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mathematics
precalculus

Questions and Answers of Precalculus

One group of people purchased 10 hot dogs and 5 soft drinks at a cost of $35.00. A second bought 7 hot dogs and 4 soft drinks at a cost of $25.25. What is the cost of a single hot dog? A single soft
A restaurant manager wants to purchase 200 sets of dishes. One design costs $25 per set, while another costs $45 per set. If she only has $7400 to spend, how many of each design should be ordered?
The average airspeed of a single engine aircraft is 150 miles per hour. If the aircraft flew the same distance in 2 hours with the wind as it flew in 3 hours against the wind, what was the wind speed?
With a tail wind, a small Piper aircraft can fly 600 miles in 3 hours. Against this same wind, the Piper can fly the same distance in 4 hours. Find the average wind speed and the average airspeed of
A recently retired couple needs $12,000 per year to supplement their Social Security. They have $150,000 to invest to obtain this income. They have decided on two investment options:AA bonds yielding
A store sells cashews for $5.00 per pound and peanuts for $1.50 per pound. The manager decides to mix 30 pounds of peanuts with some cashews and sell the mixture for $3.00 per pound. How many pounds
A movie theater charges $9.00 for adults and $7.00 for senior citizens. On a day when 325 people paid an admission, the total receipts were $2495. How many who paid were adults? How many were seniors?
In 2005 there was a total of 55 commercial and noncommercial orbital launches worldwide. In addition, the number of noncommercial orbital launches was one more than twice the number of commercial
The length of fence required to enclose a rectangular field is 3000 meters.What are the dimensions of the field if it is known that the difference between its length and width is 50 meters?
The perimeter of a rectangular floor is 90 feet. Find the dimensions of the floor if the length is twice the width.
Solve each system of equations. If the system has no solution, say that it is inconsistent. х+ 4у — 3z — -8 3х — у+ 3г %3D 12 х+ у+ 62 3D 1
Solve each system of equations. If the system has no solution, say that it is inconsistent. z = -3 2х — 4у + z%3D -7 -2х + 2у — 3г %3D 4 х+2у —
Solve each system of equations. If the system has no solution, say that it is inconsistent. х — у + 2%3D -4 2х — Зу + 42 %3D — 15 5х + 2z = 12 у — 2z %3D 12 5х +
Solve each system of equations. If the system has no solution, say that it is inconsistent. х+ у — z 3D Зх — 2у + 3-5 6. х+ 3у — 2z %3 14
Solve each system of equations. If the system has no solution, say that it is inconsistent. - 2y + 2z = 6. 7х — Зу + 2z %3D —1 2х - Зу + 42 %3D 0
Solve each system of equations. If the system has no solution, say that it is inconsistent. 2х - 2у + 32 3D6 4х — Зу + 2z %3D 0 -2х + Зу — 72 %3D 1
Solve each system of equations. If the system has no solution, say that it is inconsistent. 2x — Зу — г %3D0 3x + 2y + 2z = 2 x + 5y + 3z = 2
Solve each system of equations. If the system has no solution, say that it is inconsistent. х — у — 23 -х + 2у - 32 3D -4 Зх — 2у - 7z%3 0
Solve each system of equations. If the system has no solution, say that it is inconsistent. 2х — Зу- г %3D 0 —х + 2у + z 3 5 Зх — 4у — г %3D 1
Solve each system of equations. If the system has no solution, say that it is inconsistent. x - y - z = 1 2x + 3y + z = 2 3x + 2y =D0
Solve each system of equations. If the system has no solution, say that it is inconsistent. 2х + у - 32 — — 2х + 2y + z%3D -7 4y — 3г %3D 7
Solve each system of equations. If the system has no solution, say that it is inconsistent. х — 2у + 3z %3 2х + у + Z3 4 —Зх + 2у — 2г%3D -10
Solve each system of equations. If the system has no solution, say that it is inconsistent. 2x + y -4 -2y + 4z = – 2z = -11 Зх
Solve each system of equations. If the system has no solution, say that it is inconsistent. х — у 6. — 3г %3D 16 2х 2y + z = 4
Solve each system of equations. If the system has no solution, say that it is inconsistent. = 0 y х 3 = 2 2y х
Solve each system of equations. If the system has no solution, say that it is inconsistent. 8 х 3 х y
Solve each system of equations. If the system has no solution, say that it is inconsistent. 2.x y = -1 3 2
Solve each system of equations. If the system has no solution, say that it is inconsistent. Зх — 5у 3D 3 15х + 5у %3D 21
Solve each system of equations. If the system has no solution, say that it is inconsistent. 3 -5 3 11
Solve each system of equations. If the system has no solution, say that it is inconsistent. 3 2 = -1 3.
