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mathematics
precalculus

Questions and Answers of Precalculus

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
In Problems 19–32, find the distance d between the points P1 and P2. P2 = (-2, 2) -2 YA 2 가 P = (1, 1) 2 x
In Problems 19–32, find the distance d between the points P1 and P2. P₁ = (-1, 1) -2 YA 2 -1 P₂=(2, 2) 2 X
Give an example to show that √a2 is not equal to a. Use it to explain why √a2 = |a|.
Show that x2 + 4 is prime.
Show that x2 + x + 1 is prime.
On the real number line, the origin is assigned the number _______.
If − 3 and 5 are the coordinates of two points on the real number line, the distance between these points is ________.
If 3 and 4 are the legs of a right triangle, the hypotenuse is_________.
Which of the following statements is true for a point (x, y) that lies in quadrant III?(a) Both x and y are positive.(b) Both x and y are negative.(c) x is positive, and y is negative.(d) x is
In Problems 19–32, find the distance d between the points P1 and P2.P1 = (3, −4); P2 = (5, 4)
In Problems 19–32, find the distance d between the points P1 and P2.P1 = (−7, 3); P2 = (4, 0)
The figure illustrates the net sales growth of Costco Wholesale Corporation from 2017 through 2021. Use the midpoint formula to estimate the net sales of Costco Wholesale Corporation in 2019. How
In Problems 19–32, find the distance d between the points P1 and P2.P1 = (−1, 0); P2 = (2, 4)
In Problems 39–46, find the midpoint of the line segment joining the points P1 and P2.P1 = (−1, 4); P2 = (8, 0)
In Problems 19–32, find the distance d between the points P1 and P2.P1 = (2, −3); P2 = (4, 2)
In Problems 19–32, find the distance d between the points P1 and P2.P1 = (−4, −3); P2 = (6, 2)
In Problems 39–46, find the midpoint of the line segment joining the points P1 and P2.P1 = (3, −4); P2 = (5, 4)
Verify that the points (0, 0), (a, 0), andare the vertices of an equilateral triangle. Then show that the midpoints of the three sides are the vertices of a second equilateral triangle. 2 DEN D
In Problems 39–46, find the midpoint of the line segment joining the points P1 and P2.P1 = (2, −3); P2 = (4, 2)
Suppose that A = (2, 5) are the coordinates of a point in the xy-plane.(a) Find the coordinates of the point if A is shifted 3 units to the left and 4 units down.(b) Find the coordinates of the point
Plot the points A = (−1, 8) and M = (2, 3) in the xy-plane. If M is the midpoint of a line segment AB, find the coordinates of B.
A Ford Focus car and a Freightliner Cascadia truck leave an intersection at the same time. The Focus heads east at an average speed of 60 miles per hour, while the Cascadia heads south at an average
Find the midpoint of each diagonal of a square with side of length s. Draw the conclusion that the diagonals of a square intersect at their midpoints. Use (0, 0), (0, s), (s, 0), and (s, s) as the
Poverty thresholds are determined by the U.S. Census Bureau. A poverty threshold represents the minimum annual household income for a family not to be considered poor. In 2013, the poverty threshold
A point P is equidistant from (−5, 1) and (4, −4). Find the coordinates of P if its y- coordinate is twice its x- coordinate.
For any parallelogram, prove that the sum of the squares of the lengths of the sides equals the sum of the squares of the lengths of the diagonals. Use (0, 0), (a, 0), (a + b, c), and (b, c) as the
In Problems 77–92, simplify each expression. 64-2/3 125,
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. -1 0 < (2x - 4)-¹ 를
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 15 + 2x - x²
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 0 < X V 2 3
In Problems 77–92, simplify each expression. -81-3/4
In Problems 87–94, expressions that occur in calculus are given. Reduce each expression to lowest terms. (2x - 5) 3x²-x³.2 (2x - 5)²
In Problems 93–100, simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. x3/4x1/3x-1/2
In Problems 91 – 106, find the quotient and the remainder. Check your work by verifying that (Quotient )(Divisor ) + Remainder = Dividend4x3 − 3x2 + x + 1 divided by x + 2
In Problems 87–94, expressions that occur in calculus are given. Reduce each expression to lowest terms. (x²+1) 3 (3x + 4). 2x (x² + 1)²
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 3x² - 12x - 36
In Problems 91 – 106, find the quotient and the remainder. Check your work by verifying that (Quotient )(Divisor ) + Remainder = Dividend3x3 − x2 + x − 2 divided by x + 2
In Problems 85–96, simplify each expression.(3−2)−1
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. x38x² 20x
In Problems 85–96, simplify each expression. √25
In Problems 85–96, simplify each expression.(2−1)−3
In Problems 93–100, simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. x2/3x1/2x-1/4
