Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition

10th Edition

ISBN: 9780134673301

Author: Waits, Foley, Kennedy, Bock Demana

Publisher: PEARSON

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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Expert Solution & Answer

Chapter P.1, Problem 45E

Solution

a.

The algebraic property illustrated by the equation 3xy=3xy .

Associate property of multiplication.

Given:

The equation is, 3xy=3xy

Concept Used:

Associative property of multiplication a⋅b⋅c=a⋅b⋅c .

Calculation:

Note that the given expression 3xy=3xy is of the form of 3⋅x⋅y=3⋅x⋅y .

Hence, it illustrates the associative property of multiplication.

b.

The algebraic property illustrated by the equation a2b=ba2 .

Commutative property of multiplication.

Given:

The equation is, a2b=ba2

Concept Used:

Commutative property of multiplication a⋅b=b⋅a .

Calculation:

Note that the given expression a2b=ba2 is of the form of a2⋅b=b⋅a2 .

Hence, it illustrates the commutative property of multiplication.

c.

The algebraic property illustrated by the equation a2b+−a2b=0 .

Additive inverse property

Given:

The equation is, a2b+−a2b=0

Concept Used:

The additive inverse of a number n is given by the same number with opposite sign and the sum of the number and its additive inverse is 0, that is, n+−n=0 .

Calculation:

Note that the given expression a2b+−a2b=0 is of the form of n+−n=0 .

Hence, it illustrates the additive inverse property.

d.

The algebraic property illustrated by the equation x+32+0=x+32 .

Additive identity property

Given:

The equation is, x+32+0=x+32

Concept Used:

The number 0 added to any number does not change the number. It is known as additive identity.

Calculation:

Note that in the given expression x+32+0=x+32 , 0 added to the expression on the left side and it remains unchanged.

Hence, it illustrates the additive identity property.

e.

The algebraic property illustrated by the equation ax+y=ax+ay .

Distributive property of multiplication over addition

Given:

The equation is, ax+y=ax+ay

Concept Used:

Distributive property, a⋅b+c=a⋅b+a⋅c .

Calculation:

Note that the given expression ax+y=ax+ay is of the form of a⋅b+c=a⋅b+a⋅c .

Hence, it illustrates the distributive property of multiplication over addition.

Chapter P.1, Problem 44E

Chapter P.1, Problem 46E

Chapter P Solutions

Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition

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Solution Summary: The author illustrates the algebraic property illustrated by the equation (3x)y=3 (xy ) and the commutative property of multiplication.

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Chapter P Solutions