Math Questions

An isometry is a transformation that preserves direction orientation distance

The coordinates of a triangle are given as A(3, 2), B(-4, 1), C(-3, -2). What are the coordinates of the image after the triangle is reflected in the line y = x? A' B' C'

Anthony sells cars. Each month, he is paid $2,000, plus a 15% commission on monthly sales above $20,000. Which function calculates his monthly earnings (E) as a function of m, his monthly sales? E(m) = 2,000+ 0.15(m-20,000) E(m) = 2,000+ 0.15(m + 20,000) E(m) = 2,000+ 15(m -20,000) E(m) = 2,000 + 15(m + 20,000)

What would be the best first step in solving this system? y = x² + 3x - 4 2x+y = 17 A. Substitute for x in the first equation. B. Isolate x in the second equation. C. Substitute for y in the second equation. D. Isolate x2 in the first equation.

Given the following information: P(A) = 0.37 P(B) = 0.19 P(A and B) = 0.1 P(B given A) = 0.27 What is the probability of A or B? Round your answer to the nearest hundredth as needed. P(A or B) =

Which expression is the simplest form of - (3x³ + x²) + 2 (x³ − 4x²)? A.-x³-9x² B. 5x³ - 8x² C. - x³ - 3x² D. 5x³ - 7x²

Use the four-step process to find f'(x) and then find f′(1), f'(2), and f'(3). f(x) = 9 + 5/x

The graph of the reciprocal parent function, f(x) = 1/x, is shifted 4 units up nand 3 units to the left to create the graph of g(x). What function is g(x)? A. g(x) = 1/x+4 +3 B. g(x)= 1/x-4 +3 c. g(x)= 1/x-3 +4 D. g(x) = 1/x+3 + 4

Approximately 75% of patients comply with physicians' recommendations post office visits.Each patient's compliance is independent of any other patient's. Of the 400 patients surveyed post office site, what is the probability that at least 300 will comply? Patients are randomly selected.

What is the probability of rolling a dice and getting a 7? A. 1/6 B. 1/7 C. 0, it is impossible to roll a 7 on a dice because the dice does not have 7 on any of its sides

There are 6 red socks and 8 black socks in a drawer. Without looking, you pick out 2 socks to wear. What is the probability of picking red, black? A. 15/91 B. 14/27 C. 24/91

A construction company is analyzing which of its older projects need renovation. Building B was built two years before building C. Building D was built two years before building B. The product of building B's age and building D's age is at least 195. If x represents the age of building C, which inequality represents this situation? A x^2 + 8x + 16 ≥ 195 B. x^2 +6x + 8 ≥ 195 C. x^2 + 4x + 4 ≥ 195 D. x^2 +42 ≥195

For - 12 ≤ x ≤ 15 the function f is defined by f(x) = x²(x + 6)² On which two intervals is the function increasing (enter intervals in ascending order)? Find the interval on which the function is positive: x = Where does the function achieve its minimum? x =

Solve 4 x + 6 = 32. A. x = 14 and x = -2 B. x= -14 and x = −2 C. x= -14 and x = 2 D. x = 14 and x = -14

If P (3,2), find the image of P under the following rotation. 180° counterclockwise about the origin

A spinner has the colors red, blue, and green on it. Maria spins it 30 times, and it lands on red 12 times. What is the experimental probability of spinning a red? A. 4/15 B. 2/5 C. 1/3

If P (2,-1), find the image of P under the following rotation. 180° counterclockwise about the origin

The circumference of a sphere was measured to be 75 cm with a possible error of 0.5 cm. Use linear approximation to estimate the maximum error in the calculated surface area. Estimate the relative error in the calculated surface area.

Solve - 6 + 8 = 15. A. x= 13 and x = -1 B. x= 13 and x = -13 C. x= -13 and x = -1 D. x= -13 and x = 1

Solve 6x - 2y = 10 for y. A. y = 3x - 10 B. y = 3x - 5 C. y = -6x + 10 D. y = 6x + 5

The owner of a baseball stadium found that he sells an average of 586 tickets to each game when he charges an average of $59 per ticket. In addition, he found that with every $6 increase in ticket price, the average number of tickets sold decreases by an average of 4. Which of the following functions describes the baseball stadium's profit in terms of x, the number of $6 increases over $59? A. P(x) = $59-$3,752x - $24x² B. P(x) = $34,574 + $3,516x C. P(x) = $34,574 + $3,280x- $24x² D. P(x) = $59+ $3,280x

Set A and the universal set U are defined as follows. U = {h, p, q, r, x, y) A = {p, r, x} Find the following sets. Write your answer in roster form or as Ø. (a) 4nØ = (b) AU A' =

What is the result when this equation is solved for y? 4x² + 10x - 2y = 6 A. y = -2x² - 5x+3 B. y = 4x² + 10x - 6 C. y = 2x² + 5x - 3 D. y=-4x² - 10x+6

What is the solution to this equation? 5(x-4)= 3x+4 A. x = -8 B. x = 12 C. x = -2 D. x = 3

An equation for the line L is: y = 3 + 5/4 (x - 12) The angle L makes with the x-axis is:

Given a function f(x) with f(− 8) = 1 and f(9) ,m= 2: There must be a number c with -8 < c < 9 and f(c) = 1.4. There might be a number c with 8 < c < 9 and f(c) = 1.4. There cannot be a number c with -8 < c < 9 and f(c) = 1.4.