In Problems 91 – 106, find the quotient and the remainder. Check your work by verifying that (Quotient )(Divisor ) + Remainder = Dividend4x3 − 3x2 + x + 1 divided by x2
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 샹 3 0 < (3x + 6)¹ <
In Problems 87–94, expressions that occur in calculus are given. Reduce each expression to lowest terms. (x² +9) 2 (2x - 5). 2x 2 (x² + 9)²
In Problems 85–96, simplify each expression. √36
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. y4 + 11y3 + 30y²
In Problems 93–100, simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. (x³y6)1/3
In Problems 85–96, simplify each expression. 2 √(-4)²
What is the domain of the variable in the expression√8 + 2x ?
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. Зуз - 18y² - 48 - У
In Problems 93–100, simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. (x4y8) 3/4
In Problems 85–96, simplify each expression. (-3)²
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 8x5+24x4 + 18x³
In Problems 93–100, simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. (x²y)¹/3 (xy²) ²/3 x2/3y2/3
In Problems 91 – 106, find the quotient and the remainder. Check your work by verifying that (Quotient )(Divisor ) + Remainder = Dividend3x5 − x2 + x − 2 divided by 3x3 − 1
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)¹/2 + 2(1+x)¹/2 x>-1
In Problems 93–100, simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. (4x-1y1/3)3/2 (xy) ³/2
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. x²y3 xy4
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. x481
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. x-²y xy²
In Problems 91 – 106, find the quotient and the remainder. Check your work by verifying that (Quotient )(Divisor ) + Remainder = Dividend−4x3 + x2 − 4 divided by x − 1
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 36x6 48x5 + 16x4
In Problems 93–100, simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. (xy)¹/4 (x²y2)¹/2 (x²y) ³/4
According to the National Center for Health Statistics, an average 30-year-old male in 2019 could expect to live at least 51.7 more years, and an average 30-year-old female in 2019 could expect to
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 6x² + 8x + 2
In Problems 93–100, simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. (16x²y-1/3) 3/4 (xy2)¹/4
In Problems 91 – 106, find the quotient and the remainder. Check your work by verifying that (Quotient )(Divisor ) + Remainder = Dividend2x4 − 3x3 + x + 1 divided by 2x2 + x + 1
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 8x2 + 6x - 2
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 2x¹/2 + x¹/2 x > 0
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. x4 - 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)³x4 (yz)² 32 xy³z
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. ².1/(x² + 1)-¹/².
The percentage method of withholding for federal income tax (2022) states that a single person whose weekly wages, after subtracting withholding allowances, are over $981, but not over $1760, shall
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. x6 2x³ + 1
In Problems 67 – 90, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (3x + 4y)(3x - 4y)
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 1
In Problems 77–92, simplify each expression. 163/2
In Problems 77 – 82, determine where each rational function R is undefined. Determine whether an asymptote or a hole appears in the graph of R at such numbers. R(x) = x³ x4 3x² + 4x - 12 3x³ + x
In Problems 67 – 90, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x + y)²
In Problems 75–86, perform the indicated operations and simplify the result. Leave your answer in factored form. 2x + 5 x x2 x - 3 x-3 (x + 1)² x + 3
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 0
In Problems 77–92, simplify each expression. 253/2
In Problems 77–92, simplify each expression. 9-3/2
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. (x + 2)(x − 3) > (x − 1)(x + 1)
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 8x2 +88x + 80
In Problems 67 – 90, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x - y)²
In Problems 75–86, perform the indicated operations and simplify the result. Leave your answer in factored form. 1- 1 1- 1 Xx
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 8 + x9 - zx
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 10x³ + 50x² + 40x
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. (x − 1)(x + 1) > (x − 3)(x + 4) - -
In Problems 77–92, simplify each expression. 16-3/2
In Problems 75–86, perform the indicated operations and simplify the result. Leave your answer in factored form. 1- 1 1 1-x
In Problems 67 – 90, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x - 2y)²

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