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College Algebra 7th Edition Robert F Blitzer - Solutions
In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. +² 12x + 36 4x - 24
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s).x2 - 7x + 4, for x = 8
Fill in each blank so that the resulting statement is true.A positive number is written in scientific notation when it is expressed in the form a × 10n, where a is __________ and n is a/an______ .
Fill in each blank so that the resulting statement is true.The conjugate of 7 + 13 is _______.
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. V25 – V16
The set {c, -4, -3, -2, -1, 0, 1, 2, 3, 4, c} is called the set of_______ .
Fill in each blank so that the resulting statement is true.To multiply 7x3(4x5 - 8x2 + 6), use the________ property to multiply each term of the trinomial_______ by the monomial _________.
In Exercises 1–25, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate.(2x - 5) - (x2 - 3x + 1)
In Exercises 9–11, rewrite each expression without absolute value bars.|-103|
Fill in each blank so that the resulting statement is true.A rational expression whose numerator or denominator or both contain rational expressions is called a/an________ rational expression or a/an________ fraction.
In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree.(-6x3 + 5x2 - 8x + 9) + (17x3 + 2x2 - 4x - 13)
In Exercises 1–18, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. V/16x4
Evaluate each exponential expression in Exercises 1–22. -3⁰
In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. x² - 8x + 16 3x - 12
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s).4 + 5(x - 7)3, for x = 9
In Exercises 9–11, rewrite each expression without absolute value bars. |√2-1|
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. V144+ V25
Fill in each blank so that the resulting statement is true.True or false: 4 × 103 is written in scientific notation.______
Fill in each blank so that the resulting statement is true.We rationalize the denominator of 5/√10 - √2 by multiplying the numerator and denominator by _______.
In Exercises 1–10, factor out the greatest common factor.x2(x - 3) + 12(x - 3)
In Exercises 1–25, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate.(2x - 5)(x2 - 3x + 1)
Fill in each blank so that the resulting statement is true.To multiply (5x + 3)(x2 + 8x + 7), begin by multiplying each term of x2 + 8x + 7 by _________. Then multiply each term of x2 + 8x + 7 by _________. Then combine_________ terms.
In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree.(-7x3 + 6x2 - 11x + 13) + (19x3 - 11x2 + 7x - 17)
In Exercises 1–18, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. x² + 2x - 3 - 3x + 2 2 X
Evaluate each exponential expression in Exercises 1–22. -90
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s).6 + 5(x - 6)3, for x = 8
In Exercises 9–11, rewrite each expression without absolute value bars. 3-√17
In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. y2 + 7y - 18 y2 - 3у + 2
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √(-13)²
Fill in each blank so that the resulting statement is true.True or false: 40 × 102 is written in scientific notation.______
In Exercises 1–10, factor out the greatest common factor.x2(2x + 5) + 17(2x + 5)
Evaluate each exponential expression in Exercises 1–22. -3⁰
In Exercises 1–25, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate.x3 + x3 - x3 . x3
Fill in each blank so that the resulting statement is true.When using the FOIL method to find (x + 7)(3x + 5), the product of the first terms is _______, the product of the outside terms is __________, the product of the inside terms is ________, and the product of the last terms is _________.
Fill in each blank so that the resulting statement is true.In the expression 3√64, the number 3 is called the______ and the number 64 is called the ________.
In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree.(17x3 - 5x2 + 4x - 3) - (5x3 - 9x2 - 8x + 11)
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s).x2 - 3(x - y), for x = 8 and y = 2
In Exercises 11–16, factor by grouping.x3 - 2x2 + 5x - 10
In Exercises 1–18, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. 5 x 10-6 20 x 10-8 (Express the answer in scientific notation.)
Fill in each blank so that the resulting statement is true.(A + B)(A - B) = ________. The product of the sum and difference of the same two terms is the square of the first term___________ the square of the second term.
In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. y² - 4y - 5 y² + 5y + 4
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. 2 √(-17)²
Evaluate each exponential expression in Exercises 1–22. 2-6
In Exercises 1–25, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate.(9a - 10b)(2a + b)
In Exercises 1–25, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. {a, c, d, e} U {c, d, f, h}
Express the distance between the numbers -17 and 4 using absolute value. Then evaluate the absolute value.
In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree.(18x4 - 2x3 - 7x + 8) - (9x4 - 6x3 - 5x + 7)
Fill in each blank so that the resulting statement is true.5√-32 = -2 because _______= -32.
