Glencoe Algebra 2 Student Edition C2014
Glencoe Algebra 2 Student Edition C2014
1st Edition
ISBN: 9780076639908
Author: McGraw-Hill Glencoe
Publisher: MCG
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 5.8, Problem 40PPS
To determine

To calculate: The zeros of the function f(t)=t431t3+308t21100t+1200 for the roller coaster is at ground level.

Expert Solution & Answer
Check Mark

Answer to Problem 40PPS

When time t is 2,4,10  and 15 the roller coaster is at ground level.

Explanation of Solution

Given information:

The function f(t)=t431t3+308t21100t+1200 represents the height of roller coaster where t denotes the time in seconds.

Formula used:

A polynomial of n degree has n zeros, which can be either real or imaginary.

Descartes’ rule of signs states that consider a polynomial P(x)=anxn++a1x+a0 with real coefficients then, the number of times the sign between coefficients changes is equal to count of positive real zeroes of P(x) or is less than this by an even number, the number of times the sign between coefficients changes is equal to count of negative real zeroes of P(x) or is less than this by an even number.

Calculation:

Consider the function f(t)=t431t3+308t21100t+1200 .

Observe that degree of polynomial is 4, so the functions has 4 zeros which can be either real or imaginary.

Descartes’ rule of signs states that consider a polynomial P(x)=anxn++a1x+a0 with real coefficients then, the number of times the sign between coefficients changes is equal to count of positive real zeroes of P(x) or is less than this by an even number.

So, count the number of times the sign changes between the coefficients of f(t)=t431t3+308t21100t+1200

There are 4, 2 or 0 positive real zeros.

Now,

  f(t)=t4+31t3+308t2+1100t+1200

Descartes’ rule of signs states that consider a polynomial P(x)=anxn++a1x+a0 with real coefficients then, the number of times the sign between coefficients changes is equal to count of negative real zeroes of P(x) or is less than this by an even number.

So, count the number of times the sign changes between the coefficients of f(t)=t4+31t3+308t2+1100t+1200 .

There are no negative real zero.

Next, construct a table with possible combinations of real and imaginary zeros.

  Number of PositiveReal zerosNumber of NegativeReal zerosNumber ofImaginary zerosTotal Numberof zeros4004+0+0=42022+0+2=40040+0+4=4

Recall that the Rational zero theorem states that provided a polynomial P(x) with integral coefficients then every rational zero is of the form pq that is a rational number in simplest form. Here, p is a factor of the constant term and q is a factor of leading coefficient.

For the provided function leading coefficient is 1 and constant term is 1200. Therefore, p is a factor of 1200 and q is a factor of 1.

The possible combinations of pq in simplest form are,

  pq=±1,±2,±3,±4,±5,±6,±8,±10,±12,±

Next, construct a table with help of synthetic substitution to compute the value of f(t) for real values of t .

  tf(t)13781264020248963843819040

As observed two zeros are resulted at t=2 and t=4 .

So, factor of the polynomial is (t2)(t4)=t26t+8 .

Now, divide the polynomial f(t)=t431t3+308t21100t+1200 by t26t+8 .

  t26t+8t225t+150t431t3+308t21100t+1200t46t3+8t225t3+300t21100t25t3+150t2200t150t2+900t+1200150t2+900t+12000

Now, the depressed polynomial is obtained is t225t+150 .

Factor the polynomial.

  t225t+150=0t215t10t+150=0t(t15)10(t15)=0(t10)(t15)=0

Either (t10)=0 or (t15)=0

That is, t=10 or t=15 .

Thus, the zeros of the function f(t)=t431t3+308t21100t+1200 are 2,4,10  and 15 .

When time t is 2,4,10  and 15 the roller coaster is at ground level.

