Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN: 9780079039897
Author: Carter
Publisher: McGraw Hill
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Question
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Chapter 9.1, Problem 64PPS

(a)

To determine

To Write:

The function in standard form.

(a)

Expert Solution
Check Mark

Answer to Problem 64PPS

The function in standard form is :

  R=10p2+100p+750

Explanation of Solution

Given Information:

The marching band is selling poinsettias to buy new uniforms. Last year the band charged $5 each, and they sold 150. They want to increase the price this year, and they expect to lose 10 sales for each $1 increase. The sales revenue R, in dollars, generated by selling the poinsettias is predicted by the function R=(5+p)(15010p) , where p is the number of $1 price increases.

Concept Used :

  • Quadratic Functions:
  • Quadratic functions are non-linear and are of the form:

  f(x)=ax2+bx+c;a0

This is the standard form of Quadratic function.

  • Shape of the graph of a Quadratic function is called Parabola.
  • Parabolas are symmetric about a central line called Axis Of Symmetry.
  • The axis of symmetry intersects a parabola only at one point , called the Vertex.

Calculation:

  R=(5+p)(15010p)..............................[given_equation]R=5(15010p)+p(15010p)..............[distributive_property_of_multiplication_over_addition]R=5(150)5(10p)+p(150)p(10p).....[distributive_property_of_multiplication_over_subtraction]R=75050p+150p10p2....................[simplify]R=10p2+100p+750

So, the function in standard form is :

  R=10p2+100p+750

(b)

To determine

To Find:

The maximum value of the function.

(b)

Expert Solution
Check Mark

Answer to Problem 64PPS

The maximum value of the function is 1000.

Explanation of Solution

Given Information:

From part (a) , the standard form of function is :

  R=10p2+100p+750

Concept Used :

  • Quadratic Functions:
  • Quadratic functions are non-linear and are of the form:

  f(x)=ax2+bx+c;a0

This is the standard form of Quadratic function.

  • Axis of Symmetry: Passes through the vertex and divides the parabola into two congruent halves.

  x=b2a

  • y-intercept = The y coordinate of the point at which the graph intersects y-axis = c
  • If a > 0 ,
  • The graph of ax2+bx+c opens upward.
  • The lowest point on the graph is the minimum.
  • If a < 0 ,
  • The graph of ax2+bx+c opens downward.
  • The highest point on the graph is the maximum.
  • The maximum or the minimum is the vertex.

Calculation:

  • In the equation R=10p2+100p+750 ; comparing it with standard form of quadratic equation , we have a = -10 , b = 100 , c = 750 .
  • Since, a = -10 < 0 .So, the function opens downward and hence the maximum value of the function occurs at the vertex.
  • Find vertex:

The p-coordinate of vertex is

  p=b2ap=1002(10)=5..........................[a=10,b=100]

The p-coordinate of the vertex is p=5

  • Substitute the value of p = 5 in the equation R=10p2+100p+750 to find the value of R:

  R=10p2+100p+750 R=10 (5) 2 +100(5)+750.................[p=5]R=250+500+750=1000

The vertex is at (5,1000) .

So, the maximum of the function is 1000.

(c)

To determine

To Find:

The price at which the poinsettias should be sold to generate the most sales revenue.

(c)

Expert Solution
Check Mark

Answer to Problem 64PPS

$10

Explanation of Solution

Given Information:

The marching band is selling poinsettias to buy new uniforms. Last year the band charged $5 each, and they sold 150. They want to increase the price this year, and they expect to lose 10 sales for each $1 increase. The sales revenue R, in dollars, generated by selling the poinsettias is predicted by the function R=10p2+100p+750 , where p is the number of $1 price increases.

The vertex is (5,1000) and is the maximum of the function.

Concept Used :

  • Quadratic Functions:
  • Quadratic functions are non-linear and are of the form:

  f(x)=ax2+bx+c;a0

This is the standard form of Quadratic function.

Calculation:

  • The vertex is (5,1000) and is the maximum of the function.
  • The maximum revenue is $1000 , when p = 5.
  • Last year , cost of each poinsettias was $5.
  • Now , there are five $1 increases.
  • So, total of $5 increase since last year.
  • The new price = 5+5 =$10.

