Basic Math Questions and Answers

A transformation T: (x,y) → (x + 3, y + 1). The image of B(4, 1) under this transformation is (7.2) (1, 0) (-1,0)

Solve |x+6 |- 7 = 8. A. x = -9 and x = -21 B. x = 9 and x = − 21 C.x = 9 and x = -9 D. x = -9 and x = 21

Select the correct answer. When two pumps are used, they can fill a tank in 60 minutes. When the first pump is used alone, the tank will be filled in 150 minutes. When x represents the time it takes the second pump to fill the tank when used alone, the situation is represented by this equation: 1/150 + 1/x = 1/60 How long would it take the second pump, working alone, to fill the tank? A 75 minutes B. 90 minutes C 100 minutes D. 120 minutes

If no denominator equals zero, which expression is equivalent to x^2+10x+25/x+5 - x^2-6/x-5? A. 2x^2-19/x-5 B. 2x^2-19/x^2-25 C. 19/x-5 D. -19/x-5

Paper lanterns are $3.50 each. Write a direct proportion equation using p for paper lanterns and c for total cost. A. 3.50c = p B. 3.5pc C. 3.50+p=c D. 3.50p = c

Jack invested $2,900 in an account paying an interest rate of 8 1/8% compounded annually. Anthony invested $2,900 in an account paying an interest rate of 8 1/2% compounded continuously. After 10 years, how much more money would Anthony have in his account than Jack, to the nearest dollar?

What is the solution to this equation? 8x-5(x-3) = 18 A. x = 7 B. x = 5 C. x = 11 D. x = 1

Friends compared the number of pets they had at home. Their results are below: 2,3,1, 0, 0, 4, 2, 2 What is the mean number of pets in their homes? A. 14 B. 2.33 C. 1.75 D. 2

Instead of walking on the sidewalk around the perimeter, students take a diagonal shortcut from corner to corner across a rectangular vacant lot that measures 82 ft. by 195 ft. To the nearest foot, how much distance do they save? 130 ft. 99 ft. 17 ft. 212 ft. 65 ft.

Sean and Colleen are raking leaves in their yard. Working together, they can clear the yard of leaves in 24 minutes. Working alone, it would take Sean 20 minutes longer to clear the yard than it would take Colleen working alone. When c is the number of minutes it would take Colleen to finish the job when working alone, the situation is modeled by this rational equation: 1/c + 1/c+20 = 1/24 How long would it take Colleen alone to clear the yard of leaves? A 12 minutes B. 14 minutes C. 28 minutes D. 40 minutes

Solve |x + 5| = -7. A. No solution B. x = 2 and x = −12 C. x = −2 and x = − 12 D. x = − 2 and x = 12

Solve |x + 4| = -7. A. No solution B. x = -3 and x = −11 C. x = 3 and x = -11 D. x = -3 and x = 11

Solve |3x + 3 |= 27. A. x = 8 and x = −8 B. x= -8 and x = 10 C. x = 8 and x = −10 D. x = −8 and x = -10

Which list of ordered pairs represents solutions to x + y = 2? (-4, 6), (0, 2), (4,2) (-4, 6), (0, 2), (4, -2) (-4,-6), (0, 2), (4,2)

A parent volunteer group is raising money by making custom hats to sell at school activities. They plan to sell the hats for $11. Each hat costs $5 to make. They spent $50 for advertising. Use n to represent the number of hats they sell. Multiply this by the money they make for each hat, then subtract the advertising cost. Which expression represents the money that the group raises? A. (11-5) n - 50 B. 50 - (11-5) n c. 11-5n-50 D. 11n-5 -50

Consider this expression. 9 / 4x^2-12x + 7x / x^2-9 The least common denominator of the two rational terms is

Solve the formula d = rt for t. A. t= d-r B. t = d/r C. t = r/d D. t = dr

The Sanchez family wants to go on a vacation in September and they begin saving in December. The Sanchez family expects the vacation to cost $1,700. Each month they will deposit 5% more than the previous month. In December, they deposit $100. How much will the Sanchez family have saved for their vacation after 9 months? Round the answer to the nearest hundredth. *

Which series of transformations will always carry an image onto the original figure? reflection over the y-axis followed by reflection over the x-axis rotation by 180° about the origin reflection over the x-axis followed by reflection over the y-axis rotation by 360° about the origin

(11.3) A local television station wants to find the number of hours per week people in the viewing area watch sporting events on television. The station surveys people at a nearby sports stadium. Is the sample biased? Explain your reasoning.

If you borrow $100 for 3 years at an annual interest rate of 9%, how much will you pay altogether?

