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earnstyle [38]
4 years ago
6

Find the volume of the rectangular prism. IN in. 4 in. 9-in. 2 I

Mathematics
1 answer:
prisoha [69]4 years ago
6 0

Answer:

V = 36 in³

Step-by-step explanation:

The volume of a rectangular prism is given by the formula V = l × w × h

Here our length is 9\frac{1}{2}, our width is 4, and our height is 4\frac{1}{2}

Plugging in these values to our formula give us V=(9\frac{1}{2})(4)(4\frac{1}{2})= 36

V = 36 in³

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we know the segment QP is an angle bisector, namely it divides ∡SQR into two equal angles, thus ∡1 = ∡2, and ∡SQR = ∡1 + ∡2.

\bf \begin{cases} \measuredangle SQR = \measuredangle 1 + \measuredangle 2\\\\ \measuredangle 2 = \measuredangle 1 = 5x-7 \end{cases}\qquad \qquad \stackrel{\measuredangle SQR}{7x+13} = (\stackrel{\measuredangle 1}{5x-7})+(\stackrel{\measuredangle 2}{5x-7}) \\\\\\ 7x+13 = 10x-14\implies 13=3x-14\implies 27=3x \\\\\\ \cfrac{27}{3}=x\implies 9=x \\\\[-0.35em] ~\dotfill\\\\ \measuredangle SQR = 7(9)+13\implies \measuredangle SQR = 76

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