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College Algebra 7th Edition Robert F Blitzer - Solutions
In Exercises 103–110, insert either , or = in the shaded area to make a true statement. |-2| 4 17 4 17
In Exercises 109–110, evaluate each expression. V 917A + 000TAA + 6^ + 69T^^
In one short sentence, five words or less, explain whatdoes to each number x. + + + 1 .4
In Exercises 109–111, simplify each rational expression. Also, list all numbers that must be excluded from the domain. x² + 2x² X x + 2
In Exercises 109–111, simplify each rational expression. Also, list all numbers that must be excluded from the domain. x² + 3x - 18 x² - 36 2
In Exercises 107–114, simplify each exponential expression.Assume that variables represent nonzero real numbers. (3x4yz-7)(3x)-3
In Exercises 111–120, use the order of operations to simplify each expression. 82 16 2².43 =
In Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (49x-²y4) 2(xy²)
In Exercises 107–114, simplify each exponential expression.Assume that variables represent nonzero real numbers. x3y4-5 -2 -3. -4--5 y
In Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (18_و) )g( ' (x6y 3) 6
In Exercises 107–114, simplify each exponential expression.Assume that variables represent nonzero real numbers. x41526 -5 -6 'y Z N -4
In Exercises 109–111, simplify each rational expression. Also, list all numbers that must be excluded from the domain. x² + 2x x² + 4x + 4 2
In Exercises 103–114, factor completely.x4 - 10x2 y2 + 9y4
In Exercises 107–110, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.(x + 1)2 = x2 + 1
In Exercises 111–120, use the order of operations to simplify each expression. 10² 100 ÷ 5².2 - 3 =
In Exercises 112–114, multiply or divide as indicated. x² + 6x + 9 x + 3 x² - 4 2 x-2
In Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. X X مادر inl 314 -6
Exercises 110–112 will help you prepare for the material covered in the first section of the next chapter.If y = 4 - x2, find the value of y that corresponds to values of x for each integer starting with -3 and ending with 3.
In Exercises 103–114, factor completely.(x - y)4 - 4(x - y)2
In Exercises 107–110, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.Suppose a square garden has an area represented by 9x2 square feet. If one side is made 7 feet longer and the other side is made 2 feet
In Exercises 111–120, use the order of operations to simplify each expression. 5.2 -3² 2 [3²-(-2)]²
In Exercises 111–113, perform the indicated operations.[(7x + 5) + 4y][(7x + 5) - 4y]
In Exercises 107–114, simplify each exponential expression.Assume that variables represent nonzero real numbers. (2-¹x-²y-¹)-²(2x-4y³)²(16x-³y³)0 -5,2 (2x-³y=-3)²
In Exercises 112–114, multiply or divide as indicated. 6x + 2 x²-1 -+-+ 3x² + x x-1
Exercises 110–112 will help you prepare for the material covered in the first section of the next chapter.If y = 1 - x2, find the value of y that corresponds to values of x for each integer starting with -3 and ending with 3.
In Exercises 111–120, use the order of operations to simplify each expression. 10+2+3.4 (12-3.2)²
In Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. x²y 7-4 4 5 y 4
America is getting older. The graph shows the projected elderly U.S. population for ages 65–84 and for ages 85 and older.The formula E = 5.8√x + 56.4 models the projected number of elderly Americans ages 65–84, E, in millions, x years after 2020.a. Use the formula to find the projected
In Exercises 103–114, factor completely.(x + y)4 - 100(x + y)2
In Exercises 112–114, multiply or divide as indicated. r2 – 5x – 24 x² - x - 12 2 ÷ x² - 10x + 16 x² + x = 6 2
The popular comic strip FoxTrot follows the off-the-wall lives of the Fox family. Youngest son Jason is forever obsessed by his love of math. In the math-themed strip shown at the top of the next column, Jason shares his opinion in a coded message about the mathematical abilities of his sister
Exercises 110–112 will help you prepare for the material covered in the first section of the next chapter.If y =|x + 1|, find the value of y that corresponds to values of x for each integer starting with -4 and ending with 2.
