High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
15th Edition
ISBN: 9780133281149
Author: Prentice Hall
Publisher: Prentice Hall
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Chapter 9.2, Problem 27PPE
To determine

The width that gives the maximum area, the maximum area and range of the function.

Expert Solution & Answer
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Answer to Problem 27PPE

  The maximum point (Vertex)is (25,625).

Maximum area = 625 ft.

Range of the function: 0A625

Explanation of Solution

Given:

You have 100 ft of string to rope off a rectangular section for a bake sale at school fair.

Function that gives the area of the section in square feet, where x is width in feet is:

  A=x2+50x

Calculation:

Compare the given function with y=ax2+bx+c .

  here;a=1b=50c=0

As the coefficient of x2 is negative, the parabola will open downwards. The vertex will be the maximum point.

  Equation of axis of symmetry is:x=b2a

Therefore, the axis of symmetry is:

  x=b2ax=(50)2(1)x=25

The x-coordinate of the given function is x=25 . Now, the A-coordinate will be:

  A=x2+50xA=(25)2+50(25)A=625So, the maximum point (Vertex)is (25,625).

The rope will reach maximum area i.e. 625 feet when the width is 25 ft.

The graph will be:

  High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9, Chapter 9.2, Problem 27PPE

The range of the function will be:

  0A625

Chapter 9 Solutions

High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9

Ch. 9.1 - Prob. 6LCCh. 9.1 - Prob. 7PPECh. 9.1 - Prob. 8PPECh. 9.1 - Prob. 9PPECh. 9.1 - Prob. 10PPECh. 9.1 - Prob. 11PPECh. 9.1 - Prob. 12PPECh. 9.1 - Prob. 13PPECh. 9.1 - Prob. 14PPECh. 9.1 - Prob. 15PPECh. 9.1 - Prob. 16PPECh. 9.1 - Prob. 17PPECh. 9.1 - Prob. 18PPECh. 9.1 - Prob. 19PPECh. 9.1 - Prob. 20PPECh. 9.1 - Prob. 21PPECh. 9.1 - Prob. 22PPECh. 9.1 - Prob. 23PPECh. 9.1 - Prob. 24PPECh. 9.1 - Prob. 25PPECh. 9.1 - Prob. 26PPECh. 9.1 - Prob. 27PPECh. 9.1 - Prob. 28PPECh. 9.1 - Prob. 29PPECh. 9.1 - Prob. 30PPECh. 