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study help
mathematics
precalculus

Questions and Answers of Precalculus

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f and t are continuous on [a, b], then
True or False.The solution of the equation 3x - 8 = 0 is 3/8.
True or False.Squaring both sides of an equation results in an equivalent equation.
True or False.√x2 = |x|.
An equation that is satisfied for every choice of the variable for which both sides are defined is called a(n) __________.
True or False.Some equations have no solution.
True or False.If the discriminant of a quadratic equation is positive, then the equation has two solutions that are negatives of one another.
True or False.Quadratic equations always have two real solutions.
The quantity b2 – 4ac is called the ______ of a quadratic equation. If it is _______, the equation has no real solution.
To solve the equation x2 + 5x = 0 by completing the square, you would _____ the number ______ to both sides.
Which of the following pairs of equations are equivalent? Explain. (a) x2 = 9, x = 3(b) x = √9, x = 3(c) (x – 1)(x – 2) = (x – 1)2; x – 2 = x – 1
Show that the real solutions of the equation ax2 + bx + c = 0 are the reciprocals of the real solutions of the equation cx2 + bx + a = 0. Assume that b2 – 4ac ≥ 0.
Show that the real solutions of the equation ax2 + bx + c = 0 are the negatives of the real solutions of the equation ax2 - bx + c = 0. Assume that b2 – 4ac ≥ 0.
Find k such that the equation x2 - kx + 4= 0 has a repeated real solution.
Find k such that the equation kx2 + x+ k= 0 has a repeated real solution.
Show that the product of the roots of a quadratic equation is c/a.
Show that the sum of the roots of a quadratic equation is - b/a.
List some formulas that occur in applications. Solve the formula for the indicated variable. Mechanics v = - gt + v0 for t
List some formulas that occur in applications. Solve the formula for the indicated variable. Mathematics S = for r
List some formulas that occur in applications. Solve the formula for the indicated variable. Chemistry PV = nRT for T
List some formulas that occur in applications. Solve the formula for the indicated variable. Mechanics ту? for R
List some formulas that occur in applications. Solve the formula for the indicated variable. Finance A = P(1 + rt) for r
List some formulas that occur in applications. Solve the formula for the indicated variable. Electricity for R R2 R1 ||
Solve the equation. The letters a, b, and c are constants.
Solve the equation. The letters a, b, and c are constants. 2 х — а х — 1 х +а
Solve the equation. The letters a, b, and c are constants. a c, c + 0 х х
Solve the equation. The letters a, b, and c are constants. х х 3 с, а # 0, Ь # 0, а # —b b. la
Solve the equation. The letters a, b, and c are constants. 1 - ax = b, a ≠ 0
Solve the equation. The letters a, b, and c are constants. ax - b = c, a ≠ 0
Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation. 2x2 - 3x - 4 = 0
Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation. 3x2 + 5x - 8 = 0
Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation. 25x2 - 20x + 4 = 0
Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation. 9x2 - 30x + 25 =
Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation. x2 + 5x + 7 = 0
Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation. x2 - 5x + 7 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. x2 + √2x – 2 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. x2 + √3x – 3 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. 2x2 = 1 - 2x
Find the real solutions, if any, of the equation. Use the quadratic formula. 4x2 = 1 - 2x
Find the real solutions, if any, of the equation. Use the quadratic formula. 4t2 + t + 1 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. 4y2 - y + 2 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. 2x2 + 5x + 3 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. 2x2 - 5x + 3 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. x2 + 5x + 3 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. x2 - 5x - 1 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. x2 + 4x + 2 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. x2- 4x + 2 = 0
Solve the equation by completing the square. 2x2- 3x - 1 = 0
Solve the equation by completing the square. 3x2 + x - 1/2 = 0
Solve the equation by completing the square. 1 + 3. 3
Solve the equation by completing the square. 3 x2 16
Solve the equation by completing the square. x2- 6x = 13
Solve the equation by completing the square. x2 + 4x = 21
Solve each equation by the Square Root Method. (3x – 2)2 = 4
Solve each equation by the Square Root Method. (2y + 3)2 = 9
Solve each equation by the Square Root Method. (x + 2)2 = 1
Solve each equation by the Square Root Method. (x – 1)2 = 4
Solve each equation by the Square Root Method. x2 = 36
Solve each equation by the Square Root Method. x2 = 25
Solve the equation. 6x - 5 = 6/x
Solve the equation. 3 = 4 + х — 2 х+ 4
Solve the equation. 4(х — 2) х — 3 3 -3 x(х — 3) х
Solve the equation. x + 12/x = 7
Solve the equation. 25x2 + 16 = 40x
Solve the equation. Solve the equation. 4x2 + 9 = 12x
Solve the equation. x(x + 1) = 12
Solve the equation. x(x - 7) + 12 = 0
Solve the equation. 3x2+ 5x + 2 = 0
Solve the equation. 2x2 - 5x - 3 = 0
Solve the equation. v2 + 7v + 12 = 0
Solve the equation. z2 + 4z - 12 = 0
Solve the equation. x2 = -8x
Solve the equation. x2 = 4x
Solve the equation. |x2 + 3x - 2| = 2
Solve the equation. |x2 + x - 1| = 1
Solve the equation. |x2 + x| = 12
Solve the equation. |x2 - 2x|= 3
Solve the equation. |x2 - 9|= 0
Solve the equation. |x2 - 4| = 0
Solve the equation. |2 - x| = -1
Solve the equation. |x - 2| =
Solve the equation. |3|x = 9
Solve the equation. |-2|x = 4
Solve the equation. |-x| = 1
Solve the equation. |-2x| = 8
Solve the equation. |1 - 2z| = 3
Solve the equation. |1 - 4t| = 5
Solve the equation. |3x - 1| = 2
Solve the equation. |2x + 3| = 5
Solve the equation. |3x| = 12
Solve the equation. |2x| = 6
Solve the equation. (2х + 3)(х — 1) х — 1 2х + 3
Solve the equation. 3 10 (x + 5)(x – 2) x + 5 || 2.
Solve the equation. (x - 5)(2x) = (x - 5)(4)
Solve the equation. (x + 2)(3x) = (x + 2)(6)
Solve the equation. -2 -3 x + 1 x + 4
Solve the equation. 3 2 2x 3 х+5
Solve the equation. 4z3 – 8z2 = 0
Solve the equation. t3 – 9t2 = 0
Solve the equation. x3 = x2

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