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mathematics
precalculus

Questions and Answers of Precalculus

Solve the equation. 2x3 – 3x2 – 8x – 3 = 0
Solve the equation. √3x + 1 = 4
Solve the equation. 2x2 – x = 0
Megan went clothes shopping and bought 2 pairs of flare jeans, 2 camisoles, and 4 T-shirts for $90.00. At the same store, Paige bought one pair of flare jeans and 3 T-shirts for $42.50, while Kara
Maximize z = 5x + 8y subject to x ≥ 0, 2x + y ≤ 8, and x – 3y ≤ -3.
Graph the system of inequalities. Tell whether the graph is bounded or unbounded, and label all corner points. к20 | y > 0 х + 2у 2 8 2.х — Зу > 2 AI
Write the partial fraction decomposition of the rational expression. 4x? – 3 x(x² + 3)?
Write the partial fraction decomposition of the rational expression. Зх + 7 (х + 3)?
Graph the system of inequalities: < 100 y? 4х — Зу 2 0
Solve the system of equations. S 2y² |2у? — 3х2 %3D 5 у — х %3D1
Solve the system of equations. Зx? + у? %3D 12 у? %3D 9х
Use Cramer’s Rule, if possible, to solve the system. 15 4х — Зу + 22 %3 -2x + y – 3z = -15 5х — 5у + 2%3 18
Use Cramer’s Rule, if possible, to solve the system. 4х + 3у 3D —23 |3х — 5у 3D 19 -23 19
Find the value of the determinant. 61 2 -4 4 2 -4 -1
Find the value of the determinant. -2 5 3 7
Solve the system of equations using matrices. If the system has no solution, say that it is inconsistent. 2х + 2y — 3z 3 5 y + 2z = 8 Зх + 5у — 8z3D —2 х -
Solve the system of equations using matrices. If the system has no solution, say that it is inconsistent. x + 2y + 4z = -3 2x + 7y + 15z = -12 4x + 7y + 13z -10
Solve the system of equations using matrices. If the system has no solution, say that it is inconsistent. 8x + 2y = 56
Solve the system of equations using matrices. If the system has no solution, say that it is inconsistent. бх + Зу 3D 12 2х — у %3D —2
Find the inverse of the nonsingular matrix. -1 B = | 2 5 -1 3 2
Find the inverse of the nonsingular matrix. 3 2 A = 5 4
Use the given matrices to compute the expression.BA 4 6 -2 5 A -4 B 1 -3 %3! 3 2 -1 8
Use the given matrices to compute the expression. CB 4 6 -2 5 A -4 B 1 -3 %3! 3 2 -1 8
Use the given matrices to compute the expression. A - 3C 4 -2 5 A -4 B 1 -3 3 2 -1
Use the given matrices to compute the expression. 2A + C -1 4 6. 1 -2 5 C = 1 -3 A = | 0 3 B = -4 3 1 2
Write the system of equations corresponding to the augmented matrix: 3 2 4 1 0 8 -2 1 3-11 -6
Write the augmented matrix corresponding to the system of equations: 5y + z = —2х — у + 6 %3D — 19 х+ 5у — 5z %3D 10 4х
Solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent. Зх + 2y - 8z %3D —3 —х 31 бх Зу +
Solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent. х — у+ 2z %3D 5 z = -2 5х + 2у + 3z
Solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent. 2y = 1 х 3 30y 18
Solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent. -2х + у %3D —7 4х + Зу %3D 9
A factory produces gasoline engines and diesel engines. Each week the factory is obligated to deliver at least 20 gasoline engines and at least 15 diesel engines. Due to physical limitations,
A factory manufactures two kinds of ceramic figurines: a dancing girl and a mermaid. Each requires three processes: molding, painting, and glazing.The daily labor available for molding is no more
If Bruce and Bryce work together for 1 hour and 20 minutes, they will finish a certain job. If Bryce and Marty work together for 1 hour and 36 minutes, the same job can be finished. If Marty and
On a flight between Midway Airport in Chicago and Ft. Lauderdale, Florida, a Boeing 737 jet maintains an airspeed of 475 miles per hour. If the trip from Chicago to Ft. Lauderdale takes 2 hours, 30
On a recent trip to the Cuyabeno Wildlife Reserve in the Amazon region of Ecuador, Mike took a 100-kilometer trip by speedboat down the Aguarico River from Chiritza to the Flotel Orellana. As Mike
A store that specializes in selling nuts has available 72 pounds (lb) of cashews and 120 lb of peanuts. These are to be mixed in 12-ounce (oz) packages as follows: a lower-priced package containing 8
A cookie company makes three kinds of cookies, oatmeal raisin, chocolate chip, and shortbread, packaged in small, medium, and large boxes. The small box contains 1 dozen oatmeal raisin and 1 dozen
A 1000-acre farm in Illinois is used to grow corn and soybeans. The cost per acre for raising corn is $65, and the cost per acre for soybeans is $45. If $54,325 has been budgeted for costs and all
A coffee distributor is blending a new coffee that will cost $6.90 per pound. It will consist of a blend of $6.00 per pound coffee and $9.00 per pound coffee. What amounts of each type of coffee
Find the general equation of the circle that passes through the three points (0, 1), (1, 0) and (-2, 1). The general equation of a circle is x2 + y2 + Dx + Ey + F = 0.
Find the quadratic function y = ax2 + bx + c that passes through the three points (0, 1), (1, 0) and (-2, 1).
