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mathematics
precalculus

Questions and Answers of Precalculus

In Problems 101–114, expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. √4x + 3. 1 2√x - 5 +
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 14 + 6x - x²
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. x6 + 2x³ + 1
In Problems 97–106, simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, assume that the base is not 0. 2 4x-² (yz)-¹ 2³x4y
In Problems 101–114, expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. (x + 1)¹/3 + x + ²(x (x +
In Problems 97–106, simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, assume that the base is not 0. 5x-2 бу-2 -3
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. x7 - x5
In Problems 101–114, expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. 3/8x + 1 33√(x -
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. X5 sx - 8x
In Problems 91 – 106, find the quotient and the remainder. Check your work by verifying that (Quotient )(Divisor ) + Remainder = Dividendx3 − a3 divided by x − a
During summer months in 2022, Omaha Public Power District charged residential customers a monthly service charge of $30, plus a usage charge of 10.25 ¢ per kilowatt hour (kWh). If one customer’s
In Problems 91 – 106, find the quotient and the remainder. Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividendx5 − a5 divided by x − a
The village of Oak Lawn charges homeowners $24.99 per quarter-year for sewer usage, plus $0.40 per 1000 gallons of water metered. In 2022, one homeowner’s quarterly bill ranged from a high of
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 16x² + 24x + 9
In Problems 101–114, expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. √1 + x - x 1 2√1 + x 1 +
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 9x² 24x + 16
In Problems 101–114, expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. 2.x 2√x² + 1 √x²
In Problems 101–114, expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. (x + 4)¹/² - 2x(x +
In your Economics 101 class, you have scores of 68, 82, 87, and 89 on the first four of five tests. To get a grade of B, the average of the first five test scores must be greater than or equal to 80
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 5+ 16x16x²
The markup over dealer’s cost of a new car ranges from 12% to 18%. If the sticker price is $18,000, over what range will the dealer’s cost vary?
In Problems 101–114, expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. (9-x²) ¹/2 + x²
A standard intelligence test has an average score of 100. According to statistical theory, of the people who take the test, the 2.5% with the highest scores will have scores of more than 1.96σ above
If a < b, Show thatThe numberis called the arithmetic mean of a and b. a < a+b 2 < b.
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 5 + 11x 16x²
In Problems 101–114, expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. x2 (x² - 1)¹/2 - (x² - 1)
Refer to Problem 111. Show that the arithmetic mean of a and b is equidistant from a and b.Data from problem 111If a The numberis called the arithmetic mean of a and b. a < a+b 2 < b.
In Problems 101–114, expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. t + z.x 2/1-(t + 2x) z* = 2/1
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 4y² - 16y + 15
Do you prefer adding two polynomials using the horizontal method or the vertical method? Write a brief position paper defending your choice.
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 9y² + 9y - 4
In Problems 101–114, expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. 1 +
For food products to be labeled “light,” the U.S. Food and Drug Administration requires that the altered product must contain either at least one-third fewer calories than the regular product or
In Problems 101–114, expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. x = -1, x 1 z (1-x²)
In Problems 107–118, find the value of each expression if x = 2 and y = −1. -2 X
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 18x²9x4
Refer to Problems 111 and 113. Show that the geometric mean of a and b is less than the arithmetic mean of a and b.Data from problem 113 Data from problem 111 a < a+b 2 < b.
In Problems 107–118, find the value of each expression if x = 2 and y = −1. 2 (√x)²
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 4 14x² 8x4 -
In Problems 107–118, find the value of each expression if x = 2 and y = −1. √x² + y² 2 2
In Problems 115–124, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. ·3(x- (x + 1)¹/2 x ≥ −1 2 (x + 1)³/2 + x.
If 0 < a < b, show that a < √ab < b. The number √ab is called the geometric mean of a and b.
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. x(x + 3) 6(x + 3)
In Problems 115–124, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. 4 (x² + 4)4/³ + x · 3/(x² + 4)¹/³ . 2x
For 0 < a < b, let h be defined byShow that a < h < b. The number h is called the harmonic mean of a and b. 1/12 = 1/2 ( ²12 + ² ) h b
Refer to Problems 111, 113, and 115. Show that the harmonic mean of a and b equals the geometric mean squared divided by the arithmetic mean.Data from problem 111is called the arithmetic mean of a
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 5(3x7) + x(3x - 7)
In Problems 115–124, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. 6x1/2(x² + x) - 8x3/2 - 8x¹/2 x ≥ 0
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. (x + 2)² = 5(x + 2)
In Problems 115–124, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. 6x1/2 (2x + 3) + x³/2.8 x ≥ 0