In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. x² + 12x + 36 x² - 36
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 5(x + 2) 14 2x for x = 10
In Exercises 11–16, factor by grouping.x3 - 3x2 + 4x - 12
Evaluate each exponential expression in Exercises 1–22 2².23
Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. V50
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s).x2 - 4(x - y), for x = 8 and y = 3
In Exercises 1–18, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate.(2x - 5)(x2 - 4x + 3)
In Exercises 13–18, state the name of the property illustrated.3 + 17 = 17 + 3
Fill in each blank so that the resulting statement is true.(A + B)2 = _________. The square of a binomial sum is the first term_________ plus 2 times the__________ plus the last term __________.
In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree.(5x2 - 7x - 8) + (2x2 - 3x + 7) - (x2 - 4x - 3)
Fill in each blank so that the resulting statement is true.If n is odd, n√an = _______. If n is even, n√an = _______.
In Exercises 11–16, factor by grouping.x3 - x2 + 2x - 2
Fill in each blank so that the resulting statement is true.a1/n = _____ .
In Exercises 1–18, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate.(5x + 3y)2
Fill in each blank so that the resulting statement is true.(A - B)2 = ___________. The square of a binomial difference is the first term squared_________ 2 times the__________ , ________ the last term squared.
Fill in each blank so that the resulting statement is true.If a ≠ 0, the degree of axnym is __________.
In Exercises 1–25, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. {a, c, d, e) {c, d, f, h}
In Exercises 13–18, state the name of the property illustrated. (6.3) 9 6 (3.9) =
In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. x² 14x + 49 x² - 49 X
Evaluate each exponential expression in Exercises 1–22. 33.32
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 7(x − 3) 2x - 16 for x = 9
Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √27
In Exercises 1–18, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. 2x + 8 x - 3 x2 +5x+4 x² - 9 X
In Exercises 13–18, state the name of the property illustrated. √3(√5 + √3)=√15 + 3
In Exercises 1–25, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. (3x²y³ − xy + 4y²) − (−2x²y³ − 3xy + 5y²) -
In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree.(8x2 + 7x - 5) - (3x2 - 4x) - (-6x3 - 5x2 + 3)
Evaluate each exponential expression in Exercises 1–22. (2²)³
In Exercises 15–32, multiply or divide as indicated. x 2 3x + 9 2x 2x + 6 4
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 2x + 3y x + 1 for x = -2 and y = 4
Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √45x² 2
In Exercises 1–25, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. 13 24x²y¹3 -2x³y -2
In Exercises 11–16, factor by grouping.x3 + 6x2 - 2x - 12
In Exercises 1–18, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. x x + 3 + 5 x-3
Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √125x²
In Exercises 13–18, state the name of the property illustrated. (6.9) 22 (6.9) •
Evaluate each exponential expression in Exercises 1–22. (33)²
In Exercises 1–18, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. 2x + 3 x² 2 ² - 7x + 12 2 x - 3
In Exercises 15–32, multiply or divide as indicated. 6x + 9 3x - 15 x -5 4x + 6
In Exercises 15–58, find each product.(x + 1)(x2 - x + 1)
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 2x + y xy - 2x for x = -2 and y = 4
Fill in each blank so that the resulting statement is true.163/4 = (4√16)3 = (__)3 = ____ .
In Exercises 13–18, state the name of the property illustrated. √3(√5 + √3)=(√5 + √3)√3
In Exercises 15–32, multiply or divide as indicated. x² - 9 करे x 2 – 3x x2 + x – 12
In Exercises 11–16, factor by grouping.3x3 - 2x2 - 6x + 4
In Exercises 1–25, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. -x-5y4. (18x-²y-1) 3
The formulaexpresses the relationship between Fahrenheit temperature, F, and Celsius temperature, C. In Exercises 17–18, use the formula to convert the given Fahrenheit temperature to its equivalent temperature on the Celsius scale.50°F C = 5 -(F - 32)
In Exercises 15–58, find each product.(x + 5)(x2 - 5x + 25)
In Exercises 1–18, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. 1 1 XI 1 3
Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √2x. V6x
Evaluate each exponential expression in Exercises 1–22. 00
In Exercises 1–25, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. 12. x
In Exercises 13–18, state the name of the property illustrated. (3.7) + (4.7) = (4.7) + (3.7)
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