## Precalculus Questions and Answers

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Find a basis for the solution space of the given homogeneous linear system. x_1 + 2x_2 + 7x_3 - 9x_4 + 31x_5 = 0\\ 2x_1 + 4x_2 + 7x_3 -11x_4 + 34x_5 = 0\\ 3x_1 + 6x_2 + 5x_3 - 11x_4 + 29x_5 = 0

Ms. Easty picked up 3 doughnuts and 4 coffees and paid $4.91. Mrs. Martin picked up 5 doughnuts and 6 coffees at the same shop and paid $7.59. How much did 1 doughnut cost? How much did 1 coffee cost?

A tree 19 feet tall casts a shadow which forms an angle of 49 degrees with the ground. How long is the shadow to the nearest hundredth?

Suppose you start at Washington, D.C. (39 N, 77 W), and travel 600 mi due south, then 600 mi due west, then 600 mi due north, and then 600 mi due east. Where will you arrive with respect to your start

A 2-mile cab costs $5. A 6-mile cab costs $9. Write an equation to model the cost: c of a cab ride miles: m.

Brett wants to paint his master bedroom. The paint costs $21 per gallon and the primer costs $15 per gallon. He does not want to exceed $185 for the paint and primer. He has determined that he needs a

Solve the system of linear equations and check any solutions algebraically. Indicate if there is no solution. If the system is dependent, express x, y, and z in terms of the parameter. 3x - 3y + 6z= 1

Given 3 + i is a root, determine all other roots of f(x) = x^4 - 2(x^3) - x^2 - 38x - 130.

An airplane has a cruising speed (speed of plane with respect to the air) of 559 mph. The wind is blowing at 56 mph 15^o north of east. The plane needs to fly from Barnesburg to Warlick Town, which is

A cell phone company offers a contract which cost C, in dollars, of t minutes to telephoning is given by C = 0.25(t - 400) + 57.95, where it is assumed that t is greater than and equal to 400 minutes.

Find (fog)(x) and (gof)(x). f(x) = sqrt(x^2 - 2), g(x) = x^2.

What is the solution for the system of equations. 9x + 8y = 21 x = 13 - 6y

The lengths of 2 sides of a triangle are 2 inches and 10 inches. Find the range of possible lengths for the third side.

Use any methods to solve the systems of equations below. y = (1/4)x - 1, (1/2)y = x - 2.

A university bookstore recently sold a wirebound graph paper notebook for $1.08, and a college ruled notebook for $3.12. At the start of the spring semester, a combination of 50 of these notebooks wer

Larry Mitchel invested part of his $32,000 advance at 7% annual simple interest and the rest at 6% annual simple interest. If this total yearly interest from both accounts was $2,050, find the amount

Solve the system: x = 3 / 2 y + 5 2 x - 3 y = 8.

Solve for x and y. y = 1 / 3 x - 1 x - y = -1.

A person with no more than $4000 to invest plans to place the money in two investments, telecommunications and pharmaceuticals. The telecommunications investment is to be no more than 3 times the phar

While shopping for clothes, Tim spent $6 less than twice what Brenda spent. Tim spent $94. How much did brenda spend?

Your company is planning to spend no less than $80,000 and no more than $100,000 on a landscaping project, which will be used as a promotional park that promotes your toaster manufacturing company. Wr

Two records and three tapes cost $31. Three records and two tapes cost $29. Find the cost of each record and tape.

Solve and graph the equations. y=4x+5 ; x-2y=4

What are two points for the solution 12x + 14y = 70 ?

If an investor invest a total of $1900.00 and one earned 4% and the other 2% and his total profit is $66, how much did he invest in both funds?

Barney and George invested the same amount in two funds. Barney earned 4% and Fred earned 2%. If they earned $420 together. How much did they each invest?

The first of 2 films lasted 9 minutes less than twice as long as the second. The combined length of the 2 films plus a 5 minutes break between them was 260 minutes. How long was the first film?

Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza for a total cost of $12.50. Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is

Find all the numbers for which the rational expression is undefined { \frac{s^3-6x}{ s^2-9} }.

3x - 2y = -5 and 4x + 3y = -18 Find the intersection.

Movie ticket is 8.00, popcorn is 5.00, and drink is 3.00. I have 40.00 to spend. How many games can I play if each game is 2.50? Translate into inequality and solve.

