angle pairs.

$\angle 1\ and\ \angle 3$ are corresponding angles and are congruent to each other.

$\angle 8\ and\ \angle 4$ are alternate exterior angles and thus congruent to each other.

$\angle 2\ and\ \angle 3$ are interior angles on the same side, and thus they are supplementary.

8 0

3 years ago

The base of a trapezoid are 24 feet and 16 feet. The height of the trapezoid is 12 feet. what is the area of the trapezoid?

kobusy [5.1K]

Answer:

240 ft^2

Step-by-step explanation:

area: (24+16)12/2=240 ft^2

(the area of a trapezoid is the sum of the bases multiplied by the height over 2.)

4 0

3 years ago

Find all solutions to the equation.<br><br> 7 sin2x - 14 sin x + 2 = -5

cestrela7 [59]

$\bf 7sin^2(x)-14sin(x)+2=-5\implies 7sin^2(x)-14sin(x)+7=0 \\\\\\ \stackrel{\textit{notice, this is just }ax^2+bx+c}{\stackrel{\stackrel{ax^2}{\downarrow }}{sin^2(x)}\stackrel{\stackrel{bx}{\downarrow }}{-2sin(x)}\stackrel{\stackrel{c}{\downarrow }}{+1}}=0\implies [sin(x)-1][sin(x)-1]=0 \\\\\\ sin(x)-1=0\implies sin(x)=1\implies \measuredangle x=sin^{-1}(1)\implies \measuredangle x=\cfrac{\pi }{2} \\\\\\ ~~~~~~~~~~~~~~\stackrel{\textit{and for all solutions using }n \in \mathbb{Z}}{\cfrac{\pi }{2}+2\pi n}$