Chapter 5 Solutions

Glencoe Algebra 2 Student Edition C2014

Ch. 5.1 - Prob. 5GPCh. 5.1 - Prob. 6AGPCh. 5.1 - Prob. 6BGPCh. 5.1 - Prob. 1CYUCh. 5.1 - Prob. 2CYUCh. 5.1 - Prob. 3CYUCh. 5.1 - Prob. 4CYUCh. 5.1 - Prob. 5CYUCh. 5.1 - Prob. 6CYUCh. 5.1 - Prob. 7CYUCh. 5.1 - Prob. 8CYUCh. 5.1 - Prob. 9CYUCh. 5.1 - Prob. 10CYUCh. 5.1 - Prob. 11CYUCh. 5.1 - Prob. 12CYUCh. 5.1 - Prob. 13CYUCh. 5.1 - Prob. 14CYUCh. 5.1 - Prob. 15CYUCh. 5.1 - Prob. 16PPSCh. 5.1 - Prob. 17PPSCh. 5.1 - Prob. 18PPSCh. 5.1 - Prob. 19PPSCh. 5.1 - Prob. 20PPSCh. 5.1 - Prob. 21PPSCh. 5.1 - Prob. 22PPSCh. 5.1 - Prob. 23PPSCh. 5.1 - Prob. 24PPSCh. 5.1 - Prob. 25PPSCh. 5.1 - Prob. 26PPSCh. 5.1 - Prob. 27PPSCh. 5.1 - Prob. 28PPSCh. 5.1 - Prob. 29PPSCh. 5.1 - Prob. 30PPSCh. 5.1 - Prob. 31PPSCh. 5.1 - Prob. 32PPSCh. 5.1 - Prob. 33PPSCh. 5.1 - Prob. 34PPSCh. 5.1 - Prob. 35PPSCh. 5.1 - Prob. 36PPSCh. 5.1 - Prob. 37PPSCh. 5.1 - Prob. 38PPSCh. 5.1 - Prob. 39PPSCh. 5.1 - Prob. 40PPSCh. 5.1 - Prob. 41PPSCh. 5.1 - Prob. 42PPSCh. 5.1 - Prob. 43PPSCh. 5.1 - Prob. 44PPSCh. 5.1 - Prob. 45PPSCh. 5.1 - Prob. 46PPSCh. 5.1 - Prob. 47PPSCh. 5.1 - Prob. 48PPSCh. 5.1 - Prob. 49PPSCh. 5.1 - Prob. 50PPSCh. 5.1 - Prob. 51PPSCh. 5.1 - Prob. 52PPSCh. 5.1 - Prob. 53PPSCh. 5.1 - Prob. 54PPSCh. 5.1 - Prob. 55PPSCh. 5.1 - Prob. 56PPSCh. 5.1 - Prob. 57PPSCh. 5.1 - Prob. 58PPSCh. 5.1 - Prob. 59PPSCh. 5.1 - Prob. 60PPSCh. 5.1 - Prob. 61PPSCh. 5.1 - Prob. 62PPSCh. 5.1 - Prob. 63PPSCh. 5.1 - Prob. 64PPSCh. 5.1 - Prob. 65HPCh. 5.1 - Prob. 66HPCh. 5.1 - Prob. 67HPCh. 5.1 - Prob. 68HPCh. 5.1 - Prob. 69HPCh. 5.1 - Prob. 70STPCh. 5.1 - Prob. 71STPCh. 5.1 - Prob. 72STPCh. 5.1 - Prob. 73STPCh. 5.1 - Prob. 74SRCh. 5.1 - Prob. 75SRCh. 5.1 - Prob. 76SRCh. 5.1 - Prob. 77SRCh. 5.1 - Prob. 78SRCh. 5.1 - Prob. 79SRCh. 5.1 - Prob. 80SRCh. 5.1 - Prob. 81SRCh. 5.1 - Prob. 82SRCh. 5.1 - Prob. 83SRCh. 5.1 - Prob. 84SRCh. 5.1 - Prob. 85SRCh. 5.1 - Prob. 86SRCh. 5.1 - Prob. 87SRCh. 5.1 - Prob. 88SRCh. 5.1 - Prob. 89SRCh. 5.1 - Prob. 90SRCh. 5.1 - Prob. 91SCh. 5.1 - Prob. 92SCh. 5.1 - Prob. 93SCh. 5.1 - Prob. 94SCh. 5.1 - Prob. 95SCh. 5.1 - Prob. 96SCh. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.2 - Prob. 1AGPCh. 5.2 - Prob. 1BGPCh. 5.2 - Prob. 2AGPCh. 5.2 - Prob. 2BGPCh. 5.2 - Prob. 3GPCh. 5.2 - Prob. 4AGPCh. 5.2 - Prob. 4BGPCh. 5.2 - Prob. 4CGPCh. 5.2 - Prob. 4DGPCh. 5.2 - Prob. 5AGPCh. 5.2 - Prob. 5BGPCh. 5.2 - Prob. 5CGPCh. 5.2 - Prob. 5DGPCh. 5.2 - Prob. 1CYUCh. 5.2 - Prob. 2CYUCh. 5.2 - Prob. 3CYUCh. 5.2 - Prob. 4CYUCh. 5.2 - Prob. 5CYUCh. 5.2 - Prob. 6CYUCh. 5.2 - Prob. 7CYUCh. 5.2 - Prob. 8CYUCh. 5.2 - Prob. 9CYUCh. 