Chapter 9 Solutions

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Ch. 9.1 - Prob. 6GPCh. 9.1 - Prob. 1CYUCh. 9.1 - Prob. 2CYUCh. 9.1 - Prob. 3CYUCh. 9.1 - Prob. 4CYUCh. 9.1 - Prob. 5CYUCh. 9.1 - Prob. 6CYUCh. 9.1 - Prob. 7CYUCh. 9.1 - Prob. 8CYUCh. 9.1 - Prob. 9CYUCh. 9.1 - Prob. 10CYUCh. 9.1 - Prob. 11CYUCh. 9.1 - Prob. 12CYUCh. 9.1 - Prob. 13CYUCh. 9.1 - Prob. 14CYUCh. 9.1 - Prob. 15CYUCh. 9.1 - Prob. 16CYUCh. 9.1 - Prob. 17CYUCh. 9.1 - Prob. 18CYUCh. 9.1 - Prob. 19CYUCh. 9.1 - Prob. 20CYUCh. 9.1 - Prob. 21CYUCh. 9.1 - Prob. 22PPSCh. 9.1 - Prob. 23PPSCh. 9.1 - Prob. 24PPSCh. 9.1 - Prob. 25PPSCh. 9.1 - Prob. 26PPSCh. 9.1 - Prob. 27PPSCh. 9.1 - Prob. 28PPSCh. 9.1 - Prob. 29PPSCh. 9.1 - Prob. 30PPSCh. 9.1 - Prob. 31PPSCh. 9.1 - Prob. 32PPSCh. 9.1 - Prob. 33PPSCh. 9.1 - Prob. 34PPSCh. 9.1 - Prob. 35PPSCh. 9.1 - Prob. 36PPSCh. 9.1 - Prob. 37PPSCh. 9.1 - Prob. 38PPSCh. 9.1 - Prob. 39PPSCh. 9.1 - Prob. 40PPSCh. 9.1 - Prob. 41PPSCh. 9.1 - Prob. 42PPSCh. 9.1 - Prob. 43PPSCh. 9.1 - Prob. 44PPSCh. 9.1 - Prob. 45PPSCh. 9.1 - Prob. 46PPSCh. 9.1 - Prob. 47PPSCh. 9.1 - Prob. 48PPSCh. 9.1 - Prob. 49PPSCh. 9.1 - Prob. 50PPSCh. 9.1 - Prob. 51PPSCh. 9.1 - Prob. 52PPSCh. 9.1 - Prob. 53PPSCh. 9.1 - Prob. 54PPSCh. 9.1 - Prob. 55PPSCh. 9.1 - Prob. 56PPSCh. 9.1 - Prob. 57PPSCh. 9.1 - Prob. 58PPSCh. 9.1 - Prob. 59PPSCh. 9.1 - Prob. 60PPSCh. 9.1 - Prob. 61PPSCh. 9.1 - Prob. 62PPSCh. 9.1 - Prob. 63PPSCh. 9.1 - Prob. 64PPSCh. 9.1 - Prob. 65PPSCh. 9.1 - Prob. 66PPSCh. 9.1 - Prob. 67PPSCh. 9.1 - Prob. 68HPCh. 9.1 - Prob. 69HPCh. 9.1 - Prob. 70HPCh. 9.1 - Prob. 71HPCh. 9.1 - Prob. 72HPCh. 9.1 - Prob. 73HPCh. 9.1 - Prob. 74HPCh. 9.1 - Prob. 75PFACh. 9.1 - Prob. 76PFACh. 9.1 - Prob. 77PFACh. 9.1 - Prob. 78PFACh. 9.1 - Prob. 79PFACh. 9.1 - Prob. 80PFACh. 9.2 - Prob. 1AGPCh. 9.2 - Prob. 1BGPCh. 9.2 - Prob. 1CGPCh. 9.2 - Prob. 1DGPCh. 9.2 - Prob. 2AGPCh. 9.2 - Prob. 2BGPCh. 9.2 - Prob. 3AGPCh. 9.2 - Prob. 3BGPCh. 9.2 - Prob. 4AGPCh. 9.2 - Prob. 4BGPCh. 