In Exercises 107–114, simplify each exponential expression.Assume that variables represent nonzero real numbers. (2-1x-3y-1)-2(2x®y4)-2(9x3y-3)0 -4-6,2 (2x y
In Exercises 115–118, add or subtract as indicated. 2x - 7 x² - 9 x - 10 2 x² - 9
In Exercises 111–113, perform the indicated operations.[(3x + y) + 1]2
The bar graph shows the total amount Americans paid in federal taxes, in trillions of dollars, and the U.S. population, in millions, from 2012 through 2015. Exercises 115–116 are based on the numbers displayed by the graph.a. In 2015, the United States government collected $3.18 trillion in
Express the area of the plane figure shown as a polynomial in standard form. x x + 3 x-1
In Exercises 103–114, factor completely.2x2 - 7xy2 + 3y4
In Exercises 111–113, perform the indicated operations.(xn + 2)(xn - 2) - (xn - 3)2
In Exercises 115–118, add or subtract as indicated. 3x x + 2 X x - 2
Exercises 115–117 will help you prepare for the material covered in the next section. In each exercise, replace the boxed question mark with an integer that results in the given product. Some trial and error may be necessary. (x-2)(x ? (x - 12) = x² - 14x + 24
The bar graph shows the total amount Americans paid in federal taxes, in trillions of dollars, and the U.S. population, in millions, from 2012 through 2015. Exercises 115–116 are based on the numbers displayed by the graph.a. In 2014, the United States government collected $3.02 trillion in
The early Greeks believed that the most pleasing of all rectangles were golden rectangles, whose ratio of width to height isThe Parthenon at Athens fits into a golden rectangle once the triangular pediment is reconstructed.Rationalize the denominator of the golden ratio. Then use a calculator and
In Exercises 103–114, factor completely.3x2 + 5xy2 + 2y4
In Exercises 111–120, use the order of operations to simplify each expression. 2(-2) - 4(-3) 5-8
In Exercises 115–118, add or subtract as indicated. X x² 2 - 9 2 x² x-1 5x+6
Exercises 115–117 will help you prepare for the material covered in the next section. In each exercise, replace the boxed question mark with an integer that results in the given product. Some trial and error may be necessary. (4x + 1)(2x ? = - - 8x² 10x - 3 -
In Exercises 111–120, use the order of operations to simplify each expression.8 - 3[-2(2 - 5) - 4(8 - 6)]
In Exercises 115–118, add or subtract as indicated. 4x 1 - 2x² + 5x - 3 x + 3 6x²+x-2
In Exercises 111–120, use the order of operations to simplify each expression.8 - 3[-2(5 - 7) - 5(4 - 2)]
In Exercises 111–120, use the order of operations to simplify each expression. (ε-)ç - (†-)9 9 - 10
In Exercises 117–120,a. Write an expression for the area of the shaded region.b. Write the expression in factored form. 2 2 2 2 3x- 2 12 2 2 3x
Your computer store is having an incredible sale. The price on one model is reduced by 40%. Then the sale price is reduced by another 40%. If x is the computer’s original price, the sale price can be modeled by (x - 0.4x) - 0.4(x - 0.4x).a. Factor out (x - 0.4x) from each term. Then simplify the
In Exercises 117–120,a. Write an expression for the area of the shaded region.b. Write the expression in factored form. 3 3 3 نیا 3 -7x- 3 73 3 3 7x
In Exercises 119–121, simplify each complex rational expression. 1 X 1 3 2 x 6
In Exercises 111–120, use the order of operations to simplify each expression. (56)²2|37| 89 3.5²
In Exercises 111–120, use the order of operations to simplify each expression. 12 ÷ 3.5|2² + 3²1 7+3-6²
The perimeter, P, of a rectangle with length l and width w is given by the formula P = 2l + 2w. The area, A, is given by the formula A = lw. In Exercises 119–120, use these formulas to find the perimeter and area of each rectangle. Express answers in simplified radical form. Remember that
Refer to the Blitzer Bonus on page 32. Use scientific notation to verify any two of the bulleted items on ways to spend $1 trillion.Blitzer Bonus Blitzer Bonus | Seven Ways to Spend $1
We have seen that the 2016 U.S. national debt was $18.9 trillion. In Exercises 117–118, you will use scientific notation to put a number like 18.9 trillion in perspective.a. Express 18.9 trillion in scientific notation.b. Four years of tuition, fees, and room and board at a public U.S. college
Your local electronics store is having an end-of-the-year sale. The price on a plasma television had been reduced by 30%. Now the sale price is reduced by another 30%. If x is the television’s original price, the sale price can be modeled by (x - 0.3x) - 0.3(x - 0.3x).a. Factor out (x - 0.3x)
In Exercises 119–121, simplify each complex rational expression. 3+ 1 12 X 16 2 X²
The perimeter, P, of a rectangle with length l and width w is given by the formula P = 2l + 2w. The area, A, is given by the formula A = lw. In Exercises 119–120, use these formulas to find the perimeter and area of each rectangle. Express answers in simplified radical form. Remember that
In Exercises 117–120,a. Write an expression for the area of the shaded region.b. Write the expression in factored form. y | -x- x + y