5.2 - Prob. 10CYUCh. 5.2 - Prob. 11CYUCh. 5.2 - Prob. 12PPSCh. 5.2 - Prob. 13PPSCh. 5.2 - Prob. 14PPSCh. 5.2 - Prob. 15PPSCh. 5.2 - Prob. 16PPSCh. 5.2 - Prob. 17PPSCh. 5.2 - Prob. 18PPSCh. 5.2 - Prob. 19PPSCh. 5.2 - Prob. 20PPSCh. 5.2 - Prob. 21PPSCh. 5.2 - Prob. 22PPSCh. 5.2 - Prob. 23PPSCh. 5.2 - Prob. 24PPSCh. 5.2 - Prob. 25PPSCh. 5.2 - Prob. 26PPSCh. 5.2 - Prob. 27PPSCh. 5.2 - Prob. 28PPSCh. 5.2 - Prob. 29PPSCh. 5.2 - Prob. 30PPSCh. 5.2 - Prob. 31PPSCh. 5.2 - Prob. 32PPSCh. 5.2 - Prob. 33PPSCh. 5.2 - Prob. 34PPSCh. 5.2 - Prob. 35PPSCh. 5.2 - Prob. 36PPSCh. 5.2 - Prob. 37PPSCh. 5.2 - Prob. 38PPSCh. 5.2 - Prob. 39PPSCh. 5.2 - Prob. 40PPSCh. 5.2 - Prob. 41PPSCh. 5.2 - Prob. 42PPSCh. 5.2 - Prob. 43HPCh. 5.2 - Prob. 44HPCh. 5.2 - Prob. 45HPCh. 5.2 - Prob. 46HPCh. 5.2 - Prob. 47HPCh. 5.2 - Prob. 48HPCh. 5.2 - Prob. 49STPCh. 5.2 - Prob. 50STPCh. 5.2 - Prob. 51STPCh. 5.2 - Prob. 52STPCh. 5.2 - Prob. 53SRCh. 5.2 - Prob. 54SRCh. 5.2 - Prob. 55SRCh. 5.2 - Prob. 56SRCh. 5.2 - Prob. 57SRCh. 5.2 - Prob. 58SRCh. 5.2 - Prob. 59SRCh. 5.2 - Prob. 60SRCh. 5.2 - Prob. 61SRCh. 5.2 - Prob. 62SRCh. 5.2 - Prob. 63SRCh. 5.2 - Prob. 64SRCh. 5.2 - Prob. 65SRCh. 5.2 - Prob. 66SRCh. 5.2 - Prob. 67SCh. 5.2 - Prob. 68SCh. 5.2 - Prob. 69SCh. 5.2 - Prob. 70SCh. 5.2 - Prob. 71SCh. 5.2 - Prob. 72SCh. 5.2 - Prob. 1ECh. 5.2 - Prob. 2ECh. 5.2 - Prob. 3ECh. 5.2 - Prob. 4ECh. 5.2 - Prob. 5ECh. 5.2 - Prob. 6ECh. 5.2 - Prob. 7ECh. 5.3 - Prob. 1AGPCh. 5.3 - Prob. 1BGPCh. 5.3 - Prob. 1CGPCh. 5.3 - Prob. 2GPCh. 5.3 - Prob. 3AGPCh. 5.3 - Prob. 3BGPCh. 5.3 - Prob. 4AGPCh. 5.3 - Prob. 4BGPCh. 5.3 - Prob. 1CYUCh. 5.3 - Prob. 2CYUCh. 5.3 - Prob. 3CYUCh. 5.3 - Prob. 4CYUCh. 5.3 - Prob. 5CYUCh. 5.3 - Prob. 6CYUCh. 5.3 - Prob. 7CYUCh. 5.3 - Prob. 8CYUCh. 5.3 - Prob. 9CYUCh. 5.3 - Prob. 10CYUCh. 5.3 - Prob. 11CYUCh. 5.3 - Prob. 12CYUCh. 5.3 - Prob. 13PPSCh. 5.3 - Prob. 14PPSCh. 5.3 - Prob. 15PPSCh. 5.3 - Prob. 16PPSCh. 5.3 - Prob. 17PPSCh. 5.3 - Prob. 18PPSCh. 5.3 - Prob. 19PPSCh. 5.3 - Prob. 20PPSCh. 5.3 - Prob. 21PPSCh. 5.3 - Prob. 22PPSCh. 5.3 - Prob. 23PPSCh. 5.3 - Prob. 24PPSCh. 5.3 - Prob. 25PPSCh. 5.3 - Prob. 26PPSCh. 5.3 - Prob. 27PPSCh. 5.3 - Prob. 28PPSCh. 5.3 - Prob. 29PPSCh. 5.3 - Prob. 30PPSCh. 5.3 - Prob. 31PPSCh. 5.3 - Prob. 32PPSCh. 5.3 - Prob. 33PPSCh. 5.3 - Prob. 34PPSCh. 5.3 - Prob. 35PPSCh. 5.3 - Prob. 36PPSCh. 5.3 - Prob. 37PPSCh. 5.3 - Prob. 38PPSCh. 5.3 - Prob. 39PPSCh. 5.3 - Prob. 40PPSCh. 5.3 - Prob. 41PPSCh. 5.3 - Prob. 42PPSCh. 5.3 - Prob. 43PPSCh. 5.3 - Prob. 44PPSCh. 5.3 - Prob. 45PPSCh. 5.3 - Prob. 46PPSCh. 5.3 - Prob. 47PPSCh. 5.3 - Prob. 48PPSCh. 5.3 - Prob. 49PPSCh. 