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mathematics
college algebra
Intermediate Algebra 13th Edition Margaret Lial, John Hornsby, Terry McGinnis - Solutions
Solve each inequality, and graph the solution set. (x - 1)(x-2)(x-4)
Factor completely. 24m2 + 2m - 15
Working together, two people can clean an office building in 5 hr. One person takes 2 hr longer than the other to clean the building alone. How long would it take the slower worker to clean the building alone? (Let x represent the time of the slower worker.) Faster Worker Rate Slower
Allen wants to buy a mat for a photograph that measures 14 in. by 20 in. He wants to have an even border around the picture when it is mounted on the mat. If the area of the mat he chooses is 352 in.2, how wide will the border be? 20 in. -14 in.→
Use the quadratic formula to solve each equation. (2x + 1)² = x +4
Graph each parabola. Give the vertex, axis of symmetry, domain, and range. f(x) = (x - 1)² + 2
Factor completely. 4t2 - 100
Graph each parabola. Give the vertex, axis of symmetry, domain, and range. x = (y + 3)²-2
Use the quadratic formula to solve each equation. (2x − 1)² = x + 2 -
Solve each inequality, and graph the solution set. (2x + 1)(3x-2)(4x + 7)
If a square piece of cardboard has 3-in. squares cut from its corners and then has the flaps folded up to form an open-top box, the volume of the box is given by the formulawhere x is the length of each side of the original piece of cardboard in inches. What original length would yield a box with
A game board is in the shape of a right triangle. The hypotenuse is 2 in. longer than the longer leg, and the longer leg is 1 in. less than twice as long as the shorter leg. How long is each side of the game board?
Graph each parabola. Give the vertex, axis of symmetry, domain, and range. x = (y - 3)² - 1
Factor completely. 8x3 + 27y3
The diagonal of a rectangular rug measures 26 ft, and the length is 4 ft more than twice the width. Find the length and width of the rug. 26 ft
A searchlight moves horizontally back and forth along a wall. The distance of the light from a starting point at t minutes is given by the quadratic functionHow long will it take before the light returns to the starting point? f(t)= 100t²300t.
Graph each parabola. Give the vertex, axis of symmetry, domain, and range. f(x) = (x - 1)² - 3
Solve each inequality, and graph the solution set. (x-4) (2x + 3) (3x - 1) = 0
Manuel is planting a vegetable garden in the shape of a right triangle. The longer leg is 3 ft longer than the shorter leg, and the hypotenuse is 3 ft longer than the longer leg. Find the lengths of the three sides of the garden.
Simplify. Express each answer in lowest terms. Assume denominators are nonzero. 5x+2 -6 15x + 6 5
Graph each parabola. Give the vertex, axis of symmetry, domain, and range. x=(y-2)² + 4
Graph each parabola. Give the vertex, axis of symmetry, domain, and range. f(x) = (x + 1)² + 1
Factor completely. 9x2 - 30xy + 25y2
Rusty and Nancy are planting flowers. Working alone, Rusty would take 2 hr longer than Nancy to plant the flowers. Working together, they do the job in 12 hr. How long would it have taken each person working alone?
A 13-ft ladder is leaning against a house. The distance from the bottom of the ladder to the house is 7 ft less than the distance from the top of the ladder to the ground. How far is the bottom of the ladder from the house? X X-7 13
Simplify. Express each answer in lowest terms. Assume denominators are nonzero. 3 2 x 5 + 6 x² - 2x
Solve each inequality, and graph the solution set. (x + 2) (4x3)(2x + 7) = 0
Graph each parabola. Give the vertex, axis of symmetry, domain, and range. X = 1 22 5 + 2y - 4
Use the quadratic formula to solve each equation. x2 - 3x + 6 = 0
Identify the vertex of each parabola. f(x) = -(x - 1)²
Joel can work through a stack of invoices in 1 hr less time than Noel can. Working together they take 11/2 hr. How long would it take each person working alone?
Graph each parabola. Give the vertex, axis of symmetry, domain, and range. f(x) = 2(x - 2)² - 4
A club swimming pool is 30 ft wide and 40 ft long. The club members want an exposed aggregate border in a strip of uniform width around the pool. They have enough material for 296 ft2. How wide can the strip be? 30 ft Pool 40 ft
Solve each inequality, and graph the solution set. x 1 x-4 0
Simplify. Express each answer in lowest terms. Assume denominators are nonzero. r S r S S r +1
Lyudmila wants to buy a rug for a room that is 20 ft long and 15 ft wide. She wants to leave an even strip of flooring uncovered around the edges of the room. How wide a strip will she have if she buys a rug with an area of 234 ft2? 15 ft Rug 20 ft
Use the quadratic formula to solve each equation. x2 - 5x + 20 = 0
Identify the vertex of each parabola. f(x) = (x 3)² +7
Graph each parabola. Give the vertex, axis of symmetry, domain, and range. X = 1 2 - 4y - 6
A washing machine can be filled in 6 min if both the hot water and the cold water taps are fully opened. Filling the washer with hot water alone takes 9 min longer than filling it with cold water alone. How long does it take to fill the washer with cold water?
