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Andre45 [30]
3 years ago
5

The front face of a laundry basket is in the shape of a trapezoid as shown. A trapezoid has a base of 24 inches, height of 12 in

ches, and top side length of 20 inches. What is the area of the front face of the laundry basket? 252 square inches 264 square inches 288 square inches 336 square inches
Mathematics
2 answers:
Sonbull [250]3 years ago
8 0

Answer:

B or 264

Step-by-step explanation:

Y_Kistochka [10]3 years ago
7 0

Answer:

264 in²

Step-by-step explanation:

Parameters given:

Base, b = 24 inches

Height, h = 12 inches

Top side length, a = 20 inches

We are told that the front face of the basket is in the shape of a trapezoid.

The area of a trapezoid is:

A = ½ * (a + b) * h

The area of the front face of the basket is:

A = ½ * (20 + 24) * 12

A = ½ * 44 * 12

A = 264 in²

The area of the front face of the basket is 264 in².

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Csc (2sin^-1(-12/13))<br> that is 2 times inverse sin of -12/13
german
Answer: -\frac{169}{120}

I'm assuming you mean this:

cosec(2sin^{-1}(\frac{-12}{13}))

Recall what the cosecant function represents. It is the reciprocal of a sine function, and is often written in this form:

\frac{1}{sinx}

So, using the sine relationship:

cosec(2sin^{-1}(\frac{-12}{13})) = \frac{1}{sin(2sin^{-1}(\frac{-12}{13}))}

Let u = sin^{-1}(\frac{-12}{13})
cosec(2sin^{-1}(\frac{-12}{13})) = \frac{1}{sin(2u)}
= \frac{1}{2sinu \cdot cosu}
= \frac{1}{2sin(sin^{-1}(\frac{-12}{13})) \cdot cos(sin^{-1}(\frac{-12}{13}))}
= \frac{1}{\frac{-24}{13} \cdot \sqrt{1 - (\frac{-12}{13})^{2}}}
= \frac{1}{\frac{-24}{13}} \cdot \frac{1}{\sqrt{1 - \frac{144}{169}}}
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