5.3 - Prob. 50PPSCh. 5.3 - Prob. 51PPSCh. 5.3 - Prob. 52PPSCh. 5.3 - Prob. 53PPSCh. 5.3 - Prob. 54PPSCh. 5.3 - Prob. 55PPSCh. 5.3 - Prob. 56PPSCh. 5.3 - Prob. 57PPSCh. 5.3 - Prob. 58PPSCh. 5.3 - Prob. 59PPSCh. 5.3 - Prob. 60PPSCh. 5.3 - Prob. 61PPSCh. 5.3 - Prob. 62PPSCh. 5.3 - Prob. 63HPCh. 5.3 - Prob. 64HPCh. 5.3 - Prob. 65HPCh. 5.3 - Prob. 66HPCh. 5.3 - Prob. 67HPCh. 5.3 - Prob. 68HPCh. 5.3 - Prob. 69STPCh. 5.3 - Prob. 70STPCh. 5.3 - Prob. 71STPCh. 5.3 - Prob. 72STPCh. 5.3 - Prob. 73SRCh. 5.3 - Prob. 74SRCh. 5.3 - Prob. 75SRCh. 5.3 - Prob. 76SRCh. 5.3 - Prob. 77SRCh. 5.3 - Prob. 78SRCh. 5.3 - Prob. 79SRCh. 5.3 - Prob. 80SRCh. 5.3 - Prob. 81SRCh. 5.3 - Prob. 82SRCh. 5.3 - Prob. 83SCh. 5.3 - Prob. 84SCh. 5.3 - Prob. 85SCh. 5.4 - Prob. 1GPCh. 5.4 - Prob. 2GPCh. 5.4 - Prob. 3GPCh. 5.4 - Prob. 4GPCh. 5.4 - Prob. 1CYUCh. 5.4 - Prob. 2CYUCh. 5.4 - Prob. 3CYUCh. 5.4 - Prob. 4CYUCh. 5.4 - Prob. 5CYUCh. 5.4 - Prob. 6CYUCh. 5.4 - Prob. 7CYUCh. 5.4 - Prob. 8CYUCh. 5.4 - Prob. 9CYUCh. 5.4 - Prob. 10CYUCh. 5.4 - Prob. 11CYUCh. 5.4 - Prob. 12CYUCh. 5.4 - Prob. 13CYUCh. 5.4 - Prob. 14PPSCh. 5.4 - Prob. 15PPSCh. 5.4 - Prob. 16PPSCh. 5.4 - Prob. 17PPSCh. 5.4 - Prob. 18PPSCh. 5.4 - Prob. 19PPSCh. 5.4 - Prob. 20PPSCh. 5.4 - Prob. 21PPSCh. 5.4 - Prob. 22PPSCh. 5.4 - Prob. 23PPSCh. 5.4 - Prob. 24PPSCh. 5.4 - Prob. 25PPSCh. 5.4 - Prob. 26PPSCh. 5.4 - Prob. 27PPSCh. 5.4 - Prob. 28PPSCh. 5.4 - Prob. 29PPSCh. 5.4 - Prob. 30PPSCh. 5.4 - Prob. 31PPSCh. 5.4 - Prob. 32PPSCh. 5.4 - Prob. 33PPSCh. 5.4 - Prob. 34PPSCh. 5.4 - Prob. 35PPSCh. 5.4 - Prob. 36PPSCh. 5.4 - Prob. 37PPSCh. 5.4 - Prob. 38PPSCh. 5.4 - Prob. 39PPSCh. 5.4 - Prob. 40PPSCh. 5.4 - Prob. 41PPSCh. 5.4 - Prob. 42PPSCh. 5.4 - Prob. 43PPSCh. 5.4 - Prob. 44PPSCh. 5.4 - Prob. 45PPSCh. 5.4 - Prob. 46PPSCh. 5.4 - Prob. 47HPCh. 5.4 - Prob. 48HPCh. 5.4 - Prob. 49HPCh. 5.4 - Prob. 50HPCh. 5.4 - Prob. 51HPCh. 5.4 - Prob. 52HPCh. 5.4 - Prob. 53HPCh. 5.4 - Prob. 54STPCh. 5.4 - Prob. 55STPCh. 5.4 - Prob. 56STPCh. 5.4 - Prob. 57STPCh. 5.4 - Prob. 58SRCh. 5.4 - Prob. 59SRCh. 5.4 - Prob. 60SRCh. 5.4 - Prob. 61SRCh. 5.4 - Prob. 62SRCh. 5.4 - Prob. 63SRCh. 5.4 - Prob. 64SRCh. 5.4 - Prob. 65SCh. 5.4 - Prob. 66SCh. 5.4 - Prob. 67SCh. 5.4 - Prob. 68SCh. 5.4 - Prob. 69SCh. 5.4 - Prob. 70SCh. 5.4 - Prob. 1ECh. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Prob. 5ECh. 5.4 - Prob. 6ECh. 5.4 - Prob. 7ECh. 5.4 - Prob. 8ECh. 5.4 - Prob. 9ECh. 5.4 - Prob. 10ECh. 5.4 - Prob. 11ECh. 5.4 - Prob. 12ECh. 5.4 - Prob. 13ECh. 5.4 - Prob. 1MCQCh. 5.4 - Prob. 2MCQCh. 5.4 - Prob. 3MCQCh. 5.4 - Prob. 4MCQCh. 5.4 - Prob. 5MCQCh. 5.4 - Prob. 6MCQCh. 5.4 - Prob. 7MCQCh. 