9.2 - Prob. 5AGPCh. 9.2 - Prob. 5BGPCh. 9.2 - Prob. 5CGPCh. 9.2 - Prob. 6GPCh. 9.2 - Prob. 7GPCh. 9.2 - Prob. 8AGPCh. 9.2 - Prob. 8BGPCh. 9.2 - Prob. 8CGPCh. 9.2 - Prob. 1CYUCh. 9.2 - Prob. 2CYUCh. 9.2 - Prob. 3CYUCh. 9.2 - Prob. 4CYUCh. 9.2 - Prob. 5CYUCh. 9.2 - Prob. 6CYUCh. 9.2 - Prob. 7CYUCh. 9.2 - Prob. 8CYUCh. 9.2 - Prob. 9CYUCh. 9.2 - Prob. 10PPSCh. 9.2 - Prob. 11PPSCh. 9.2 - Prob. 12PPSCh. 9.2 - Prob. 13PPSCh. 9.2 - Prob. 14PPSCh. 9.2 - Prob. 15PPSCh. 9.2 - Prob. 16PPSCh. 9.2 - Prob. 17PPSCh. 9.2 - Prob. 18PPSCh. 9.2 - Prob. 19PPSCh. 9.2 - Prob. 20PPSCh. 9.2 - Prob. 21PPSCh. 9.2 - Prob. 22PPSCh. 9.2 - Prob. 23PPSCh. 9.2 - Prob. 24PPSCh. 9.2 - Prob. 25PPSCh. 9.2 - Prob. 26PPSCh. 9.2 - Prob. 27PPSCh. 9.2 - Prob. 28PPSCh. 9.2 - Prob. 29PPSCh. 9.2 - Prob. 30PPSCh. 9.2 - Prob. 31PPSCh. 9.2 - Prob. 32PPSCh. 9.2 - Prob. 33PPSCh. 9.2 - Prob. 34PPSCh. 9.2 - Prob. 35PPSCh. 9.2 - Prob. 36PPSCh. 9.2 - Prob. 37PPSCh. 9.2 - Prob. 38PPSCh. 9.2 - Prob. 39PPSCh. 9.2 - Prob. 40PPSCh. 9.2 - Prob. 41PPSCh. 9.2 - Prob. 42HPCh. 9.2 - Prob. 43HPCh. 9.2 - Prob. 44HPCh. 9.2 - Prob. 45HPCh. 9.2 - Prob. 46HPCh. 9.2 - Prob. 47PFACh. 9.2 - 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Prob. 5GPCh. 9.5 - Prob. 1CYUCh. 9.5 - Prob. 2CYUCh. 9.5 - Prob. 3CYUCh. 9.5 - Prob. 4CYUCh. 9.5 - Prob. 5CYUCh. 9.5 - Prob. 6CYUCh. 9.5 - Prob. 7CYUCh. 9.5 - Prob. 8CYUCh. 9.5 - Prob. 9CYUCh. 9.5 - Prob. 10CYUCh. 9.5 - Prob. 11CYUCh. 9.5 - Prob. 12CYUCh. 9.5 - Prob. 13PPSCh. 9.5 - Prob. 14PPSCh. 9.5 - Prob. 15PPSCh. 9.5 - Prob. 16PPSCh. 9.5 - Prob. 17PPSCh. 9.5 - Prob. 18PPSCh. 9.5 - Prob. 19PPSCh. 9.5 - Prob. 20PPSCh. 9.5 - Prob. 21PPSCh. 9.5 - Prob. 22PPSCh. 9.5 - Prob. 23PPSCh. 9.5 - Prob. 24PPSCh. 9.5 - Prob. 25PPSCh. 9.5 - Prob. 26PPSCh. 9.5 - Prob. 27PPSCh. 9.5 - Prob. 28PPSCh. 9.5 - Prob. 29PPSCh. 9.5 - Prob. 30PPSCh. 9.5 - Prob. 31PPSCh. 9.5 - Prob. 32PPSCh. 9.5 - Prob. 33PPSCh. 9.5 - Prob. 34PPSCh. 9.5 - Prob. 35PPSCh. 9.5 - Prob. 36PPSCh. 