9.1 - Prob. 31PPECh. 9.1 - Prob. 32PPECh. 9.1 - Prob. 33PPECh. 9.1 - Prob. 34PPECh. 9.1 - Prob. 35PPECh. 9.1 - Prob. 36PPECh. 9.1 - Prob. 37PPECh. 9.1 - Prob. 38PPECh. 9.1 - Prob. 39PPECh. 9.1 - Prob. 40PPECh. 9.1 - Prob. 41PPECh. 9.1 - Prob. 42PPECh. 9.1 - Prob. 43PPECh. 9.1 - Prob. 44PPECh. 9.1 - Prob. 45PPECh. 9.1 - Prob. 46PPECh. 9.1 - Prob. 47PPECh. 9.1 - Prob. 48PPECh. 9.1 - Prob. 49PPECh. 9.1 - Prob. 50STPCh. 9.1 - Prob. 51STPCh. 9.1 - Prob. 52STPCh. 9.1 - Prob. 53STPCh. 9.1 - Prob. 54STPCh. 9.1 - Prob. 55MRCh. 9.1 - Prob. 56MRCh. 9.1 - Prob. 57MRCh. 9.1 - Prob. 58MRCh. 9.1 - Prob. 59MRCh. 9.1 - Prob. 60MRCh. 9.1 - Prob. 61MRCh. 9.1 - Prob. 62MRCh. 9.1 - Prob. 63MRCh. 9.2 - Prob. 1PCh. 9.2 - Prob. 2PCh. 9.2 - Prob. 1LCCh. 9.2 - Prob. 2LCCh. 9.2 - Prob. 3LCCh. 9.2 - Prob. 4LCCh. 9.2 - Prob. 5LCCh. 9.2 - Prob. 6LCCh. 9.2 - Prob. 7PPECh. 9.2 - Prob. 8PPECh. 9.2 - Prob. 9PPECh. 9.2 - Prob. 10PPECh. 9.2 - Prob. 11PPECh. 9.2 - Prob. 12PPECh. 9.2 - Prob. 13PPECh. 9.2 - Prob. 14PPECh. 9.2 - Prob. 15PPECh. 9.2 - Prob. 16PPECh. 9.2 - Prob. 17PPECh. 9.2 - Prob. 18PPECh. 9.2 - Prob. 19PPECh. 9.2 - Prob. 20PPECh. 9.2 - Prob. 21PPECh. 9.2 - Prob. 22PPECh. 9.2 - Prob. 23PPECh. 9.2 - Prob. 24PPECh. 9.2 - Prob. 25PPECh. 9.2 - Prob. 26PPECh. 9.2 - Prob. 27PPECh. 9.2 - Prob. 28PPECh. 9.2 - Prob. 29PPECh. 9.2 - Prob. 30PPECh. 9.2 - Prob. 31PPECh. 9.2 - Prob. 32PPECh. 9.2 - Prob. 33PPECh. 9.2 - Prob. 34PPECh. 9.2 - Prob. 35PPECh. 9.2 - Prob. 36PPECh. 9.2 - Prob. 1MRCh. 9.2 - Prob. 6CBCh. 9.2 - Prob. 7CBCh. 9.2 - Prob. 8CBCh. 9.2 - Prob. 9CBCh. 9.2 - Prob. 15CBCh. 9.2 - Prob. 16CBCh. 9.2 - Prob. 17CBCh. 9.2 - Prob. 18CBCh. 9.3 - Prob. 1PCh. 9.3 - Prob. 2PCh. 9.3 - Prob. 3PCh. 9.3 - Prob. 1LCCh. 9.3 - Prob. 2LCCh. 9.3 - Prob. 3LCCh. 9.3 - Prob. 4LCCh. 9.3 - Prob. 5LCCh. 9.3 - Prob. 6LCCh. 9.3 - Prob. 7LCCh. 9.3 - Prob. 8PPECh. 9.3 - Prob. 9PPECh. 9.3 - Prob. 10PPECh. 9.3 - Prob. 11PPECh. 9.3 - Prob. 12PPECh. 9.3 - Prob. 13PPECh. 9.3 - Prob. 14PPECh. 9.3 - Prob. 15PPECh. 9.3 - Prob. 16PPECh. 