Graph each parabola. Give the vertex, axis of symmetry, domain, and range. f(x) = 3(x - 2)² + 1
Solve each inequality, and graph the solution set. x + 1 x-5 0<
Identify the vertex of each parabola. x = (y - = (y - 3)² - 4 2
Two cars left an intersection at the same time, one heading due south and the other due east. Later they were exactly 95 mi apart. The car heading east had gone 38 mi less than twice as far as the car heading south. How far had each car traveled? X U S 2x - 38 — (CM) 95 E
Graph each parabola. Give the vertex, axis of symmetry, domain, and range. x = 3y² + 12y + 5
Solve each equation. Check the solutions. x = V7x 10 − -
Use the quadratic formula to solve each equation.r2 - 6r + 14 = 0
Two pipes together can fill a tank in 2 hr. One of the pipes, used alone, takes 3 hr longer than the other to fill the tank. How long would each pipe take to fill the tank alone?
Use the quadratic formula to solve each equation.t2 + 4t + 11 = 0
A rectangle has a length 2 m less than twice its width. When 5 m are added to the width, the resulting figure is a square with an area of 144 m2. Find the dimensions of the original rectangle.
William Froude was a 19th century naval architect who used the following expression, known as the Froude number, in shipbuilding.This expression was also used by R. McNeill Alexander in his research on dinosaurs.Use this expression to find the value of v (in meters per second), given g = 9.8 m per
Solve each equation. Check the solutions.x4 + 48 = 16x2
The following exercises are not grouped by type. Solve each equation. 12x4 11x² +2=0
The following exercises are not grouped by type. Solve each equation. 2(1 + √r)² = 13(1 + √r) - 6
The following exercises are not grouped by type. Solve each equation. 8x4+1 11x² =
The following exercises are not grouped by type. Solve each equation. 8x6 + 513x³ + 64 = 0
The following exercises are not grouped by type. Solve each equation. 2x4-9x² = -2
The following exercises are not grouped by type. Solve each equation. (x² + x)² + 12 = 8(x² + x)
The following exercises are not grouped by type. Solve each equation. x610x³ -9
The following exercises are not grouped by type. Solve each equation. 6 = 7(2w3)-¹ + 3(2-3)-²
The following exercises are not grouped by type. Solve each equation. 2m6+ 11m³ + 5 = 0
Match each logarithmic equation in Column I with the corresponding exponential equation in Column II. I (a) log1/3 3 = -1 (b) log5 1 = 0 (c) log₂ √2= 2 (d) log10 1000 = 3 1 (e) logg V8 = (f) log4 4 = 1 3 II A. 81/38 ()' 3 B. = 3 C. 4¹ = 4 D. 21/2 = √2 E. 5⁰ = 1 F. 10³ = 1000
The following exercises are not grouped by type. Solve each equation. 2x4+x²30
The following exercises are not grouped by type. Solve each equation. 4x4 + 5x² + 1 = 0 -
Determine whether each statement of a logarithmic property is true or false. If it is false, correct it by changing the right side of the equation. logh x + logb y = logb (x + y)
William Froude was a 19th century naval architect who used the following expression, known as the Froude number, in shipbuilding.This expression was also used by R. McNeill Alexander in his research on dinosaurs.Use this expression to find the value of v (in meters per second), given g = 9.8 m per
Solve each inequality, and graph the solution set. (5r – 3)2 2x + 1 VI
A model rocket is projected vertically upward from the ground. Its distance s in feet above the ground after t seconds is given by the quadratic functionWork Exercises in order, to see how quadratic equations and inequalities are related.At what times will the rocket be more than 624 ft above the
A model rocket is projected vertically upward from the ground. Its distance s in feet above the ground after t seconds is given by the quadratic functionWork Exercises in order, to see how quadratic equations and inequalities are related.At what times will the rocket be 624 ft above the ground? Let
Solve each equation. Check the solutions.9x4 - 25x2 + 16 = 0
If a function is made up of ordered pairs in such a way that the same y-value appears in a correspondence with two different x-values, thenA. The function is one-to-one B. The function is not one-to-oneC. Its graph does not pass the vertical line testD. It has an inverse function associated
In each problem, find the following.(a) A function R(x) that describes the total revenue received(b) The graph of the function from part (a)(c) The number of unsold seats that will produce the maximum revenue(d) The maximum revenueA charter bus charges a fare of $48 per person, plus $2 per person
Use the formula A = P(1 + r)2 to find the interest rate r at which a principal P of $10,000 will increase to $10,920.25 in 2 yr.