9.5 - Prob. 37PPSCh. 9.5 - Prob. 38PPSCh. 9.5 - Prob. 39PPSCh. 9.5 - Prob. 40PPSCh. 9.5 - Prob. 41PPSCh. 9.5 - Prob. 42HPCh. 9.5 - Prob. 43HPCh. 9.5 - Prob. 44HPCh. 9.5 - Prob. 45HPCh. 9.5 - Prob. 46PFACh. 9.5 - Prob. 47PFACh. 9.5 - Prob. 48PFACh. 9.5 - Prob. 49PFACh. 9.5 - Prob. 50PFACh. 9.5 - Prob. 51PFACh. 9.5 - Prob. 52PFACh. 9.5 - Prob. 53PFACh. 9.6 - Prob. 1AGPCh. 9.6 - Prob. 1BGPCh. 9.6 - Prob. 1CGPCh. 9.6 - Prob. 1DGPCh. 9.6 - Prob. 2AGPCh. 9.6 - Prob. 2BGPCh. 9.6 - Prob. 3AGPCh. 9.6 - Prob. 3BGPCh. 9.6 - Prob. 4AGPCh. 9.6 - Prob. 4BGPCh. 9.6 - Prob. 1CYUCh. 9.6 - Prob. 2CYUCh. 9.6 - Prob. 3CYUCh. 9.6 - Prob. 4CYUCh. 9.6 - Prob. 5CYUCh. 9.6 - Prob. 6CYUCh. 9.6 - Prob. 7CYUCh. 9.6 - Prob. 8CYUCh. 9.6 - Prob. 9CYUCh. 9.6 - Prob. 10CYUCh. 9.6 - Prob. 11CYUCh. 9.6 - Prob. 12CYUCh. 9.6 - Prob. 13CYUCh. 9.6 - Prob. 14CYUCh. 9.6 - Prob. 15CYUCh. 9.6 - Prob. 16PPSCh. 9.6 - Prob. 17PPSCh. 9.6 - Prob. 18PPSCh. 9.6 - Prob. 19PPSCh. 9.6 - Prob. 20PPSCh. 9.6 - Prob. 21PPSCh. 9.6 - Prob. 22PPSCh. 9.6 - Prob. 23PPSCh. 9.6 - Prob. 24PPSCh. 9.6 - Prob. 25PPSCh. 9.6 - Prob. 26PPSCh. 9.6 - Prob. 27PPSCh. 9.6 - Prob. 28PPSCh. 9.6 - Prob. 29PPSCh. 9.6 - Prob. 30PPSCh. 9.6 - Prob. 31PPSCh. 9.6 - Prob. 32PPSCh. 9.6 - Prob. 33PPSCh. 9.6 - Prob. 34PPSCh. 9.6 - 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Prob. 18PPSCh. 9.8 - Prob. 19PPSCh. 9.8 - Prob. 20PPSCh. 9.8 - Prob. 21PPSCh. 9.8 - Prob. 22PPSCh. 9.8 - Prob. 23PPSCh. 9.8 - Prob. 24PPSCh. 9.8 - Prob. 25PPSCh. 9.8 - Prob. 26PPSCh. 9.8 - Prob. 27PPSCh. 9.8 - Prob. 28PPSCh. 9.8 - Prob. 29PPSCh. 9.8 - Prob. 30PPSCh. 9.8 - Prob. 31HPCh. 9.8 - Prob. 32HPCh. 9.8 - Prob. 33HPCh. 9.8 - Prob. 34HPCh. 9.8 - Prob. 35HPCh. 9.8 - Prob. 36PFACh. 9.8 - Prob. 37PFACh. 9.8 - Prob. 38PFACh. 9.8 - Prob. 39PFACh. 9.8 - Prob. 40PFACh. 9.8 - Prob. 41PFACh. 9.9 - Prob. 1AGPCh. 9.9 - Prob. 1BGPCh. 9.9 - Prob. 2AGPCh. 9.9 - Prob. 2BGPCh. 9.9 - Prob. 3AGPCh. 9.9 - Prob. 3BGPCh. 9.9 - Prob. 3CGPCh. 