Basic Math Questions and Answers

Which of the following is the result of the equation below after completing the square and factoring? A. (x-5/2)² = 9/4 B. (x+5/2)² = 9/4 C. (x+5)² = 41/4 D. (x+5/2)² = 41/4

Which of the following numbers must be added to complete the square in the equation below? x^2+22x-50 A. 50 B. 121 C. 11 D. 22

An isometry is a transformation that preserves direction orientation distance

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.

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

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

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

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:

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

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 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.

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?

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

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

We created this inequality to represent how Amy can meet her revenue goals: -100x² +15,750x + 212,500 ≥ 243,600 In this activity, you'll solve this inequality to find the minimum ticket price Amy should charge to meet her minimum revenue goal.

A child pulls a wagon with a force of 34 pounds. The handle of the wagon makes an angle of 30° with the ground. Express the force vector F in terms of i and j.

Find an ordered pair (x, y) that is a solution to the equation. 4x+y=5

Which one of the following describes the solution set of |x + 7| <3? The interval from -co to 4 together with the interval from 10 to ∞ The interval from 4 to 10. The interval from -10 to -4. The interval from -∞ to -10 together with the interval from -4 to ∞. The interval from -4 to 10.

Which of the following statements is true of a reflection? Select all that apply. It is an isometry. It slides a plane. The transformation is done over a line of reflection. It flips a plane about a fixed line. It changes the size of the figure being reflected.

A 61/4-inch circular power saw rotates at 4,800 revolutions per minute. (Round your answers to two decimal places.) 4 (a) Find the angular speed of the saw blade in radians per minute. rad/min (b) Find the linear speed (in feet per minute) of one of the 24 cutting teeth as they contact the wood being cut. ft/min

The drug concentration in the bloodstream t hours after injection is given approximately by C(t) = 4.95 e ¹,0sts5, where C(t) is the concentration in milligrams per milliliter. (A) What is the rate of change of concentration after 1 hour? After 5 hours? (B) Graph C.

Noah creates a scatter plot showing the relationship between number of free throws made in a basketball game and the number of points scored. The correlation coefficient for the line of best fit is 0.76. Are the two variables correlated? Explain your reasoning. b. Do either of the variables cause the other to change? Explain your reasoning.

There are x ducks in a pond. The number of swans in the pond is equal to the square root of the number of ducks. If the total number of swans and ducks in the pond is 12, find the number of ducks. 16 9 3 4

A store is offering 25% off all shoes. Declan purchases shoes and clothes. The expression representing his total cost (including 8% tax) is c+(1-0.25)s+0.08[e+ (1-0.25) s). Which term represents the cost of the shoes after the discount? A. (1-0.25) B. 0.08[c+ (1-0.25) s] C. le+ (1-0.25) s] D. (1-0.25)s

A pyramid is 24 ft tall. A scaled model has a height of 2 ft and is 1 foot wide at the base. Identify the scale factor that was used to create the model. A. 1/12 C. 12 B. 1/24 D. 22

Angle 0 is between 0° and 360°, sin 0= -0.97437006. Which of the following intervals contain a possible measure for 0? There is at least one correct response. Choose all correct responses. The interval from 100° to 125°. The interval from 55° to 80°. The interval from 235° to 260°. The interval from 280° to 305°. There is no such angle.

The equation y = -143x³ + 1810x² - 187x+2231 where x represents the time in years since January 1, 1983 is a mathematical model for the number of AIDS cases, y, in some population between the years 1983 and 1991. According to this model, how long after January 1, 1983 was the number of AIDS cases in this population 26,488? Round your answer to one decimal place. 4.4 years 04.3 years 4.6 years 04.7 years 05.1 years

Triangle ABC is translated onto its image, triangle A'B'C'. Use the given vertices of the triangles to answer parts A and B. A(-6, 0) B(-1, 0) C(-5, 3) A'(-2, 4) B'(3, 4) C'(-1, 7) Part A: Use the distance formula to prove that the translation was an isometric transformation. Include all of your work in your final answer. Part B: Use complete sentences to describe the translation that maps triangle ABC onto its image.

Solve 4ax + 5ax = 6ax +9 for x. Assume a ≠ 0. A. x = 3/a B. x = 2a C. x = 1/2a D. x= 3a

Solve |2x - 7 ≥ 11. A. x≤-2 or x ≥ 7 B. x≤-2 or x ≥ 8 C. x≤-2 or x ≥ 9 D. x≤ 3 or x ≥ 6