9.3 - Prob. 17PPECh. 9.3 - Prob. 18PPECh. 9.3 - Prob. 19PPECh. 9.3 - Prob. 20PPECh. 9.3 - Prob. 21PPECh. 9.3 - Prob. 22PPECh. 9.3 - Prob. 23PPECh. 9.3 - Prob. 24PPECh. 9.3 - Prob. 25PPECh. 9.3 - Prob. 26PPECh. 9.3 - Prob. 27PPECh. 9.3 - Prob. 28PPECh. 9.3 - Prob. 29PPECh. 9.3 - Prob. 30PPECh. 9.3 - Prob. 31PPECh. 9.3 - Prob. 32PPECh. 9.3 - Prob. 33PPECh. 9.3 - Prob. 34PPECh. 9.3 - Prob. 35PPECh. 9.3 - Prob. 36PPECh. 9.3 - Prob. 37PPECh. 9.3 - Prob. 38PPECh. 9.3 - Prob. 39PPECh. 9.3 - Prob. 40PPECh. 9.3 - Prob. 41PPECh. 9.3 - Prob. 42PPECh. 9.3 - Prob. 43PPECh. 9.3 - Prob. 44PPECh. 9.3 - Prob. 45PPECh. 9.3 - Prob. 46PPECh. 9.3 - Prob. 47PPECh. 9.3 - Prob. 48PPECh. 9.3 - Prob. 49PPECh. 9.3 - Prob. 50PPECh. 9.3 - Prob. 51PPECh. 9.3 - Prob. 52PPECh. 9.3 - Prob. 53PPECh. 9.3 - Prob. 54PPECh. 9.3 - Prob. 55PPECh. 9.3 - Prob. 56PPECh. 9.3 - Prob. 57PPECh. 9.3 - Prob. 1MPCh. 9.3 - Prob. 1CBCh. 9.3 - Prob. 2CBCh. 9.3 - Prob. 3CBCh. 9.3 - Prob. 4CBCh. 9.3 - Prob. 5CBCh. 9.3 - Prob. 6CBCh. 9.4 - Prob. 1PCh. 9.4 - Prob. 2PCh. 9.4 - Prob. 3PCh. 9.4 - Prob. 4PCh. 9.4 - Prob. 1LCCh. 9.4 - Prob. 2LCCh. 9.4 - Prob. 3LCCh. 9.4 - Prob. 4LCCh. 9.4 - Prob. 5LCCh. 9.4 - Prob. 6LCCh. 9.4 - Prob. 7LCCh. 9.4 - Prob. 8PPECh. 9.4 - Prob. 9PPECh. 9.4 - Prob. 10PPECh. 9.4 - Prob. 11PPECh. 9.4 - Prob. 12PPECh. 9.4 - Prob. 13PPECh. 9.4 - Prob. 14PPECh. 9.4 - Prob. 15PPECh. 9.4 - Prob. 16PPECh. 9.4 - Prob. 17PPECh. 9.4 - Prob. 18PPECh. 9.4 - Prob. 19PPECh. 9.4 - Prob. 20PPECh. 9.4 - Prob. 21PPECh. 9.4 - Prob. 22PPECh. 9.4 - 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Prob. 26MCQCh. 9.4 - Prob. 27MCQCh. 9.4 - Prob. 28MCQCh. 9.4 - Prob. 29MCQCh. 9.4 - Prob. 30MCQCh. 9.5 - Prob. 1PCh. 9.5 - Prob. 2PCh. 9.5 - Prob. 3PCh. 9.5 - Prob. 4PCh. 9.5 - Prob. 1LCCh. 9.5 - Prob. 2LCCh. 9.5 - Prob. 3LCCh. 9.5 - Prob. 4LCCh. 9.5 - Prob. 5LCCh. 9.5 - Prob. 6LCCh. 9.5 - Prob. 7PPECh. 9.5 - Prob. 8PPECh. 9.5 - Prob. 9PPECh. 9.5 - Prob. 10PPECh. 9.5 - Prob. 11PPECh. 9.5 - Prob. 12PPECh. 9.5 - Prob. 13PPECh. 9.5 - Prob. 14PPECh. 