5.4 - Prob. 8MCQCh. 5.4 - Prob. 9MCQCh. 5.4 - Prob. 10MCQCh. 5.4 - Prob. 11MCQCh. 5.4 - Prob. 12MCQCh. 5.4 - Prob. 13MCQCh. 5.4 - Prob. 14MCQCh. 5.4 - Prob. 15MCQCh. 5.4 - Prob. 16MCQCh. 5.4 - Prob. 17MCQCh. 5.4 - Prob. 18MCQCh. 5.4 - Prob. 19MCQCh. 5.4 - Prob. 20MCQCh. 5.4 - Prob. 21MCQCh. 5.5 - Prob. 1ECh. 5.5 - Prob. 2ECh. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - Prob. 5ECh. 5.5 - Prob. 6ECh. 5.5 - Prob. 7ECh. 5.5 - Prob. 8ECh. 5.5 - Prob. 9ECh. 5.5 - Prob. 1AGPCh. 5.5 - Prob. 1BGPCh. 5.5 - Prob. 2AGPCh. 5.5 - Prob. 2BGPCh. 5.5 - Prob. 3AGPCh. 5.5 - Prob. 3BGPCh. 5.5 - Prob. 4GPCh. 5.5 - Prob. 5AGPCh. 5.5 - Prob. 5BGPCh. 5.5 - Prob. 6AGPCh. 5.5 - Prob. 6BGPCh. 5.5 - Prob. 1CYUCh. 5.5 - Prob. 2CYUCh. 5.5 - Prob. 3CYUCh. 5.5 - Prob. 4CYUCh. 5.5 - Prob. 5CYUCh. 5.5 - Prob. 6CYUCh. 5.5 - Prob. 7CYUCh. 5.5 - Prob. 8CYUCh. 5.5 - Prob. 9CYUCh. 5.5 - Prob. 10CYUCh. 5.5 - Prob. 11CYUCh. 5.5 - Prob. 12CYUCh. 5.5 - Prob. 13CYUCh. 5.5 - Prob. 14CYUCh. 5.5 - Prob. 15CYUCh. 5.5 - Prob. 16CYUCh. 5.5 - Prob. 17CYUCh. 5.5 - Prob. 18CYUCh. 5.5 - Prob. 19CYUCh. 5.5 - Prob. 20PPSCh. 5.5 - Prob. 21PPSCh. 5.5 - Prob. 22PPSCh. 5.5 - Prob. 23PPSCh. 5.5 - Prob. 24PPSCh. 5.5 - Prob. 25PPSCh. 5.5 - Prob. 26PPSCh. 5.5 - Prob. 27PPSCh. 5.5 - Prob. 28PPSCh. 5.5 - Prob. 29PPSCh. 5.5 - Prob. 30PPSCh. 5.5 - Prob. 31PPSCh. 5.5 - Prob. 32PPSCh. 5.5 - Prob. 33PPSCh. 5.5 - Prob. 34PPSCh. 5.5 - Prob. 35PPSCh. 5.5 - Prob. 36PPSCh. 5.5 - Prob. 37PPSCh. 5.5 - Prob. 38PPSCh. 5.5 - Prob. 39PPSCh. 5.5 - Prob. 40PPSCh. 5.5 - Prob. 41PPSCh. 5.5 - Prob. 42PPSCh. 5.5 - Prob. 43PPSCh. 5.5 - Prob. 44PPSCh. 5.5 - Prob. 45PPSCh. 5.5 - Prob. 46PPSCh. 5.5 - Prob. 47PPSCh. 5.5 - Prob. 48PPSCh. 5.5 - Prob. 49PPSCh. 5.5 - Prob. 50PPSCh. 5.5 - Prob. 51PPSCh. 5.5 - Prob. 52PPSCh. 5.5 - Prob. 53PPSCh. 5.5 - Prob. 54PPSCh. 5.5 - Prob. 55PPSCh. 5.5 - Prob. 56PPSCh. 5.5 - Prob. 57PPSCh. 5.5 - Prob. 58PPSCh. 5.5 - Prob. 59PPSCh. 5.5 - Prob. 60PPSCh. 5.5 - Prob. 61PPSCh. 5.5 - Prob. 62PPSCh. 5.5 - Prob. 63PPSCh. 5.5 - Prob. 64PPSCh. 5.5 - Prob. 65PPSCh. 5.5 - Prob. 66PPSCh. 5.5 - Prob. 67PPSCh. 5.5 - Prob. 68PPSCh. 5.5 - Prob. 69PPSCh. 5.5 - Prob. 70PPSCh. 5.5 - Prob. 71PPSCh. 5.5 - Prob. 72PPSCh. 5.5 - Prob. 73PPSCh. 5.5 - Prob. 74PPSCh. 5.5 - Prob. 75PPSCh. 5.5 - Prob. 76PPSCh. 5.5 - Prob. 77PPSCh. 5.5 - Prob. 78PPSCh. 5.5 - Prob. 79HPCh. 5.5 - Prob. 80HPCh. 5.5 - Prob. 81HPCh. 5.5 - Prob. 82HPCh. 5.5 - Prob. 83HPCh. 5.5 - Prob. 84STPCh. 5.5 - Prob. 85STPCh. 5.5 - Prob. 86STPCh. 5.5 - Prob. 87STPCh. 