<img src="https://tex.z-dn.net/?f=1%2F2x%5E3%20%2B%20x%20-7%20%3D%20-3%5Csqrt%7Bx%7D%20%20-1" id="TexFormula1" title="1/2x^3 + x

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3 years ago

10

-7 = -3\sqrt{x} -1" alt="1/2x^3 + x -7 = -3\sqrt{x} -1" align="absmiddle" class="latex-formula">
what is the value of x?
A. 13/8
B. 15/8
C.27/16
D. 25/16

1 answer:

Margaret [11]3 years ago

5 0

Answer:

none of the above

Step-by-step explanation:

The problem as written cannot have any of the solutions offered.

For any of those choices, the right side expression will be irrational. The left side expression will be rational for any rational value of x, so cannot be equal to the right-side expression.

The solution is an irrational number near ...

x ≈ 1.33682898582

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Part 1) The shape is a trapezoid

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Part 3) The area is $937.5\ units^2$

Step-by-step explanation:

step 1

Plot the figure to better understand the problem

we have

A(-28,2),B(-21,-22),C(27,-8),D(-4,9)

using a graphing tool

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see the attached figure

step 2

Find the perimeter

we know that

The perimeter of the trapezoid is equal to

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$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

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A(-28,2),B(-21,-22)

substitute in the formula

$d=\sqrt{(-22-2)^{2}+(-21+28)^{2}}$

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substitute in the formula

$d=\sqrt{(-8+22)^{2}+(27+21)^{2}}$

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C(27,-8),D(-4,9)

substitute in the formula

$d=\sqrt{(9+8)^{2}+(-4-27)^{2}}$

$d=\sqrt{(17)^{2}+(-31)^{2}}$

$d=\sqrt{1,250}$

$d_C_D=25\sqrt{2}\ units$

Find the distance AD

we have

A(-28,2),D(-4,9)

substitute in the formula

$d=\sqrt{(9-2)^{2}+(-4+28)^{2}}$

$d=\sqrt{(7)^{2}+(24)^{2}}$

$d=\sqrt{625}$

$d_A_D=25\ units$

Find the perimeter

$P=25+50+25\sqrt{2}+25$

$P=(100+25\sqrt{2})\ units$

simplify

$P=25(4+\sqrt{2})\ units$ ----> exact value

$P=135.4\ units$

therefore

The perimeter is $25(4+\sqrt{2})\ units$ or approximately $135.4\ units$

step 3

Find the area

The area of trapezoid is equal to

$A=\frac{1}{2}[BC+AD]AB$

substitute the given values

$A=\frac{1}{2}[50+25]25=937.5\ units^2$

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