9.5 - Prob. 15PPECh. 9.5 - Prob. 16PPECh. 9.5 - Prob. 17PPECh. 9.5 - Prob. 18PPECh. 9.5 - Prob. 19PPECh. 9.5 - Prob. 20PPECh. 9.5 - Prob. 21PPECh. 9.5 - Prob. 22PPECh. 9.5 - Prob. 23PPECh. 9.5 - Prob. 24PPECh. 9.5 - Prob. 25PPECh. 9.5 - Prob. 26PPECh. 9.5 - Prob. 27PPECh. 9.5 - Prob. 28PPECh. 9.5 - Prob. 29PPECh. 9.5 - Prob. 30PPECh. 9.5 - Prob. 31PPECh. 9.5 - Prob. 32PPECh. 9.5 - Prob. 33PPECh. 9.5 - Prob. 34PPECh. 9.5 - Prob. 35PPECh. 9.5 - Prob. 36PPECh. 9.5 - Prob. 37PPECh. 9.5 - Prob. 38PPECh. 9.5 - Prob. 39PPECh. 9.5 - Prob. 40PPECh. 9.5 - Prob. 41PPECh. 9.5 - Prob. 42PPECh. 9.5 - Prob. 43PPECh. 9.5 - Prob. 44PPECh. 9.5 - Prob. 45PPECh. 9.5 - Prob. 46PPECh. 9.5 - Prob. 47PPECh. 9.5 - Prob. 48PPECh. 9.5 - Prob. 49PPECh. 9.5 - Prob. 50STPCh. 9.5 - Prob. 51STPCh. 9.5 - Prob. 52STPCh. 9.5 - Prob. 53STPCh. 9.5 - Prob. 54STPCh. 9.5 - Prob. 55STPCh. 9.5 - Prob. 56STPCh. 9.5 - Prob. 57MRCh. 9.5 - Prob. 58MRCh. 9.5 - Prob. 59MRCh. 9.5 - Prob. 60MRCh. 9.5 - Prob. 61MRCh. 9.5 - Prob. 62MRCh. 9.5 - Prob. 63MRCh. 9.5 - Prob. 64MRCh. 9.5 - Prob. 65MRCh. 9.5 - Prob. 66MRCh. 9.6 - Prob. 1PCh. 9.6 - Prob. 2PCh. 9.6 - Prob. 3PCh. 9.6 - Prob. 4PCh. 9.6 - Prob. 1LCCh. 9.6 - Prob. 2LCCh. 9.6 - Prob. 3LCCh. 9.6 - Prob. 4LCCh. 9.6 - Prob. 5LCCh. 9.6 - Prob. 6LCCh. 9.6 - Prob. 7PPECh. 9.6 - Prob. 8PPECh. 9.6 - Prob. 9PPECh. 9.6 - Prob. 10PPECh. 9.6 - Prob. 11PPECh. 9.6 - Prob. 12PPECh. 9.6 - Prob. 13PPECh. 9.6 - Prob. 14PPECh. 9.6 - Prob. 15PPECh. 9.6 - Prob. 16PPECh. 9.6 - Prob. 17PPECh. 9.6 - Prob. 18PPECh. 9.6 - Prob. 19PPECh. 9.6 - Prob. 20PPECh. 9.6 - Prob. 21PPECh. 9.6 - Prob. 22PPECh. 9.6 - Prob. 23PPECh. 9.6 - Prob. 24PPECh. 9.6 - Prob. 25PPECh. 9.6 - Prob. 26PPECh. 9.6 - Prob. 27PPECh. 9.6 - Prob. 28PPECh. 9.6 - Prob. 29PPECh. 9.6 - Prob. 30PPECh. 9.6 - Prob. 31PPECh. 9.6 - Prob. 32PPECh. 9.6 - Prob. 33PPECh. 9.6 - Prob. 34PPECh. 9.6 - Prob. 35PPECh. 9.6 - Prob. 36PPECh. 9.6 - Prob. 37PPECh. 9.6 - Prob. 38PPECh. 9.6 - Prob. 39PPECh. 9.6 - Prob. 40PPECh. 9.6 - Prob. 41PPECh. 9.6 - Prob. 42PPECh. 