5.5 - Prob. 88SRCh. 5.5 - Prob. 89SRCh. 5.5 - Prob. 90SRCh. 5.5 - Prob. 91SRCh. 5.5 - Prob. 92SRCh. 5.5 - Prob. 93SRCh. 5.5 - Prob. 94SRCh. 5.5 - Prob. 95SRCh. 5.5 - Prob. 96SRCh. 5.5 - Prob. 97SCh. 5.5 - Prob. 98SCh. 5.5 - Prob. 99SCh. 5.6 - Prob. 1AGPCh. 5.6 - Prob. 1BGPCh. 5.6 - Prob. 2GPCh. 5.6 - Prob. 3GPCh. 5.6 - Prob. 1CYUCh. 5.6 - Prob. 2CYUCh. 5.6 - Prob. 3CYUCh. 5.6 - Prob. 4CYUCh. 5.6 - Prob. 5CYUCh. 5.6 - Prob. 6CYUCh. 5.6 - Prob. 7CYUCh. 5.6 - Prob. 8PPSCh. 5.6 - Prob. 9PPSCh. 5.6 - Prob. 10PPSCh. 5.6 - Prob. 11PPSCh. 5.6 - Prob. 12PPSCh. 5.6 - Prob. 13PPSCh. 5.6 - Prob. 14PPSCh. 5.6 - Prob. 15PPSCh. 5.6 - Prob. 16PPSCh. 5.6 - Prob. 17PPSCh. 5.6 - Prob. 18PPSCh. 5.6 - Prob. 19PPSCh. 5.6 - Prob. 20PPSCh. 5.6 - Prob. 21PPSCh. 5.6 - Prob. 22PPSCh. 5.6 - Prob. 23PPSCh. 5.6 - Prob. 24PPSCh. 5.6 - Prob. 25PPSCh. 5.6 - Prob. 26PPSCh. 5.6 - Prob. 27PPSCh. 5.6 - Prob. 28PPSCh. 5.6 - Prob. 29PPSCh. 5.6 - Prob. 30PPSCh. 5.6 - Prob. 31PPSCh. 5.6 - Prob. 32PPSCh. 5.6 - Prob. 33PPSCh. 5.6 - Prob. 34PPSCh. 5.6 - Prob. 35PPSCh. 5.6 - Prob. 36HPCh. 5.6 - Prob. 37HPCh. 5.6 - Prob. 38HPCh. 5.6 - Prob. 39HPCh. 5.6 - Prob. 40HPCh. 5.6 - Prob. 41HPCh. 5.6 - Prob. 42HPCh. 5.6 - Prob. 43HPCh. 5.6 - Prob. 44STPCh. 5.6 - Prob. 45STPCh. 5.6 - Prob. 46STPCh. 5.6 - Prob. 47STPCh. 5.6 - Prob. 48SRCh. 5.6 - Prob. 49SRCh. 5.6 - Prob. 50SRCh. 5.6 - Prob. 51SRCh. 5.6 - Prob. 52SRCh. 5.6 - Prob. 53SRCh. 5.6 - Prob. 54SRCh. 5.6 - Prob. 55SRCh. 5.6 - Prob. 56SRCh. 5.6 - Prob. 57SRCh. 5.6 - Prob. 58SCh. 5.6 - Prob. 59SCh. 5.6 - Prob. 60SCh. 5.6 - Prob. 61SCh. 5.6 - Prob. 62SCh. 5.6 - Prob. 63SCh. 5.7 - Prob. 1AGPCh. 5.7 - Prob. 1BGPCh. 5.7 - Prob. 1CGPCh. 5.7 - Prob. 1DGPCh. 5.7 - Prob. 2GPCh. 5.7 - Prob. 3GPCh. 5.7 - Prob. 4GPCh. 5.7 - Prob. 1CYUCh. 5.7 - Prob. 2CYUCh. 5.7 - Prob. 3CYUCh. 5.7 - Prob. 4CYUCh. 5.7 - Prob. 5CYUCh. 5.7 - Prob. 6CYUCh. 5.7 - Prob. 7CYUCh. 5.7 - Prob. 8CYUCh. 5.7 - Prob. 9CYUCh. 5.7 - Prob. 10CYUCh. 5.7 - Prob. 11CYUCh. 5.7 - Prob. 12CYUCh. 5.7 - Prob. 13CYUCh. 5.7 - Prob. 14CYUCh. 5.7 - Prob. 15CYUCh. 5.7 - Prob. 16CYUCh. 5.7 - Prob. 17PPSCh. 5.7 - Prob. 18PPSCh. 5.7 - Prob. 19PPSCh. 5.7 - Prob. 20PPSCh. 5.7 - Prob. 21PPSCh. 5.7 - Prob. 22PPSCh. 5.7 - Prob. 23PPSCh. 5.7 - Prob. 24PPSCh. 5.7 - Prob. 25PPSCh. 5.7 - Prob. 26PPSCh. 5.7 - Prob. 27PPSCh. 5.7 - Prob. 28PPSCh. 5.7 - Prob. 29PPSCh. 5.7 - Prob. 30PPSCh. 5.7 - Prob. 31PPSCh. 5.7 - Prob. 32PPSCh. 5.7 - Prob. 33PPSCh. 5.7 - Prob. 34PPSCh. 5.7 - Prob. 35PPSCh. 5.7 - Prob. 36PPSCh. 5.7 - Prob. 37PPSCh. 5.7 - Prob. 38PPSCh. 5.7 - Prob. 39PPSCh. 5.7 - Prob. 40PPSCh. 5.7 - Prob. 41PPSCh. 5.7 - Prob. 42PPSCh. 5.7 - Prob. 43PPSCh. 5.7 - Prob. 44PPSCh. 5.7 - Prob. 45PPSCh. 5.7 - Prob. 46PPSCh. 