Math Questions

Evaluate 4(x − 3) + 5x − x² for x = 2. A. 2 B. 11 C. 16 D. -2

Consider this equation. 10x +25/3x + 12=5x/x+4 How many valid solutions does the equation have? The equation has valid solution(s).

A map that was created using a scale of 1 inch : 3 miles shows a lake with an area of 4.5 square inches. What is the actual area of the lake?

3, 4, 5, 5, 6, 9, 12 What is the range? A. 9 B. 5 C. 12 D. 7

Jason hired a luxury car service. The service charges a fixed rate of $4.92, regardless of the number of miles traveled, plus an additional $3.79 per mile. If Jason wants to spend no more than $4.20 per mile, what is the minimum number of miles he should travel? 12 1 6 0

The y-intercept of the parent quartic function, f(3) = 4, is translated 3 units to the right and 1 unit down. Which equation represents this transformation? A g(t) = (x-3)^4 - 1 B. g(t) = (x+3)^4 - 1 C. g(s) = (x-1)^4 +3 D. g(x) = (x+1)^4 +3

A retailer is having a promotional sale for 35% off all items. There is a 7% sales tax added to the price. Which represents the situation, where x is the original cost of the item(s)? f(x) = 0.35x represents the discount price and g(x)=0.07x represents the price after taxes. The total price would be (f.g)(x) = 0.35(0.07x) = 0.0245x. f(x) = 0.65x represents the discount price and g(x)=0.07x represents the price after taxes. The total price would be (f.g)(x) = 0.65(0.07x)=0.0455x. f(x) = 1.07x represents the price after taxes and g(x) = 0.65x represents the discount price. The total price would be (f.g)(x) = 1.07(0.65x)=0.6955x. f(x) = 1.07x represents the price after taxes and g(x) = 0.35x represents the discount price. The total price would be (f.g)(x) = 0.35(1.07x) = 0.3745x.

A rotation is an isometry that moves a plane across a line of symmetry moves a plane in a straight line motion moves a plane as a nor image moves a plane about a fixed point

Consider this product. x^2-3x-10/x^2-6x+5 . x-2/x-5 The simplest form of this product has a numerator of and a denominator of The expression has an excluded value of x =

The height of a vertical cliff is 450 meters. The angle of elevation from a ship to the top of the cliff is 23°. The ship is x meters from the bottom of the cliff. Draw a diagram to show this information, then solve for x.

Finance. Suppose that $4,100 is invested at 3.2% annual interest rate, compounded monthly. How much money will be in the account in (A) 10 months? (B) 20 years? (A) Amount after 10 months: $ (Round to the nearest cent.)

A bag contains three red peppers and four green peppers. You take a pepper from the bag and eat it. You then take another pepper and eat it. a. Calculate the probability you eat two red peppers. b. Calculate the probability you do not eat a red pepper. c. Calculate the probability you eat at least one red pepper.

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)

What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y - 1 = 0? 4x-y-6=0 4x+y+6=0 4x+y-6=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

Two samples are taken with the following numbers of successes and sample sizes r1 = 30 r₂ = 22 n₁ = 75 n₂ = 77 Find a 94% confidence interval, round answers to the nearest thousandth. ____<P1-P2<___

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

Use geometric formulas to find the unsigned area between the graph of y=f(x) and the x-axis over the indicated interval. f(x)=x+10; [-1,11] The area between f(x) and the x-axis is.____ (Type an exact answer, using as needed.)

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

A math class consists of 35 students, 20 female and 15 male. Three students are selected at random, one at a time, to participate in a probability experiment (selected in order without replacement). (a) What is the probability that a male is selected, then two females? (b) What is the probability that a female is selected, then two males? (c) What is the probability that two females are selected, then one male? (d) What is the probability that three males are selected? (e) What is the probability that three females are selected?

What is the slope of the line that passes through (-2, 7) and (4, 9)? slope = -1/3 slope = 3 slope = 1/3

A cat has a litter of 7 kittens. Find the probability that exactly 4 of the kittens are female. Assume that male and female births are equally likely. Estimate the probability to five decimal places if necessary. A) 0.00781 B) 0.54688 C) 0.27344 D) 2.1875

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

Which function displays this end behavior? As x approaches negative infinity, y approaches negative infinity. As x approaches positive infinity, y approaches negative infinity. A y = (2x)^1/3 - 7 B. y = -3x^2 + 4 C. y = -2x^3 - 1 D. y = -x^1/2 + 5

A baseball is travelling on a path given by the equation y = -0.011x² + 1.15x + 1.22. The profile of the bleachers in the outfield can be modelled with the equation y = 0.6x - 72. All distances are in metres. a) Determine the maximum height of the ball. b) Does the ball reach the bleachers for a home run? Justify your answer.

A model of a building is constructed using a scale of 1 inch: 4.5 feet. If the model is 12 inches tall, then the actual building is ___feet tall.

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

A carpool service has 2,000 daily riders. A one-way ticket costs $5.00. The service estimates that for each $1.00 increase to the one-way fare 100 passengers will find other means of transportation. Let x represent the number of $1.00 increases in ticket price. Choose the inequality to represent the values of x that would allow the carpool service to have revenue of at least $12,000. Then, use the inequality to select all the correct statements. The price of a one-way ticket that will maximize revenue is $7.50. 100x^2 + 1,500x - 10,000 ≤ 12,000 100x^2 - 1,500x - 10,000 ≥ 12,000 -100x^2 + 1,500x + 10,000 ≥ 12,000 The maximum profit the company can make is $15,625.00. The maximum profit the company can make is $4,125.00. The price of a one-way ticket that will maximize revenue is $12.50.

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. *

Choose the option that best completes the statement. Following a translation, the measures of the angles in a pre-image are in the opposite orientation of the corresponding angles in its image. are congruent to the measures of the corresponding angles in its image. are larger or smaller based on the scale factor used of the corresponding angles in its image. are at the same angle displacement about a given point.

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.

What is the equation of the line that passes through (-3, -1) and has a slope of 3/5? Put your answer in slope-intercept form. y= -3/5x - 4/5 y= 3/5x + 4/5 y= 3/5x - 4/5

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