Find A so that the system in Problem 97 is inconsistent. Data From Problem 97Find A so that the system of equations has infinitely many solutions. 2х + 5у %3D 5 4х + 10у %3D А
Find A so that the system of equations has infinitely many solutions. 2х + 5у %3D 5 4х + 10у %3D А
Solve the linear programming problem. Minimize z = 3x + y subject to x ≥ 0, y ≥ 0, y ≤ 6, 2x + y ≥ 4
Solve the linear programming problem. Minimize z = 3x + 5y subject to x ≥ 0, y ≥ 0, x + y ≥ 1, 3x + 2y ≥ 12, x + 3y ≤ 12
Solve the linear programming problem. Maximize z = 2x + 4y subject to x ≥ 0, y ≥ 0, x + y ≤ 6, x ≥ 2
Solve the linear programming problem. Maximize z = 3x + 4y subject to x ≥ 0, y ≥ 0, 3x + 2y ≥ 6, x + y ≤ 8
Graph each system of inequalities. x² + y > 1 x + y < 4
Graph each system of inequalities. ГysR ху S 4
Graph each system of inequalities. Sy sx - 1 х — х — у— 3
Graph each system of inequalities. S² + y? < 16 x + y >2
Graph the system of inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. х2 0 y 2 0 Зх + у s9 2х + 3у 2 6
Graph the system of inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. y 2 0 2х + у s8 x + 2y > 2
Graph the system of inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. х2 0 y 2 0 Зх + у2 6 2х + у > 2
Graph the system of inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. х2 0 y > 0 х+ уs 4 2х + 3у < 6
Graph the system of inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. Jx - 2y < 6 12х + у > 2 х
Graph the system of inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. -2x + y < 2 x + y > 2
Graph the inequality. x ≥ y2
Graph the inequality. y ≤ x2
Graph the inequality. 2x - 3y ≥ 6
Graph the inequality. 3x + 4y ≤ 12
Solve the system of equations. x + x + y = y + 2 2 - y x + 1 =
Solve the system of equations. х — Зх + y? + у%3D —2 х + y + 1 = y
Solve the system of equations. Зx? + 2ху — 2у? %3D 6 ху — 2у + 4 3D 0
Solve the system of equations. 3x + 4xy + 5y² = 8 x² + 3xy + 2y² = 0
Solve the system of equations. 2x2 + y = 9 x² + y° = 9
Solve the system of equations. + y? %3D бу %3 Зу
Solve the system of equations. 3x – y? = 1 7x2 – 2y – 5 = 0 3.
Solve the system of equations. /2ху + у? — 10 (Зу? ху %3D 2
Solve the system of equations. Sx² + y? = 16 | 2х — у? 3D —8 2.x
Solve the system of equations. 2х + у + 3 %3D 0 x? + y = 5
Write the partial fraction decomposition of the rational expression. 4 (x + 4)(x – 1)
Write the partial fraction decomposition of the rational expression. (x² + 1)(x² – 1)
Write the partial fraction decomposition of the rational expression. x + 1 (x² + 16)
Write the partial fraction decomposition of the rational expression. (r+4)? 2.
Write the partial fraction decomposition of the rational expression. Зx (х — 2)(x + 1)
Write the partial fraction decomposition of the rational expression. х (х + 9)(х + 1)
Write the partial fraction decomposition of the rational expression.
Write the partial fraction decomposition of the rational expression. 4 2(x – 1)
Write the partial fraction decomposition of the rational expression. х (х + 2)(х — 3)
Write the partial fraction decomposition of the rational expression. x(х — 4)
Use properties of determinants to find the value of the determinant if it is known that х y 8. У ь х a
Use properties of determinants to find the value of the determinant if it is known that х y 8. 2х у У 2a b
Use Cramer’s Rule, if applicable, to solve the system. х — у+ z%3 2х + 3у — z %3D —2 Зx у — 9г %3D 9
Use Cramer’s Rule, if applicable, to solve the system. 6. х+ 2у — z %3 2х — у + 3z 3D —13 Зх — — —16 2y + 3z
Use Cramer’s Rule, if applicable, to solve the system. Зх — 4у — 12 — 0 5х + 2y + 6 %3D 0
Use Cramer’s Rule, if applicable, to solve the system. 2х + 3у — 13 — 0 Зх — 2у 3D 0
Use Cramer’s Rule, if applicable, to solve the system. Jx - Зу %3D —5 2х + Зу —
Use Cramer’s Rule, if applicable, to solve the system. х — 2у 3D 4 Зх + 2у 3D 4 ||
Find the value of the determinant. -2 1 2 3 -1 4 2
Find the value of the determinant. 2 1 -3 2 6
Find the value of the determinant. 2 3 10 -1 2
Find the value of the determinant. 1 4 4 0 -1 2 6 4 1 3
Find the value of the determinant. -4 3
Find the value of the determinant. 3 4 3
Solve each system of equations using matrices. If the system has no solution, say that it is inconsistent. (- 3y + 3z – t = x + 2y – z 4 = -3 x + 37 + 2t = 3 x + y + 5z =
Solve each system of equations using matrices. If the system has no solution, say that it is inconsistent. y - z - t = 2х + у — z+ 2t %3D 3 х — 2у — 2z — 3t %3D 3x – 4y + z + 5t = -3 ||
Solve each system of equations using matrices. If the system has no solution, say that it is inconsistent. 4х — Зу + 52%3D 0 2х + 4y — 3z %3D 0 бх + 2у + z%3D 0
Solve each system of equations using matrices. If the system has no solution, say that it is inconsistent. y + z = 0 y – 5z – 6 = 0| z - 1 = 0 х- 2х — 2у + z — 1 3D 0

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