Solve each system of equations. If the system has no solution, say that it is inconsistent. х + у%3D —2 х — 2у 3D 8
Solve each system of equations. If the system has no solution, say that it is inconsistent. 2х + 3у 3 6 х - у з 2
Solve each system of equations. If the system has no solution, say that it is inconsistent. | 3х — 2у %3D0 |5х + 10у %3D 4
Solve each system of equations. If the system has no solution, say that it is inconsistent. S 2x – 3y = -1 10x + y = 11
Solve each system of equations. If the system has no solution, say that it is inconsistent. Зх — у %3D 7 - y = |9х — Зу %3D 21
Solve each system of equations. If the system has no solution, say that it is inconsistent. x + 2y = 4 2х + 4y 3D 8 х
Solve each system of equations. If the system has no solution, say that it is inconsistent. 3D —1 3х + Зу 4х + у3 3
Solve each system of equations. If the system has no solution, say that it is inconsistent. S 2x - y = 0 4x + 2y = 12
Solve each system of equations. If the system has no solution, say that it is inconsistent. х — у 3D5 -3х + Зу 3 2
Solve each system of equations. If the system has no solution, say that it is inconsistent. S2x 2х + у %3D 1 4х + 2у 3 3
Solve each system of equations. If the system has no solution, say that it is inconsistent. 2 2х + 4y — 3 Зх — 5у — —10
Solve each system of equations. If the system has no solution, say that it is inconsistent. J3к ( 5х + 4y 3D 1 %3D
Solve each system of equations. If the system has no solution, say that it is inconsistent. S4x 4х + 5y %3D —3 -2y = -8
Solve each system of equations. If the system has no solution, say that it is inconsistent. 3x = 24 х x + 2y = 0
Solve each system of equations. If the system has no solution, say that it is inconsistent. Sx + 3y = 2х — Зу %3D -8
Solve each system of equations. If the system has no solution, say that it is inconsistent. | 5х — у %3D21 2х + 3у %3D - 12
Solve each system of equations. If the system has no solution, say that it is inconsistent. Jx + 2y = -7 х+ у3 —3
Solve each system of equations. If the system has no solution, say that it is inconsistent. Sx + y = 8 * - y = 4
Verify that the values of the variables listed are solutions of the system of equations. – 5z = 5y - z = -17 —х — бу + 52 - х%3 4, у %3D —3, г %3D2; (4, —3, 2) 4х 24
Verify that the values of the variables listed are solutions of the system of equations. Зх + Зу + 2г 3D 4 х — Зу + z3 10 5х — 2у - 32 3 8 х%3D2, у %3D -2, г3 2; (2, —2, 2)
Verify that the values of the variables listed are solutions of the system of equations. 4х 8x + 5y —х — у+52 %3D6 х %3D2, у %3D -3, г %3D 1; – z = 0 (2, –3, 1)
Verify that the values of the variables listed are solutions of the system of equations. Зх + 3у + 22 %3 х — у — 23 2y – 3z = -8 х%3D 1, у %3D —1, г %3D 2;B (1, –1, 2)
Verify that the values of the variables listed are solutions of the system of equations. х — у %3D3 y = 1-3х + у %3D 1 х%3D —2, у %3D -5; (-2, –5)
Verify that the values of the variables listed are solutions of the system of equations. y = 3 - х + у %3 3 y = х%3 4, у = 1; (4, 1)
Verify that the values of the variables listed are solutions of the system of equations. 2x + y = 19 Зх — 4y %3D = 2; (*-) -- 2.
Verify that the values of the variables listed are solutions of the system of equations. Зх — 4y 3D 4 -x — Зу х %3 2, у (f)
Verify that the values of the variables listed are solutions of the system of equations. |3х + 2у 3D 2 1x - 7y = -30 х%3D —2, у %3 4; (-2,4)
Verify that the values of the variables listed are solutions of the system of equations. S2x - y = 5 [5x + 2y = 8 x = 2, y = -1; (2, –1)
If the lines that make up a system of two linear equations are coincident, then the system is________and the equations are________.
If the solution to a system of two linear equations containing two unknowns is x = 3, y= -2, then the lines intersect at the point________.
If a system of equations has one solution, the system is_________ and the equations are ________.
If a system of equations has no solution, it is said to be ______.