We have seen that the 2016 U.S. national debt was $18.9 trillion. In Exercises 117–118, you will use scientific notation to put a number like 18.9 trillion in perspective.a. Express 18.9 trillion in scientific notation.b. Each year, Americans spend $254 billion on summer vacations. Express this
In Exercises 119–121, simplify each complex rational expression. 3 3 + 1 x + 3 1 x + 3
In 2012, the United States government spent more than it had collected in taxes, resulting in a budget deficit of $1.09 trillion.a. Express 1.09 trillion in scientific notation.b. There are approximately 32,000,000 seconds in a year. Write this number in scienfic notation.c. Use your answers from
In Exercises 121–122, find the formula for the volume of the region outside the smaller rectangular solid and inside the larger rectangular solid. Then express the volume in factored form. a b b a 4a
In Exercises 117–120,a. Write an expression for the area of the shaded region.b. Write the expression in factored form. X X y y X x y
In Exercises 121–122, find the formula for the volume of the region outside the smaller rectangular solid and inside the larger rectangular solid. Then express the volume in factored form. a b a b a За
Explain how to add V3+ V12.
Explain how to simplify V10. V5.
Describe what it means to rationalize a denominator. Use both in your explanation. 1 √5 and 1 5 + √5
The maximum heart rate, in beats per minute, that you should achieve during exercise is 220 minus your age:The following bar graph shows the target heart rate ranges for four types of exercise goals. The lower and upper limits of these ranges are fractions of the maximum heart rate, 220 - a.
In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number.A number decreased by the sum of the number and four
Describe what it means to raise a number to a power. In your description, include a discussion of the difference between -52 and (-5)2.
What difference is there in simplifying (-5)³ and (-5)4?
The maximum heart rate, in beats per minute, that you should achieve during exercise is 220 minus your age:The following bar graph shows the target heart rate ranges for four types of exercise goals. The lower and upper limits of these ranges are fractions of the maximum heart rate, 220 - a.
In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number.A number decreased by the difference between eight and the number
Why must a and b represent nonnegative numbers when we write Is it necessary to use this restriction in the case of Va. Vb = Vab?
Explain the product rule for exponents. Use 23 · 25 in your explanation.
The bar graph shows the average cost of tuition and fees at private four-year colleges in the United States.The formulamodels the average cost of tuition and fees, T, at private U.S. colleges for the school year ending x years after 2000. Use this information to solve Exercises 131–132.a. Use the
In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number.Six times the product of negative five and a number
The bar graph shows the average cost of tuition and fees at private four-year colleges in the United States.The formulamodels the average cost of tuition and fees, T, at private U.S. colleges for the school year ending x years after 2000. Use this information to solve Exercises 131–132.a. Use the
Explain the power rule for exponents. Use (32)4 in your explanation.
Using an example, explain how to factor out the greatest common factor of a polynomial.
In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number.Ten times the product of negative four and a number
In Exercises 129–132, determine whether each statement makes sense or does not make sense, and explain your reasoning.The joke in this Peanuts cartoon would be more effective if Woodstock had rationalized the denominator correctly in the last frame. YOU'RE LUCKY, DO YOU KNOW THAT, BIRD?
Explain the quotient rule for exponents. Use 58/52 in your explanation.
Suppose that a polynomial contains four terms. Explain how to use factoring by grouping to factor the polynomial.
In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number.The difference between the product of five and a number and twice the number
What does am/n mean?
Why is (-3x2)(2x-5) not simplified? What must be done to simplify the expression?
Explain how to factor 3x2 + 10x + 8.
In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number.The difference between the product of six and a number and negative two times the number
Describe the kinds of numbers that have rational fifth roots.
How do you know if a number is written in scientific notation?
Explain how to factor the difference of two squares. Provide an example with your explanation.
In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number.The difference between eight times a number and six more than three times the number
Explain how to convert from scientific to decimal notation and give an example.
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