5.7 - Prob. 47PPSCh. 5.7 - Prob. 48PPSCh. 5.7 - Prob. 49PPSCh. 5.7 - Prob. 50PPSCh. 5.7 - Prob. 51PPSCh. 5.7 - Prob. 52PPSCh. 5.7 - Prob. 53PPSCh. 5.7 - Prob. 54PPSCh. 5.7 - Prob. 55PPSCh. 5.7 - Prob. 56HPCh. 5.7 - Prob. 57HPCh. 5.7 - Prob. 58HPCh. 5.7 - Prob. 59HPCh. 5.7 - Prob. 60HPCh. 5.7 - Prob. 61STPCh. 5.7 - Prob. 62STPCh. 5.7 - Prob. 63STPCh. 5.7 - Prob. 64STPCh. 5.7 - Prob. 65SRCh. 5.7 - Prob. 66SRCh. 5.7 - Prob. 67SRCh. 5.7 - Prob. 68SRCh. 5.7 - Prob. 69SRCh. 5.7 - Prob. 70SRCh. 5.7 - Prob. 71SRCh. 5.7 - Prob. 72SRCh. 5.7 - Prob. 73SRCh. 5.7 - Prob. 74SCh. 5.7 - Prob. 75SCh. 5.7 - Prob. 76SCh. 5.7 - Prob. 1ECh. 5.7 - Prob. 2ECh. 5.7 - Prob. 3ECh. 5.7 - Prob. 4ECh. 5.7 - Prob. 5ECh. 5.7 - Prob. 6ECh. 5.7 - Prob. 7ECh. 5.7 - Prob. 8ECh. 5.8 - Prob. 1AGPCh. 5.8 - Prob. 1BGPCh. 5.8 - Prob. 2GPCh. 5.8 - Prob. 3AGPCh. 5.8 - Prob. 3BGPCh. 5.8 - Prob. 1CYUCh. 5.8 - Prob. 2CYUCh. 5.8 - Prob. 3CYUCh. 5.8 - Prob. 4CYUCh. 5.8 - Prob. 5CYUCh. 5.8 - Prob. 6CYUCh. 5.8 - Prob. 7CYUCh. 5.8 - Prob. 8CYUCh. 5.8 - Prob. 9CYUCh. 5.8 - Prob. 10PPSCh. 5.8 - Prob. 11PPSCh. 5.8 - Prob. 12PPSCh. 5.8 - Prob. 13PPSCh. 5.8 - Prob. 14PPSCh. 5.8 - Prob. 15PPSCh. 5.8 - Prob. 16PPSCh. 5.8 - Prob. 17PPSCh. 5.8 - Prob. 18PPSCh. 5.8 - Prob. 19PPSCh. 5.8 - Prob. 20PPSCh. 5.8 - Prob. 21PPSCh. 5.8 - Prob. 22PPSCh. 5.8 - Prob. 23PPSCh. 5.8 - Prob. 24PPSCh. 5.8 - Prob. 25PPSCh. 5.8 - Prob. 26PPSCh. 5.8 - Prob. 27PPSCh. 5.8 - Prob. 28PPSCh. 5.8 - Prob. 29PPSCh. 5.8 - Prob. 30PPSCh. 5.8 - Prob. 31PPSCh. 5.8 - Prob. 32PPSCh. 5.8 - Prob. 33PPSCh. 5.8 - Prob. 34PPSCh. 5.8 - Prob. 35PPSCh. 5.8 - Prob. 36PPSCh. 5.8 - Prob. 37PPSCh. 5.8 - Prob. 38PPSCh. 5.8 - Prob. 39PPSCh. 5.8 - Prob. 40PPSCh. 5.8 - Prob. 41PPSCh. 5.8 - Prob. 42PPSCh. 5.8 - Prob. 43PPSCh. 5.8 - Prob. 44PPSCh. 5.8 - Prob. 45PPSCh. 5.8 - Prob. 46HPCh. 5.8 - Prob. 47HPCh. 5.8 - Prob. 48HPCh. 5.8 - Prob. 49HPCh. 5.8 - Prob. 50HPCh. 5.8 - Prob. 51HPCh. 5.8 - Prob. 52STPCh. 5.8 - Prob. 53STPCh. 5.8 - Prob. 54STPCh. 5.8 - Prob. 55STPCh. 5.8 - Prob. 56SRCh. 5.8 - Prob. 57SRCh. 5.8 - Prob. 58SRCh. 5.8 - Prob. 59SRCh. 5.8 - Prob. 60SRCh. 5.8 - Prob. 61SRCh. 5.8 - Prob. 62SRCh. 5.8 - Prob. 63SRCh. 5.8 - Prob. 64SCh. 5.8 - Prob. 65SCh. 5.8 - Prob. 66SCh. 5.8 - Prob. 67SCh. 5.8 - Prob. 68SCh. 5.8 - Prob. 69SCh. 5 - Prob. 1QCCh. 5 - Prob. 2QCCh. 5 - Prob. 3QCCh. 5 - Prob. 4QCCh. 5 - Prob. 5QCCh. 5 - Prob. 6QCCh. 5 - Prob. 7QCCh. 5 - Prob. 8QCCh. 5 - Prob. 9QCCh. 5 - Prob. 10QCCh. 5 - Prob. 11QCCh. 5 - Prob. 12QCCh. 5 - Prob. 13QCCh. 5 - Prob. 14QCCh. 5 - Prob. 15QCCh. 5 - Prob. 1SGRCh. 5 - Prob. 2SGRCh. 5 - Prob. 3SGRCh. 