9.9 - Prob. 4AGPCh. 9.9 - Prob. 4BGPCh. 9.9 - Prob. 1CYUCh. 9.9 - Prob. 2CYUCh. 9.9 - Prob. 3CYUCh. 9.9 - Prob. 4CYUCh. 9.9 - Prob. 5CYUCh. 9.9 - Prob. 6CYUCh. 9.9 - Prob. 7CYUCh. 9.9 - Prob. 8CYUCh. 9.9 - Prob. 9CYUCh. 9.9 - Prob. 10CYUCh. 9.9 - Prob. 11CYUCh. 9.9 - Prob. 12PPSCh. 9.9 - Prob. 13PPSCh. 9.9 - Prob. 14PPSCh. 9.9 - Prob. 15PPSCh. 9.9 - Prob. 16PPSCh. 9.9 - Prob. 17PPSCh. 9.9 - Prob. 18PPSCh. 9.9 - Prob. 19PPSCh. 9.9 - Prob. 20PPSCh. 9.9 - Prob. 21PPSCh. 9.9 - Prob. 22PPSCh. 9.9 - Prob. 23PPSCh. 9.9 - Prob. 24PPSCh. 9.9 - Prob. 25PPSCh. 9.9 - Prob. 26PPSCh. 9.9 - Prob. 27PPSCh. 9.9 - Prob. 28PPSCh. 9.9 - Prob. 29PPSCh. 9.9 - Prob. 30PPSCh. 9.9 - Prob. 31PPSCh. 9.9 - Prob. 32PPSCh. 9.9 - Prob. 33PPSCh. 9.9 - Prob. 34PPSCh. 9.9 - Prob. 35PPSCh. 9.9 - Prob. 36PPSCh. 9.9 - Prob. 37PPSCh. 9.9 - Prob. 38PPSCh. 9.9 - Prob. 39PPSCh. 9.9 - Prob. 40PPSCh. 9.9 - Prob. 41PPSCh. 9.9 - Prob. 42PPSCh. 9.9 - Prob. 43PPSCh. 9.9 - Prob. 44PPSCh. 9.9 - Prob. 45PPSCh. 9.9 - Prob. 46PPSCh. 9.9 - Prob. 47PPSCh. 9.9 - Prob. 48HPCh. 9.9 - Prob. 49HPCh. 9.9 - Prob. 50HPCh. 9.9 - Prob. 51HPCh. 9.9 - Prob. 52HPCh. 9.9 - Prob. 53PFACh. 9.9 - Prob. 54PFACh. 9.9 - Prob. 55PFACh. 9.9 - Prob. 56PFACh. 9.9 - Prob. 57PFACh. 9.9 - Prob. 58PFACh. 9.9 - Prob. 59PFACh. 9 - Prob. 1MCQCh. 9 - Prob. 2MCQCh. 9 - Prob. 3MCQCh. 9 - Prob. 4MCQCh. 9 - Prob. 5MCQCh. 9 - Prob. 6MCQCh. 9 - Prob. 7MCQCh. 9 - Prob. 8MCQCh. 9 - Prob. 9MCQCh. 9 - Prob. 10MCQCh. 9 - Prob. 11MCQCh. 9 - Prob. 12MCQCh. 9 - Prob. 13MCQCh. 9 - Prob. 14MCQCh. 9 - Prob. 15MCQCh. 9 - Prob. 16MCQCh. 9 - Prob. 17MCQCh. 9 - Prob. 18MCQCh. 9 - Prob. 19MCQCh. 9 - Prob. 20MCQCh. 9 - Prob. 21MCQCh. 9 - Prob. 22MCQCh. 9 - Prob. 23MCQCh. 9 - Prob. 24MCQCh. 9 - Prob. 25MCQCh. 9 - Prob. 26MCQCh. 9 - Prob. 27MCQCh. 9 - Prob. 1SGRCh. 9 - Prob. 2SGRCh. 9 - Prob. 3SGRCh. 9 - Prob. 4SGRCh. 9 - Prob. 5SGRCh. 9 - Prob. 6SGRCh. 9 - Prob. 7SGRCh. 9 - Prob. 8SGRCh. 9 - Prob. 9SGRCh. 9 - Prob. 10SGRCh. 