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vredina [299]
3 years ago
5

You work for a company that produces custom picture frames. A new customer needs to frame a piece of rectangular artwork with di

mensions of 11 x 15 in. They don't want the framed art to be too big so they want to limit its area to 320 inches ^ 2. What should the width of the frame be to accommodate their wishes?
1) None of the choices are correct.

2) x² + 16 =800

3) x² + 8x + 16 = 800

4) x² 16x + 64 = 800
Mathematics
1 answer:
miskamm [114]3 years ago
4 0

Answer:

None of the choices are correct.

Step-by-step explanation:

Let x be the width of the frame,

The framed art cannot me more than 320 square inches

(11 + 2x) \times (15+2x) \leq 320

(165 +30x +22x +4x^2 ) \leq 320

4x^2+52x + 165 \leq 320

4x^2 +52x + 165-320 \leq 0

4x^2 +52x - 155\leq 0

By using the quadratic formula

x = \frac{-b\pm \sqrt{(b^2-4ac)}}{2a}

x = \frac{-52\pm \sqrt{(52^2-4(4)(-155))}}{2(4)}

x = \frac{-52\pm \sqrt{(2704+2480)}}{2(4)}

x = \frac{-52\pm \sqrt{(5184)}}{2(4)}

x = \frac{-52\pm 72}{2(4)}

x = \frac{20}{8}

x= \frac{5}{2}

x = 2.5

Frame must not be more than 2.5 inches wide.

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