a. Answer The required area of the existing patio is 600 square feet. Explanation Given information: The amount of area to the area of the patio by expanding the existing patio = 464 square feet Calculation: The area of the existing patio is: A old = 30 ⋅ 20 = 600 Hence, the required area of the existing patio is 600 square feet. b. To determine To write: An equation to model the area of the new patio. Answer The required equation is x 2 + 50 x − 464 = 0 . Explanation Given information: The amount of area to the area of the patio by expanding the existing patio = 464 square feet Calculation: The area of the existing patio is: A old = 30 ⋅ 20 = 600 The given difference between the area of the extended area A new and the existing patio is 464 square feet that is, A new − A old = 464 ( 30 + x ) ( 20 + x ) − 600 = 464 x 2 + 30 x + 20 x + 600 − 600 = 464 x 2 + 50 x − 464 = 0 Hence, the required equation is x 2 + 50 x − 464 = 0 . c. To determine To calculate: The distance x for which the length of the patio should be expanded. Answer The required distance x for which the length of the patio should be expanded is 8 feet. Explanation Given information: The amount of area to the area of the patio by expanding the existing patio = 464 square feet Formula used: Quadratic formula : x = − b ± b 2 − 4 a c 2 a Calculation: The area of the existing patio is: A old = 30 ⋅ 20 = 600 The given difference between the area of the extended area A new and the existing patio is 464 square feet that is, A new − A old = 464 ( 30 + x ) ( 20 + x ) − 600 = 464 x 2 + 30 x + 20 x + 600 − 600 = 464 x 2 + 50 x − 464 = 0 Solve the above equation for x by using the quadratic formula x = − b ± b 2 − 4 a c 2 a . x = − ( 50 ) ± 50 2 − 4 ( 1 ) ( − 464 ) 2 ( 1 ) x = − 50 ± 4356 2 x = − 50 ± 66 2 Solve for x . x = − 50 + 66 2 x = 16 2 x = 8 And, x = − 50 − 66 2 x = − 116 2 x = − 58 But the distance cannot be negative. So, x = 8 Hence, the required distance x for which the length of the patio should be expanded is 8 feet.

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

1st Edition

ISBN: 9781680331165

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Chapter 3.3, Problem 16Q

To determine

To calculate: The area of the existing patio.

Expert Solution

Answer to Problem 16Q

The required area of the existing patio is 600 square feet.

Explanation of Solution

Given information:

The amount of area to the area of the patio by expanding the existing patio = 464 square feet

Calculation:

The area of the existing patio is:

Aold=30⋅20=600

Hence, the required area of the existing patio is 600 square feet.

To determine

To write: An equation to model the area of the new patio.

Expert Solution

Answer to Problem 16Q

The required equation is x2+50x−464=0 .

Explanation of Solution

Given information:

The amount of area to the area of the patio by expanding the existing patio = 464 square feet

Calculation:

The area of the existing patio is:

Aold=30⋅20=600

The given difference between the area of the extended area Anew and the existing patio is 464 square feet that is,

Anew−Aold=464(30+x)(20+x)−600=464x2+30x+20x+600−600=464x2+50x−464=0

Hence, the required equation is x2+50x−464=0 .

To determine

To calculate: The distance x for which the length of the patio should be expanded.

Expert Solution

Answer to Problem 16Q

The required distance x for which the length of the patio should be expanded is 8 feet.

Explanation of Solution

Given information:

The amount of area to the area of the patio by expanding the existing patio = 464 square feet

Formula used:

Quadratic formula:

x=−b±b2−4ac2a

Calculation:

The area of the existing patio is:

Aold=30⋅20=600

The given difference between the area of the extended area Anew and the existing patio is 464 square feet that is,

Anew−Aold=464(30+x)(20+x)−600=464x2+30x+20x+600−600=464x2+50x−464=0

Solve the above equation for x by using the quadratic formula x=−b±b2−4ac2a .

x=−(50)±502−4(1)(−464)2(1)x=−50±43562x=−50±662

Solve for x .

x=−50+662x=162x=8

And, x=−50−662x=−1162x=−58

But the distance cannot be negative.

So, x=8

Hence, the required distance x for which the length of the patio should be expanded is 8 feet.

Chapter 3.3, Problem 15Q

Chapter 3.3, Problem 17Q

Chapter 3 Solutions

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

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