In Problems 115–124, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. 3(x² + 4)4/3+x. 4(x² + 4)¹/³ - 2x
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. (x - 1)²2(x - 1)
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. (3x - 2)3 - 27
In Problems 107–118, find the value of each expression if x = 2 and y = −1.xy
The inequality x2 + 1 < −5 has no real solution. Explain why.
In Problems 107–118, find the value of each expression if x = 2 and y = −1.yx
In Problems 115–124, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. 2x (3x + 4)4/³ + x².4(3x + 4)¹/³
How would you explain to a fellow student the underlying reason for the multiplication properties for inequalities ? That is, the sense (direction) of an inequality remains the same if each side is
Find the value of the expression 4x3 + 3x2 − x + 2 if x = 1. What is the value if x = 2?
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. (5x+1)3 − 1
In Problems 115–124, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. 4(3x + 5)¹/³(2x + 3) ³/2 + 3(3x + 5) 4/3 (2x
What is the value of (666)4 -? 4 (222)
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 3(x² + 10x + 25) - 4(x + 5)
In Problems 115–124, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. 6(6x + 1)¹/3 (4x − 3)³/2 + 6(6x + 1)4/³
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. x³ + 2x² x - 2
In Problems 115–124, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. 8x¹/3 - 4x-2/3 0 x
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 7(x² - 6x + 9) + 5(x-3)
In Problems 115–124, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. 3 3.x-1/2 + x1/2 0
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. x3 - 3x² - x + 3
What is the value of (0.1)3 (20)3?
In Problems 123–130, use a calculator to evaluate each expression. Round your answer to three decimal places.(8.2)6
In Problems 123–130, use a calculator to evaluate each expression. Round your answer to three decimal places.(3.7)5
In Problems 123–130, use a calculator to evaluate each expression. Round your answer to three decimal places.(6.1)−3
In Problems 125–132, use a calculator to approximate each radical. Round your answer to two decimal places. √2
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. I- x + √x - DX
In Problems 125–132, use a calculator to approximate each radical. Round your answer to two decimal places. √√7 L
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. I + x + √x + x
In Problems 125–132, use a calculator to approximate each radical. Round your answer to two decimal places. درا
In Problems 125–132, use a calculator to approximate each radical. Round your answer to two decimal places. 2+√3 3-√5
In Problems 125–132, use a calculator to approximate each radical. Round your answer to two decimal places. 5
In Problems 125–132, use a calculator to approximate each radical. Round your answer to two decimal places. √5-2 √2 + 4
A Shell station stores its gasoline in underground tanks that are right circular cylinders lying on their sides. See the illustration. The volume V of gasoline in the tank (in gallons) is given by
In Problems 123–130, use a calculator to evaluate each expression. Round your answer to three decimal places.(2.2)−5
In Problems 125–132, use a calculator to approximate each radical. Round your answer to two decimal places. 2√3 - 34 √2
In Problems 125–132, use a calculator to approximate each radical. Round your answer to two decimal places. 33/√/5 -√2 √3
The final velocity v of an object in feet per second (ft/ sec) after it slides down a frictionless inclined plane of height h feet iswhere v0 is the initial velocity (in ft/sec) of the object.(a)
In Problems 127–136, expressions that occur in calculus are given. Factor each expression completely. 4(x + 5)³(x - 1)² + (x + 5)4.2(x - 1)
In Problems 123–130, use a calculator to evaluate each expression. Round your answer to three decimal places.(−2.8)6
In Problems 127–136, expressions that occur in calculus are given. Factor each expression completely. 2(3x - 5) 3(2x + 1)³ + (3x - 5)² - 3(2x + 1)².2
The period T, in seconds, of a pendulum of length l, in feet, may be approximated using the formulaIn Problems 135 and 136, express your answer both as a square root and as a decimal.Find the period
In Problems 123–130, use a calculator to evaluate each expression. Round your answer to three decimal places.−(2.8)6
In Problems 127–136, expressions that occur in calculus are given. Factor each expression completely. (4x - 3)² + x2(4x - 3). 4 2
In Problems 127–136, expressions that occur in calculus are given. Factor each expression completely. 3(4x + 5)².4(5x + 1)² + (4x + 5)³.2(5x + 1).5
In Problems 123–130, use a calculator to evaluate each expression. Round your answer to three decimal places.(−8.11)−4
In Problems 127–136, expressions that occur in calculus are given. Factor each expression completely. 3x²(3x + 4)2 + x3 . 2(3x + 4). 3
The period T, in seconds, of a pendulum of length l, in feet, may be approximated using the formulaIn Problems 135 and 136, express your answer both as a square root and as a decimal.Find the period
In Problems 123–130, use a calculator to evaluate each expression. Round your answer to three decimal places.−(8.11)−4
In Problems 19–32, find the distance d between the points P1 and P2. УА 2FP2 = (2, 1) P1 = (0,0) -2 -1 2 x X
Choose the expression that equals the distance between two points (x1, y1) and (x2, y2). (a) √√(x₂-x₂)² + (y₁ - y₁)² (b) √√(x₂ + x₁)² = (y₂ + ₁)² (c) √√(x₂-x₁)² =
In Problems 19–32, find the distance d between the points P1 and P2. P2 = (-2, 1) -2 УА 2 -1 _P1 = (0, 0) 2 x

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