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study help
mathematics
college algebra
College Algebra 12th edition Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels - Solutions
To answer each question, refer to the following basic graphs.Which one is the graph of ƒ(x) = x2? What is its domain? C. A. B. 123 -8 F. E. D. Ho х G. Н. I. 8. 2- -2 8. -2 2.
Fill in the blank(s) to correctly complete each sentence.The circle with equation x2 + y2 = 49 has center with coordinates ____________ and radius equal to _______________.
Find the distance between each pair of points, and give the coordinates of the midpoint of the line segment joining them.P(3, -1), Q(-4, 5)
Match the set described in Column I with the correct interval notation from Column II. Choices in Column II may be used once, more than once, or not at all. II (a) Domain of f(x) = Vx + 3 A. [-3, 0) B. [3, ) (b) Range of f(x) = Vx – 3 C. (-∞, 0) (c) Domain of f(x) = x² – 3 D. [0, ∞) (d)
Fill in the blank(s) to correctly complete each sentence.The graph of the line y - 3 = 4(x - 8) has slope__________and passes through the point (8, ________).
Fill in the blank(s) to correctly complete each sentence.The domain of the relation {(3, 5), (4, 9), (10, 13)} is.
For A(-4, 2) and B(-8, -3), find d(A, B), the distance between A and B.
Fill in the blank to correctly complete each sentence.The point (-1, 3) lies in quadrant ________ in the rectangular coordinate system.
For the line passing through the points (-3, 5) and (-1, 9), find the following.(a) The slope-intercept form of its equation.(b) Its x-intercept.
Fill in the blank(s) to correctly complete each sentence.To graph the function ƒ(x) = x2 - 3, shift the graph of y = x2 down _______units.
Without using paper and pencil, evaluate each expression given the following functions. ƒ(x) = x + 1 and g(x) = x2 (ƒ + g) (2)
Match the description in Column I with the correct response in Column II. Some choices may not be used.A linear function whose graph has y-intercept (0, 6) A. f(x) = 5x В. f(x) — Зх + 6 С. f(х) — —8 D. f(x) — х? Е. х + у%3D —6 Е. f(x) — Зх + 4 G. 2x – y = –4 Н. х %3D 9
These summary exercises provide practice with some of the concepts covered so far in this chapter.For the points P and Q, find (a) The distance d(P, Q), (b) The coordinates of the midpoint of the segment PQ, (c) An equation for the line through the two points. Write the equation in
Write each statement using an absolute value equation or inequality.t is no less than 0.01 unit from 5.
Work each problem.Show that -√2/2 -√2/2 i is a square root of i.
Work each problem.Show that √2/2 + √2/2 i is a square root of i.
Solve each inequality. Give the solution set using interval notation.x2 - 3x ≥ 5
Write each statement using an absolute value equation or inequality.p is at least 3 units from 1.
Write each statement using an absolute value equation or inequality.k is 12 units from 6.
Solve each equation or inequality.|x2 + 4x| > 0
Solve each equation or inequality.|x2 + 4x| ≤ 0
Solve each equation or inequality.|7 - 2x| ≤ - 9
Solve each equation or inequality.|4x - 12| ≥ - 3
Solve each equation or inequality.|7x + 8| - 6 > - 3
Solve each equation or inequality.|3x + 7| - 5 > 5
Solve each equation or inequality. 1 < 3 -x + 3
Solve each equation or inequality.|7x - 3| > 4
Solve each equation or inequality.|8 - 5x| ≥ 2
Solve each equation or inequality.|2x + 9| ≤ 3
In this section we introduced methods of solving equations quadratic in form by substitution and solving equations involving radicals by raising each side of the equation to a power. Suppose we wish to solve x - √x - 12 = 0. We can solve this equation using either of the two methods. To see how
Solve each equation or inequality.|x + 10| = |x - 11|
Solve each equation or inequality.|5x - 1| = |2x + 3|
Solve each equation or inequality. 8х — 1 – 7 = 0 Зх + 2
Solve each equation or inequality. - 9 = 0 2 - Зх
Work each problem.Show that -3 - 4i is a solution of the equation x2 + 6x + 25 = 0.
Solve each equation or inequality.|2 - x| = 3
Work each problem.Show that -3 + 4i is a solution of the equation x2 + 6 x + 25 = 0.
Solve each equation or inequality.|x + 4| = 7
Work each problem.Show that -2 - i is a solution of the equation x2 + 4x + 5 = 0.
Without actually solving the inequality, explain why -4 must be in the solution set of > 0. х+4 2х + 1
Work each problem.Show that –2 + i is a solution of the equation x2 + 4x + 5 = 0.
Without actually solving the inequality, explain why 3 cannot be in the solution set of 14x + 9 < 0.
Work each problem.Show that –√3/2 + 1/2 i is a cube root of i.
The total amount paid by the U.S. government to individuals for Social Security retirement and disability insurance benefits during the period 2004–2013 can be approximated by the linear model y = 35.7x + 486, where x = 0 corresponds to 2004, x = 1 corresponds to 2005, and so on. The variable y
Work each problem.Show that –√3/2 + 1/2 i is a cube root of i.
A projectile is launched upward from the ground. Its height s in feet above the ground after t seconds is given by the following equation. s = -16t2 + 320t(a) After how many seconds in the air will it hit the ground?(b) During what time interval is the projectile more than 576 ft above the
A company produces earbuds. The revenue from the sale of x units of these earbuds is R = 8x.The cost to produce x units of earbuds is C = 3x + 1500. In what interval will the company at least break even?