A desk and a chair cost $200 as a set. If the desk costs 4 times more than the chair, how much does each one cost?

Beaver Stadium has a capacity of 1081 more than Michigan Stadium. If the combined capacity for the two stadiums is 213,483, find the capacity of each stadium?

Boy and Girl sells mixtures of almonds and raisins. A kilogram of almonds and raisins cost $300 and $125, respectively. If the final cost of the mixture is $1,400 and the mixture contains 7.5 kg of th

The sum of 3 numbers is 24. Twice the smallest number is 2 less than the largest number and the largest number is equal to the sum of the other two. What are the three numbers?

Find a power function of the form y=ab^x whose graph passes through the points (4,4) and (16,8).

Solve using set builder notation. 12 x - 25 is greater than or equal to 3 x - 5 (x + 6).

Two records and three tapes cost $31. Three records and two tapes cost $29. Find the total cost of each record and each tape.

The larger of the two is 1 less than 3 times the smaller number . If twice the smaller number is increased by the larger number, the result is 18 more than the larger number. Find both numbers.

Tom bowled 135 and 145 in his two first games. Write and Solve a compound inequality to find the possible values for a third game that would give him an average between 120 and 130, inclusive.

John earns $3 more than hugh. Leslie earns $2 less than twice Hugh. Together they earn $101. How much does Hugh earn?

Austin and Kaitlyn Kojan invested $195,000 in a business venture. If Kaitlyn invested 2 times as much as Austin invested, how much money did Kaitlyn invest?

Company A charges $110 for the truck and $55 per hour for the movers. Company B charges $100 for the truck and $60 per hour for the movers. Create a cost equation for each company where y is the total

You and a friend eat tacos. You order 2 tacos and 5 burritos which equals $19. Your friend orders 1 taco and 4 burritos which equals $14. Find the cost of a taco and a burrito.

Kendra owns a restaurant. She decides to charge $1.50 for 2 eggs and 1 piece of toast and $0.90 for 1 egg and 1 piece of toast. How much money is she charging for each egg and each piece of toast?

John and Kathleen each improved their yards planting rose bushes and shrubs. They bought their supplies from the same store. John spent $228 on 12 rose bushes and 11 shrubs. Kathleen spent $108 on 6 r

Sara needs to buy some tuna. Each can costs $0.79 and she has a coupon for $2 off entire purchase, how many cans of tuna can she buy for less than $7? (translate into inequality and solve)

A large pizza costs $8.95 plus $0.65 for each additional topping. Remi paid $10.90 for a large pizza. How many additional toppings did he get?

Jake Jenkins earned $9000 last year by giving tennis lessons. He invested part at 7% simple interest and the rest at 4%. He earned a total of $540 in interest. How much did he invest at 4%?

Polly has 8 more nickels than quarters. If she has $3.40, how many of each does she have?

A video game manufacturer is planning to market a new machine. The fixed costs are $550,000 and the variable costs are $120 per machine. The wholesale price of the machine will be $140. How many game

The sum of two numbers is 48. If one-third of one number is 5 greater than one-sixth of another number, which of the following is the smaller number? (a) 6 (b) 22 (c) 26 (d) 42

Greg invested his savings in two investment funds. The amount he invested in Fund A was 3 times as much as the amount he invested in Fund B. Fund A returned a 6% profit and Fund B returned a 7% profit

The acme widget company has $13,000 available for making widgets. part of the money is spent on an advanced widget-bending machine costing $1,000. the manufacturing cost for each widget is $3. how man

A sample of 600 grams of a radioactive substance decays according to the function { A(t) = 600e^{-0.045t} } where t is the time in years. How much of the substance will be left in the sample after 2

An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are { 4^o } and { 6.5^o }. How far apart are the ships?

Mary had 25000 dollars to invest. she invested part of that amount at 3% annual interest and part at 5% annual interest for one year. the amount of interest she earned for both investments was 1100. h

The relationship between Celsius(C) and Fahrenheit (F) degrees of measuring temperature is linear. Find an equation relating the two if { 1^o C } corresponds to { 50^o F } and { 30^o C } corre

The measures of two sides of a parallelogram are 28 in and 42 in. If the longer diagonal has measure 58 in, find the measures of the angles at the vertices.

Sara has twice as much money as Miguel. If she had $6 more, she would have 4/3 as much money as he has. How much money does each have now?