9.6 - Prob. 43PPECh. 9.6 - Prob. 44PPECh. 9.6 - Prob. 45PPECh. 9.6 - Prob. 46PPECh. 9.6 - Prob. 47PPECh. 9.6 - Prob. 48PPECh. 9.6 - Prob. 49PPECh. 9.6 - Prob. 50STPCh. 9.6 - Prob. 51STPCh. 9.6 - Prob. 52STPCh. 9.6 - Prob. 53STPCh. 9.6 - Prob. 54STPCh. 9.6 - Prob. 55MRCh. 9.6 - Prob. 56MRCh. 9.6 - Prob. 57MRCh. 9.6 - Prob. 58MRCh. 9.6 - Prob. 59MRCh. 9.6 - Prob. 60MRCh. 9.6 - Prob. 61MRCh. 9.7 - Prob. 1PCh. 9.7 - Prob. 2PCh. 9.7 - Prob. 3PCh. 9.7 - Prob. 1LCCh. 9.7 - Prob. 2LCCh. 9.7 - Prob. 3LCCh. 9.7 - Prob. 4LCCh. 9.7 - Prob. 5LCCh. 9.7 - Prob. 6PPECh. 9.7 - Prob. 7PPECh. 9.7 - Prob. 8PPECh. 9.7 - Prob. 9PPECh. 9.7 - Prob. 10PPECh. 9.7 - Prob. 11PPECh. 9.7 - Prob. 12PPECh. 9.7 - Prob. 13PPECh. 9.7 - Prob. 14PPECh. 9.7 - Prob. 15PPECh. 9.7 - Prob. 16PPECh. 9.7 - Prob. 17PPECh. 9.7 - Prob. 18PPECh. 9.7 - Prob. 19PPECh. 9.7 - Prob. 20PPECh. 9.7 - Prob. 21PPECh. 9.7 - Prob. 22PPECh. 9.7 - Prob. 23PPECh. 9.7 - Prob. 24PPECh. 9.7 - Prob. 25PPECh. 9.7 - Prob. 26PPECh. 9.7 - Prob. 27PPECh. 9.7 - Prob. 28STPCh. 9.7 - Prob. 29STPCh. 9.7 - Prob. 30STPCh. 9.7 - Prob. 31STPCh. 9.7 - Prob. 32MRCh. 9.7 - Prob. 33MRCh. 9.7 - Prob. 34MRCh. 9.7 - Prob. 35MRCh. 9.7 - Prob. 36MRCh. 9.7 - Prob. 37MRCh. 9.7 - Prob. 4CBCh. 9.8 - Prob. 1PCh. 9.8 - Prob. 2PCh. 9.8 - Prob. 3PCh. 9.8 - Prob. 4PCh. 9.8 - Prob. 1LCCh. 9.8 - Prob. 2LCCh. 9.8 - Prob. 3LCCh. 9.8 - Prob. 4LCCh. 9.8 - Prob. 5LCCh. 9.8 - Prob. 6LCCh. 9.8 - Prob. 7LCCh. 9.8 - Prob. 8PPECh. 9.8 - Prob. 9PPECh. 9.8 - Prob. 10PPECh. 9.8 - Prob. 11PPECh. 9.8 - Prob. 12PPECh. 9.8 - Prob. 13PPECh. 9.8 - Prob. 14PPECh. 9.8 - Prob. 15PPECh. 9.8 - Prob. 16PPECh. 9.8 - Prob. 17PPECh. 9.8 - Prob. 18PPECh. 9.8 - Prob. 19PPECh. 9.8 - Prob. 20PPECh. 9.8 - Prob. 21PPECh. 9.8 - Prob. 22PPECh. 9.8 - Prob. 23PPECh. 9.8 - Prob. 24PPECh. 9.8 - Prob. 25PPECh. 9.8 - Prob. 26PPECh. 9.8 - Prob. 27PPECh. 9.8 - Prob. 28PPECh. 9.8 - Prob. 29PPECh. 9.8 - Prob. 30PPECh. 9.8 - Prob. 31PPECh. 9.8 - Prob. 32PPECh. 9.8 - Prob. 33PPECh. 9.8 - Prob. 34PPECh. 9.8 - Prob. 35PPECh. 