Guideline levels for indoor ozone are less than 50 parts per billion (ppb). In a scientific study, a Purafil air filter was used to reduce an initial ozone concentration of 140 ppb. The filter removed 43% of the ozone.(a) What is the ozone concentration after the Purafil air filter is used?(b) What
Use the technique described in to solve each inequality. Write each solution set in interval notation.-x2(2x - 3)2 ≤ 0
Simplify each power of i.1/i-12
Simplify each power of i.i40
If applicable, and properties of absolute value to solve each equation or inequality. |9 - x/7 + 8x| ≥ 0
Use the technique described in to solve each inequality. Write each solution set in interval notation.(x + 1)2 (x - 3) < 0
Simplify each power of i.i32
Use the technique described in to solve each inequality. Write each solution set in interval notation.16x - x3 ≥ 0
Simplify each power of i.i27
Solve each inequality. Give the solution set using interval notation.2x3 - 3x2 - 5x < 0
Solve each inequality. Give the solution set using interval notation.x3 - 16x ≤ 0
Use the technique described in to solve each inequality. Write each solution set in interval notation.(x + 5)(3x - 4)(x + 2) ≥ 0
Simplify each power of i.i26
If applicable, and properties of absolute value to solve each equation or inequality. x2 + 2 11 3 х
Inequalities that involve more than two factors, such as (3x - 4)(x + 2)(x + 6) ≤ 0, can be solved using an extension of the method shown in to see how the method is extended.Plot the three solutions in Exercise 87 on a number line, using closed circles because of the non strict inequality,
Complex numbers are used to describe current I, voltage E, and impedance Z (the opposition to current). These three quantities are related by the equation E = IZ, which is known as Ohm’s Law.Thus, if any two of these quantities are known, the third can be found. In each exercise, solve the
Solve each inequality. Give the solution set using interval notation. 3 х — 4 x + 2
Solve each inequality. Give the solution set using interval notation. 3 х — 1 х+ 3 VI
Simplify each power of i.1/i-11
Use the technique described in to solve each inequality. Write each solution set in interval notation.x2(x + 4)2 ≥ 0
Use the technique described in to solve each inequality. Write each solution set in interval notation.x3 + 3x2 - 16x ≤ 48
Simplify each power of i.i-14
Solve each inequality. Give the solution set using interval notation. 5х + 2 + 1
Use the technique described in to solve each inequality. Write each solution set in interval notation.x3 + 4x2 - 9x ≥ 36
Solve each inequality. Give the solution set using interval notation. Зх — 2 4>0 х
Simplify each power of i.i–13
Use the technique described in to solve each inequality. Write each solution set in interval notation.(x - 5)2 (x + 1) < 0
Solve each inequality. Give the solution set using interval notation. x + 7 2x + 1 1
Solve each inequality. Give the solution set using interval notation. Зх + 6 >0 х — 5
If applicable, and properties of absolute value to solve each equation or inequality. |x - 4/3x + 1| ≥ 0
If applicable, and properties of absolute value to solve each equation or inequality. |x2 + 10| < 0
Use the technique described in to solve each inequality. Write each solution set in interval notation.4x - x3 ≥ 0
Simplify each power of i.i23
If applicable, and properties of absolute value to solve each equation or inequality. |x4 + 2x2 + 1| < 0
Use the technique described in to solve each inequality. Write each solution set in interval notation.(2x - 3)(x + 2)(x - 3) ≥ 0
Simplify each power of i.i22
Solve each inequality. Give the solution set using interval notation.6x2 - 11x < 10
If applicable, and properties of absolute value to solve each equation or inequality. |x2 + 1| - |2x| = 0
Inequalities that involve more than two factors, such as (3x - 4)(x + 2)(x + 6) ≤ 0, can be solved using an extension of the method shown in to see how the method is extended.On a single number line, do the following.(a) Graph the intervals that satisfy the inequality, including endpoints. This
Simplify each power of i.i29
Solve each inequality. Give the solution set using interval notation.x2 + 4x - 21 > 0
If applicable, and properties of absolute value to solve each equation or inequality. |6x3 + 23x2 + 7x| = 0
Inequalities that involve more than two factors, such as (3x - 4)(x + 2)(x + 6) ≤ 0, can be solved using an extension of the method shown in to see how the method is extended.The number line from Exercise 88 should show four intervals formed by the three points. For each interval, choose a test
Simplify each power of i.i25
Solve each inequality. Give the solution set using interval notation.x2 + 3x - 4 ≤ 0
If applicable, and properties of absolute value to solve each equation or inequality. |4x2 - 23x - 6| = 0
Solve each inequality. Give the solution set using interval notation.-8 > 3x - 5 > -12
If applicable, and properties of absolute value to solve each equation or inequality. |2x2 - 3x| = 5
If applicable, and properties of absolute value to solve each equation or inequality. |3x2 + x| = 14
Inequalities that involve more than two factors, such as (3x - 4)(x + 2)(x + 6) ≤ 0, can be solved using an extension of the method shown in to see how the method is extended.Use the zero-factor property to solve (3x - 4)(x + 2)(x + 6) = 0.
Find each product. Write answers in standard form.(3 – i)(3 + i)(2 – 6i
Complex numbers are used to describe current I, voltage E, and impedance Z (the opposition to current). These three quantities are related by the equation E = IZ, which is known as Ohm’s Law.Thus, if any two of these quantities are known, the third can be found. In each exercise, solve the
Solve each inequality. Give the solution set using interval notation.5 ≤ 2x - 3 ≤ 7
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