(a) Graph the line: 3x + 4y = 12 (b) What is the slope of a line parallel to this line?
Solve the equation: 3x + 4 = 8 - x.
Find the rectangular equation of the curve x = 5 tan t, y = 5 sec? t, т TT
Solve the equation cot(2θ) = 1 , where 0° < θ < 90.
What is the domain of the function 3 f(x) sin x + cos x
Find a polar equation for the circle with center at the point (0, 4) and radius 4. Graph this circle.
Find a polar equation for the line containing the origin that makes an angle of 30° with the positive x-axis.
Find all the solutions of the equation sin(2θ) = 0.5.
Find an equation for each of the following graphs: (a) Line: (b) Circle: (c) Ellipse: (d) Parabola: (e) Hyperbola:(f) Exponential: У 2.
f(x) = log4(x – 2)(a) Solve f(x) = 2. (b) Solve f(x) ≤ 2.
(a) Find the domain and range of y = 3x + 2.(b) Find the inverse of y = 3x + 2 and state its domain and range.
For what numbers, x is 6 –x ≥ x2?
In the complex number system, solve the equation9x4 + 33x3 – 71x2 – 57x – 10 = 0
For f(x) = - 3x2 + 5x - 2 f(x + h) – f(x) h + 0
Identify each conic without completing the square or rotating axes. 2x2 + 5xy + 3y2 + 3x – 7 = 0
Find an equation of the conic described; graph the equation. Hyperbola: center (2, 2), vertex (2, 4), contains the point (2 + √10, 5)
Find an equation of the conic described; graph the equation. Ellipse: center (0, 0), vertex (0, -4), focus (0, 3)
Find an equation of the conic described; graph the equation. Parabola: focus (-1, 4.5) vertex (-1, 3)
Identify each equation. If it is a parabola, give its vertex, focus, and directrix; if an ellipse, give its center, vertices, and foci; if a hyperbola, give its center, vertices, foci, and
Identify each equation. If it is a parabola, give its vertex, focus, and directrix; if an ellipse, give its center, vertices, and foci; if a hyperbola, give its center, vertices, foci, and
Identify each equation. If it is a parabola, give its vertex, focus, and directrix; if an ellipse, give its center, vertices, and foci; if a hyperbola, give its center, vertices, foci, and
Mary’s train leaves at 7:15 AM and accelerates at the rate of 3 meters per second per second. Mary, who can run 6 meters per second, arrives at the train station 2 seconds after the train has
In a test of their recording devices, a team of seismologists positioned two of the devices 2000 feet apart, with the device at point A to the west of the device at point B.At a point between the
The figure below shows the specifications for an elliptical ceiling in a hall designed to be a whispering gallery. Where are the foci located in the hall? 80'-
A bridge is built in the shape of a semielliptical arch. The bridge has a span of 60 feet and a maximum height of 20 feet. Find the height of the arch at distances of 5, 10, and 20 feet from the
A bridge is built in the shape of a parabolic arch. The bridge has a span of 60 feet and a maximum height of 20 feet. Find the height of the arch at distances of 5, 10, and 20 feet from the center.
A searchlight is shaped like a paraboloid of revolution. If a light source is located 1 foot from the vertex along the axis of symmetry and the opening is 2 feet across, how deep should the mirror be
. Describe the collection of points in a plane so that the distance from each point to the point (5, 0) is five-fourths of its distance from the line x = 16/5.
Describe the collection of points in a plane so that the distance from each point to the point (3, 0) is three-fourths of its distance from the line x = 16/3.
Find an equation of the ellipse whose foci are the vertices of the hyperbola x2 + 4y2 = 16 and whose vertices are the foci of this hyperbola.
Find an equation of the hyperbola whose foci are the vertices of the ellipse 4x2 + 9y2 = 36 and whose vertices are the foci of this ellipse.
Find parametric equations for an object that moves along the ellipse x2/16 + y2/9 = 1with the motion described.The motion begins at (0, 3) is clockwise, and requires 5 seconds for a complete
Find parametric equations for an object that moves along the ellipse x2/16 + y2/9 = 1with the motion described.The motion begins at (4, 0) is counterclockwise, and requires 4 seconds for a complete
Find two different parametric equations for each rectangular equation. y = 2x2 – 8
Find two different parametric equations for each rectangular equation. y = -2x + 4
Graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. x = t3/2, y = 2t + 4; t ≥ 0
Graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. x = sec2 t, y = tan2 t; 0 ≤ t ≤ π/4
Graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. x = ln t, y = t3 t > 0

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