9.8 - Prob. 36PPECh. 9.8 - Prob. 37STPCh. 9.8 - Prob. 38STPCh. 9.8 - Prob. 39STPCh. 9.8 - Prob. 40STPCh. 9.8 - Prob. 41STPCh. 9.8 - Prob. 42MRCh. 9.8 - Prob. 43MRCh. 9.8 - Prob. 44MRCh. 9.8 - Prob. 45MRCh. 9.8 - Prob. 46MRCh. 9.8 - Prob. 47MRCh. 9.8 - Prob. 48MRCh. 9.8 - Prob. 49MRCh. 9.8 - Prob. 50MRCh. 9 - Prob. 1GRCh. 9 - Prob. 2GRCh. 9 - Prob. 3GRCh. 9 - Prob. 4GRCh. 9 - Prob. 5GRCh. 9 - Prob. 6GRCh. 9 - Prob. 7GRCh. 9 - Prob. 8GRCh. 9 - Prob. 9GRCh. 9 - Prob. 10GRCh. 9 - Prob. 11GRCh. 9 - Prob. 12GRCh. 9 - Prob. 13GRCh. 9 - Prob. 14GRCh. 9 - Prob. 15GRCh. 9 - Prob. 16GRCh. 9 - Prob. 17GRCh. 9 - Prob. 18GRCh. 9 - Prob. 19GRCh. 9 - Prob. 20GRCh. 9 - Prob. 21GRCh. 9 - Prob. 22GRCh. 9 - Prob. 23GRCh. 9 - Prob. 24GRCh. 9 - Prob. 25GRCh. 9 - Prob. 26GRCh. 9 - Prob. 27GRCh. 9 - Prob. 1CRCh. 9 - Prob. 2CRCh. 9 - Prob. 3CRCh. 9 - Prob. 4CRCh. 9 - Prob. 5CRCh. 9 - Prob. 6CRCh. 9 - Prob. 7CRCh. 9 - Prob. 8CRCh. 9 - Prob. 9CRCh. 9 - Prob. 10CRCh. 9 - Prob. 11CRCh. 9 - Prob. 12CRCh. 9 - Prob. 13CRCh. 9 - Prob. 14CRCh. 9 - Prob. 15CRCh. 9 - Prob. 16CRCh. 9 - Prob. 17CRCh. 9 - Prob. 18CRCh. 9 - Prob. 19CRCh. 9 - Prob. 20CRCh. 9 - Prob. 21CRCh. 9 - Prob. 22CRCh. 9 - Prob. 23CRCh. 9 - Prob. 24CRCh. 9 - Prob. 25CRCh. 9 - Prob. 26CRCh. 9 - Prob. 27CRCh. 9 - Prob. 28CRCh. 9 - Prob. 29CRCh. 9 - Prob. 30CRCh. 9 - Prob. 31CRCh. 9 - Prob. 32CRCh. 9 - Prob. 33CRCh. 9 - Prob. 34CRCh. 9 - Prob. 35CRCh. 9 - Prob. 36CRCh. 9 - Prob. 37CRCh. 9 - Prob. 38CRCh. 9 - Prob. 39CRCh. 9 - Prob. 40CRCh. 9 - Prob. 41CRCh. 9 - Prob. 42CRCh. 9 - Prob. 43CRCh. 9 - Prob. 44CRCh. 9 - 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Prob. 13CCSRCh. 9 - Prob. 14CCSRCh. 9 - Prob. 15CCSRCh. 9 - Prob. 16CCSRCh. 9 - Prob. 17CCSRCh. 9 - Prob. 18CCSRCh. 9 - Prob. 19CCSRCh. 9 - Prob. 20CCSRCh. 9 - Prob. 21CCSRCh. 9 - Prob. 22CCSRCh. 9 - Prob. 23CCSRCh. 9 - Prob. 24CCSRCh. 9 - Prob. 25CCSRCh. 9 - Prob. 26CCSRCh. 9 - Prob. 27CCSRCh. 9 - Prob. 28CCSRCh. 9 - Prob. 29CCSRCh. 9 - Prob. 30CCSR
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