Select the correct answer. Which of the following functions is the inverse of this function? f (x) = x + 2 / 7 A. p(x)=7x - 2 B. q(x) = -x + 2 / 7 C. r (x) = 7 / x+2 D. s(x)=2x + 7

The following student work is incorrect. The directions say to factor complete. Identify the step that there is an error and explain the error. Step 1: 4x³+36x Step 2: 4x (x² + 9) Step 3: 4x (x + 3) (x + 3) The error is in step 2 because the GCF was not factored out correctly The error is in step 2 because the GCF is not correct The error is in step 3. x² + 9 is prime and cannot be factored.

Solve-2x-6> 3x + 14. A. x<-4 B. x>-5 C. x>-4 D. x < -5

Without actually performing the calculations indicated, choose to how many significant digits the answer to the calculation should be expressed. A. (0.196) (0.08215) (295) / 1.1 b. (4.215 +3.991+2.442) / 0.42 c. (6.219 +5.98) / 3.1159

Joe's New Car dealership lists the following prices for this year's models. $10,469, $12,895, $15,499, $17,999, $18,595, $21,245, $10,395, $14,985 What is the range in prices? A $15,260 B $15,242 C $10,850 D $10,776

Solve |X + 5| = -8 A. x = −3 and x = 13 B. No solution C. x = 3 and x = −13 D. x = -3 and x = −13

If P = (-1,-1), find the image of P under the following rotation. 180° counterclockwise about the origin

A system of linear equations contains two equations with negative reciprocal slopes. Select the correct statement. A. The system will have two solutions. B. The system may have no solution. C. The system will have one solution. D. The system may have infinitely many solutions.

A triangle is reflected across the line x= 2. Which of the following is true? The image and pre-image have the same orientation. The image and pre-image have different sizes. The image and the pre-image are congruent. The image and pre-image are separated by a given angle.

Tami rolled a die 20 times. 14 times it landed on an even number; 6 times it landed on an odd number. What is her experimental probability of it landing on an odd number? A. 1/2 B. 7/10 C. 3/10

Find all real numbers a such that a² = a-2. Explain why this does not violate the exponential function property which states a* = a' if and only if x = y.

Jada saw a music video that her favorite artist recently posted online. The equation v(t) = 320.4^t represents the number of views of the video, t days since Jada saw the video. 1. Find v(-2). 2. What does u(-2) represent in this situation?

f(x) = 4x² + 3x - 2 g(x) = 6x³ – 3x² - 4 Find (f + g)(x). A. (f+g)(x) = 10x³ - 6 B. (f+g)(x) = 6x³ + 7x² + 3x + 2 C. (f+g)(x) = 6x³ + 4x² 6 D. (f+g)(x) = 6x³ + x² + 3x 6

What is the equation of the line with an x-intercept of -1 and a y-intercept of 2? y=2x-2 y = 2x + 2 y=-2x+2

Solve 14x7y= 21 for y. A. y = 14x + 3 B. y = 2x - 21 C. y = 2x - 3 D. y = -14x + 21

To earn full credit for this question, use your own sheet of paper to solve the problem, showing all steps of your work. The highway mileage (mpg) for a sample of 8 different models of a car company can be found below. 17, 20, 23, 27, 36, 29, 32, 36 Find the 5-number summary, check for any outliers using fences, and create a boxplot.

Let u=-51+2j and v=-51-5j. Decompose u into two vectors u, and u₂, where u, is parallel to v and u, is orthogonal to v. Write your answers in the form ai+bj.

Suppose that a guitar company estimates that its monthly cost is C(x) = 400x² + 600x and its monthly revenue is R(x) = -0.4x³ + 600x²200x + 500, where x is in thousands of guitars sold. The profit is the difference between the revenue and the cost. What is the profit function, P(x)? A. P(x) = 0.4x³ + 200x² 800x +500 B. P(x) = -0.4x³ + 1000x² + 400x +500 c. P(x) = 0.4x³ 200x² +800x 500 D. P(x) = 0.4x³ + 200x² 800x + 500

Use implicit differentiation to find y' and then evaluate y' at the point (3,5). y - 3x² +2=0

Solve |x- 4 + 6 = 15. A. x= 13 and x = -13 B. x = 13 and x = -5 C. x= -13 and x = 5 D. x= -13 and x = -5

A 60 ft. long swimming pool is to be constructed. The pool will be 3 ft. deep at one end and 12 ft. deep at the other. To the nearest degree, what will be the measure of the acute angle the bottom of the pool makes with the wall at the deep end? 78° 83° 81° 80° 84°

The Thompson family took a $300,000 mortgage loan, with no down payment, at an annual rate of 3.6% compounded monthly for 30 years. Calculate the family's monthly payment. Round the answer to the nearest hundredth.

Which expression is the simplest form of 5(2x-3) - 3(x+4) / 9 A. 7x-27 /9 B. 13x - 27/9 C. 7X - 3 / 9 D. 7x - 3

There are 12 marbles in a box. 8 are purple, and 4 are green. What is the probability of picking a purple marble and then another purple marble, without replacing the first marble? A. 14/33 B. 1/11 C. 8/33