Solve 4 |x + 7| = 24. A. x = 13 and x=-1 B. x= -13 and x = -1 C. x= -13 and x = 1 D. x= 13 and x = -13

The minimum of the graph of a quadratic function is located at (-1, 2). The point (2, 20) is also on the parabola. Which function represents the situation? f(x) = (x + 1)² +2 f(x) = (x - 1)² +2 f(x) = 2(x + 1)² + 2 f(x) = 2(x - 1)² + 2

Solve |7x + 21| = 14x. Identify the solution and an extraneous solution. A. Solution: x = 1; extraneous solution: x = -3 B. Solution: x = 3; extraneous solution: x = -3 C. Solution: x = -1; extraneous solution: x = 3 D. Solution: x = 3; extraneous solution: x=-1

Which expression is the simplest form of 4x³ - x² +2 (x³ - 3x²)? A. 4x³ - 6x² B. 6x³ - 7x² C. 2x³ - 6x² D. 6x³ - 4x²

Determine the value of y, if x is 10. y = |x|+8

(11.3) Classify the following samples as biased or unbiased. a. A radio station asks listeners to call in and participate in a poll about radio advertisements. b. Every fourth person who enters a grocery store is asked whether he or she thinks airline prices are reasonable. c) A sports league randomly selects five players from each team to complete a survey about fan behavior.

Ten students compared their test percentage grades: 93,77,100,68,94, 83, 86, 88, 93,85 What is their median percentage score? A. 83.4 C. 87 B. 86.7 D. 88.5

Solve |7x+42| = 14x. Identify the solution and an extraneous solution. A. Solution: x= -2; extraneous solution: x= 6 B. Solution: x = 2; extraneous solution: x= -6 C. Solution: x = 6; extraneous solution: x= -6 D. Solution: x= 6; extraneous solution: x=-2

A swimming pool at Mary's house is 7 m long. 5 m wide, and 1.5 m deep. The water-resistant paint needed for the pool costs $5 per square meter. How much will it cost to paint the interior surfaces of the pool? $71 $76 $106 $355

Drew's neighbor pays him $35 to mow her lawn and she always gives him a 20% tip. He decides to mow the lawn with his friend and split the earnings evenly. How much will each of them make?

The dimensions of a rectangular prism are 8 m x1 9 m x 10 m. If the dimensions of the rectangular prism are increased by 4, then find the volume of the new prism. 1,284 m³ 2,184m3 4,182 m³ 8,142 m³

Select the correct answer. Which expression is equivalent to the given expression? 3x^2 + 5x-7(x²+4) A-4x² + 5x - 28 B.4x^2+ 5x - 4 C.x²+28 D. x² +4

Which set of angles could NOT form a triangle? A. Three acute angles B. One right angle, two acute angles C. One right angle, one acute angle, one obtuse angle D. One obtuse angle, two acute angles

(11.2) Which of the following is a parameter? Ten out of 25 people surveyed chose "red." The total collected at a fund-raiser was $5,281. Seventy-five percent of the freshmen surveyed voted for Lucy.

Contestants in a long distance race run 5 kilometers due south. The runners then turn right and head west towards the finish line. If the straight line distance from start to finish is 13 kilometers, what is the distance that the contestants traveled while heading west? 17 km 14 km 12 km

Kristin Wilson lives in Spartanburg, South Carolina, and wishes to visit relatives in the following South Carolina cities: Sumter and Greenville. In how many ways can she visit each of these cities and return to her home in Spartanburg?

Solve |x + 3| = -7. A. x=-4 and x = -10 B. No solution C. x = 4 and x = -10 D. x = -4 and x = 10

Does the equation below represent a direct proportion? If yes, identify the constant of proportionality. y = 2.4x A. No B. Yes, -2.4 C. Yes, 2.4 D. Yes, 2

Select the correct answer. Find the quotient. 2x-3 / x ÷ 7/x^2 A. 7/x(2x-3) B. 7x/2x-3 C. 2x-3/7x D. x(2x-3)/7

Which algebraic expression represents this word description? The difference between the product of nine and a number, and five A. 9x-5 B. 9(5-x) C. 9(x - 5) D. 5-9x

Harold can make 9 pizzas in an hour. Write an equation that shows the relationship between hours (h) and pizzas (p). A. h+9=p B. 9p = h C. 9h=p D. hp = 9

A petri dish of bacteria grow continuously at a rate of 200% each day. If the petri dish began with 10 bacteria, how many bacteria are there after 5 days? Use the exponential growth function f(t)= ae^rt, and give your answer to the nearest whole number. You may use the Desmos scientific calculator: https://www.desmos.com/scientific.

A professor must randomly select 4 students to participate in a mock debate. There are 20 students in his class. In how many different ways can these students be selected, if the order of selection does not matter?

A blueprint shows an apartment with an area of 15 square inches. If the blueprint's scale is 1 inch : 8 feet, what will the actual square footage of the apartment be?

John runs 3 miles in 1/2 of an hour. At the same pace, how many miles will he run in 1 hour? 6 1/4 miles 6 miles 3 3/4 miles

There is a direct path from Gayle's house to the store. Due to construction, the direct route is closed and Gayle must travel 6 miles east and then 8 miles north in order to get to the store. How long is the direct path from Gayle's house to the store? 10 miles 12 miles 14 miles

A car travels 67 miles per hour. Write an equation that shows the relationship between hours (h) and miles (m). A. 67h=m B. 67 = hm C. h+67=m D. none of the above

On a map, the scale shown is 1 inch 3 miles. If an island is 0.5 square inches on the map, what is the actual area of the island?

Sets C and D are subsets of the universal set U. These sets are defined as follows. U = {q, r, x, y, z} C = {x, z} D={q, y, z} Find the following sets. Write your answer in roster form or as Ø. (a) CUD' = (b) C'nd' =