9 - Prob. 11SGRCh. 9 - Prob. 12SGRCh. 9 - Prob. 13SGRCh. 9 - Prob. 14SGRCh. 9 - Prob. 15SGRCh. 9 - Prob. 16SGRCh. 9 - Prob. 17SGRCh. 9 - Prob. 18SGRCh. 9 - Prob. 19SGRCh. 9 - Prob. 20SGRCh. 9 - Prob. 21SGRCh. 9 - Prob. 22SGRCh. 9 - Prob. 23SGRCh. 9 - Prob. 24SGRCh. 9 - Prob. 25SGRCh. 9 - Prob. 26SGRCh. 9 - Prob. 27SGRCh. 9 - Prob. 28SGRCh. 9 - Prob. 29SGRCh. 9 - Prob. 30SGRCh. 9 - Prob. 31SGRCh. 9 - Prob. 32SGRCh. 9 - Prob. 33SGRCh. 9 - Prob. 34SGRCh. 9 - Prob. 35SGRCh. 9 - Prob. 36SGRCh. 9 - Prob. 37SGRCh. 9 - Prob. 38SGRCh. 9 - Prob. 39SGRCh. 9 - Prob. 40SGRCh. 9 - Prob. 41SGRCh. 9 - Prob. 42SGRCh. 9 - Prob. 43SGRCh. 9 - Prob. 44SGRCh. 9 - Prob. 45SGRCh. 9 - Prob. 46SGRCh. 9 - Prob. 47SGRCh. 9 - Prob. 48SGRCh. 9 - Prob. 49SGRCh. 9 - Prob. 50SGRCh. 9 - Prob. 51SGRCh. 9 - Prob. 52SGRCh. 9 - Prob. 53SGRCh. 9 - Prob. 54SGRCh. 9 - Prob. 55SGRCh. 9 - Prob. 56SGRCh. 9 - Prob. 57SGRCh. 9 - Prob. 58SGRCh. 9 - Prob. 59SGRCh. 9 - Prob. 60SGRCh. 9 - Prob. 61SGRCh. 9 - Prob. 62SGRCh. 9 - Prob. 63SGRCh. 9 - Prob. 64SGRCh. 9 - Prob. 65SGRCh. 9 - Prob. 66SGRCh. 9 - Prob. 67SGRCh. 9 - Prob. 68SGRCh. 9 - Prob. 69SGRCh. 9 - Prob. 70SGRCh. 9 - Prob. 71SGRCh. 9 - Prob. 1PTCh. 9 - Prob. 2PTCh. 9 - Prob. 3PTCh. 9 - Prob. 4PTCh. 9 - Prob. 5PTCh. 9 - Prob. 6PTCh. 9 - Prob. 7PTCh. 9 - Prob. 8PTCh. 9 - Prob. 9PTCh. 9 - Prob. 10PTCh. 9 - Prob. 11PTCh. 9 - Prob. 12PTCh. 9 - Prob. 13PTCh. 9 - Prob. 14PTCh. 9 - Prob. 15PTCh. 9 - Prob. 16PTCh. 9 - Prob. 17PTCh. 9 - Prob. 18PTCh. 9 - Prob. 19PTCh. 9 - Prob. 20PTCh. 9 - Prob. 21PTCh. 9 - Prob. 22PTCh. 9 - Prob. 23PTCh. 9 - Prob. 24PTCh. 9 - Prob. 25PTCh. 9 - Prob. 26PTCh. 9 - Prob. 27PTCh. 9 - Prob. 28PTCh. 9 - Prob. 29PTCh. 9 - Prob. 1PFACh. 9 - Prob. 2PFACh. 9 - Prob. 3PFACh. 9 - Prob. 4PFACh. 9 - Prob. 5PFACh. 9 - Prob. 6PFACh. 9 - Prob. 7PFACh. 9 - Prob. 8PFACh. 9 - Prob. 9PFACh. 9 - Prob. 10PFACh. 9 - Prob. 11PFACh. 9 - Prob. 12PFACh. 9 - Prob. 13PFA
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