5 - Prob. 4SGRCh. 5 - Prob. 5SGRCh. 5 - Prob. 6SGRCh. 5 - Prob. 7SGRCh. 5 - Prob. 8SGRCh. 5 - Prob. 9SGRCh. 5 - Prob. 10SGRCh. 5 - Prob. 11SGRCh. 5 - Prob. 12SGRCh. 5 - Prob. 13SGRCh. 5 - Prob. 14SGRCh. 5 - Prob. 15SGRCh. 5 - Prob. 16SGRCh. 5 - Prob. 17SGRCh. 5 - Prob. 18SGRCh. 5 - Prob. 19SGRCh. 5 - Prob. 20SGRCh. 5 - Prob. 21SGRCh. 5 - Prob. 22SGRCh. 5 - Prob. 23SGRCh. 5 - Prob. 24SGRCh. 5 - Prob. 25SGRCh. 5 - Prob. 26SGRCh. 5 - Prob. 27SGRCh. 5 - Prob. 28SGRCh. 5 - Prob. 29SGRCh. 5 - Prob. 30SGRCh. 5 - Prob. 31SGRCh. 5 - Prob. 32SGRCh. 5 - Prob. 33SGRCh. 5 - Prob. 34SGRCh. 5 - Prob. 35SGRCh. 5 - Prob. 36SGRCh. 5 - Prob. 37SGRCh. 5 - Prob. 38SGRCh. 5 - Prob. 39SGRCh. 5 - Prob. 40SGRCh. 5 - Prob. 41SGRCh. 5 - Prob. 42SGRCh. 5 - Prob. 43SGRCh. 5 - Prob. 44SGRCh. 5 - Prob. 45SGRCh. 5 - Prob. 46SGRCh. 5 - Prob. 47SGRCh. 5 - Prob. 48SGRCh. 5 - Prob. 49SGRCh. 5 - Prob. 50SGRCh. 5 - Prob. 51SGRCh. 5 - Prob. 52SGRCh. 5 - Prob. 53SGRCh. 5 - Prob. 54SGRCh. 5 - Prob. 55SGRCh. 5 - Prob. 56SGRCh. 5 - Prob. 1PTCh. 5 - Prob. 2PTCh. 5 - Prob. 3PTCh. 5 - Prob. 4PTCh. 5 - Prob. 5PTCh. 5 - Prob. 6PTCh. 5 - Prob. 7PTCh. 5 - Prob. 8PTCh. 5 - Prob. 9PTCh. 5 - Prob. 10PTCh. 5 - Prob. 11PTCh. 5 - Prob. 12PTCh. 5 - Prob. 13PTCh. 5 - Prob. 14PTCh. 5 - Prob. 15PTCh. 5 - Prob. 16PTCh. 5 - Prob. 17PTCh. 5 - Prob. 18PTCh. 5 - Prob. 19PTCh. 5 - Prob. 20PTCh. 5 - Prob. 21PTCh. 5 - Prob. 22PTCh. 5 - Prob. 23PTCh. 5 - Prob. 24PTCh. 5 - Prob. 25PTCh. 5 - Prob. 1STPCh. 5 - Prob. 2STPCh. 5 - Prob. 3STPCh. 5 - Prob. 4STPCh. 5 - Prob. 5STPCh. 5 - Prob. 6STPCh. 5 - Prob. 7STPCh. 5 - Prob. 8STPCh. 5 - Prob. 9STPCh. 5 - Prob. 10STPCh. 5 - Prob. 11STPCh. 5 - Prob. 12STPCh. 5 - Prob. 13STPCh. 5 - Prob. 14STPCh. 5 - Prob. 15STPCh. 5 - Prob. 16STPCh. 5 - Prob. 17STP
Knowledge Booster
Background pattern image
Algebra
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:PEARSON
Text book image
Contemporary Abstract Algebra
Algebra
ISBN:9781305657960
Author:Joseph Gallian
Publisher:Cengage Learning
Text book image
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Text book image
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:9780135163078
Author:Michael Sullivan
Publisher:PEARSON
Text book image
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:9780980232776
Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press
Text book image
College Algebra (Collegiate Math)
Algebra
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education
Introduction to Algebra: Using Variables; Author: Professor Dave Explains;https://www.youtube.com/watch?v=WZdZhuUSmpM;License: Standard YouTube License, CC-BY