A model rocket is projected vertically upward from the ground. Its distance s in feet above the ground after t seconds is given by the quadratic functionWork Exercises in order, to see how quadratic equations and inequalities are related.At what times will the rocket be less than 624 ft above the
A model rocket is projected vertically upward from the ground. Its distance s in feet above the ground after t seconds is given by the quadratic functionWork Exercises in order, to see how quadratic equations and inequalities are related.At what times will the rocket be at ground level? Let s(t) =
Solve each equation. Check the solutions. (x + 3)2 + 5(x + 3) +6=0
Solve each equation. Check the solutions. (x-4)² + (x-4) - 20 = 0
Recall that corresponding sides of similar triangles are proportional. Use this fact to find the lengths of the indicated sides of each pair of similar triangles. Check all possible solutions in both triangles. Sides of a triangle cannot be negative (and are not drawn to scale here). Side
Find the discriminant. Use it to determine whether the solutions for each equation areA. Two rational numbers B. One rational numberC. Two irrational numbers D. Two nonreal complex numbers.Tell whether the equation can be solved using the zero-factor property, or if the quadratic formula
Total spending (in billions of dollars) in the United States from all sources on physician and clinical services for the years 2000–2016 are shown in the bar graph. One model for the data is the quadratic functionHere, x = 0 represents 2000, x = 2 represents 2002, and so on. Use the graph and the
Total spending (in billions of dollars) in the United States from all sources on physician and clinical services for the years 2000–2016 are shown in the bar graph. One model for the data is the quadratic functionHere, x = 0 represents 2000, x = 2 represents 2002, and so on. Use the graph and the
Total spending (in billions of dollars) in the United States from all sources on physician and clinical services for the years 2000–2016 are shown in the bar graph. One model for the data is the quadratic functionHere, x = 0 represents 2000, x = 2 represents 2002, and so on. Use the graph and the
Total spending (in billions of dollars) in the United States from all sources on physician and clinical services for the years 2000–2016 are shown in the bar graph. One model for the data is the quadratic functionHere, x = 0 represents 2000, x = 2 represents 2002, and so on. Use the graph and the
Recall that corresponding sides of similar triangles are proportional. Use this fact to find the lengths of the indicated sides of each pair of similar triangles. Check all possible solutions in both triangles. Sides of a triangle cannot be negative (and are not drawn to scale here). Side
Find the discriminant for each quadratic equation. Use it to tell whether the equation can be solved using the zero-factor property, or the quadratic formula should be used instead. Then solve each equation.(a) 3x2 + 13x = -12 (b) 2x2 + 19 = 14x
Solve each equation. Check the solutions.z4 + 72 = 17z2
In the 1939 classic movie The Wizard of Oz, Ray Bolger’s character, the Scarecrow, wants a brain. When the Wizard grants him his “Th.D.” (Doctor of Thinkology), the Scarecrow replies with the following statement.Scarecrow: The sum of the square roots of any two sides of an isosceles triangle
Solve each equation. Check the solutions. 3(m + 4)²8= 2(m + 4)
Find the value of a, b, or c so that each equation will have exactly one rational solution.p2 + bp + 25 = 0
Find the value of a, b, or c so that each equation will have exactly one rational solution.r2 - br + 49 = 0
In the 1939 classic movie The Wizard of Oz, Ray Bolger’s character, the Scarecrow, wants a brain. When the Wizard grants him his “Th.D.” (Doctor of Thinkology), the Scarecrow replies with the following statement.Scarecrow: The sum of the square roots of any two sides of an isosceles triangle
Find the value of a, b, or c so that each equation will have exactly one rational solution.am2 + 8m + 1 = 0
Solve each equation. Check the solutions. 3 7 2p+2 6 (2p+ 2)²
Find the value of a, b, or c so that each equation will have exactly one rational solution.4m2 + 12m + c = 0
Solve each equation. Check the solutions. 2 − 6(z − 1) −² = (z − 1)-¹ -
Solve each equation. Check the solutions.x2/3 - 2x1/3 - 3 = 0
Solve each equation. Check the solutions. 3 — 2(x − 1) −¹ = (x − 1)-² - -
One solution of 4x2 + bx - 3 = 0 is - 5/2. Find b and the other solution.
Solve each equation. Check the solutions.r2/3 + r1/3 - 12 = 0
The following exercises are not grouped by type. Solve each equation. (x - 2)² + 5(x - ²) - 4 = 2 0=
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