Basic Math Questions and Answers

Harold moves no more than 43 of his sheep and goats into another field. Fewer than 22 of the animals are goats. Let s represent the number of sheep and g represent the number of goats. Which two inequalities represent this situation? A. s> 22 B. g <22 C. s+ g≤ 43 D. s-gs 43

Grace bought a television for $329 and some DVDs for $5.75 each. Write an equation to find out how many DVDs Grace bought if she spent a total of $363.50. 329 +5.75m = 363.50

Stacy is building a candy house. She worked on it 3 hours before lunch and 6 hours after lunch. How many total hours did Stacy spend working on the candy house? Give your answer as a mixed number in simplest form. Enter the number that belongs in the green box.

There is a spinner with 11 equal areas, numbered 1 through 11. If the spinner is spun one time, what is the probability that the result is a multiple of 2 or a multiple of 5?

Solve 5ax + 6ax = 7ax+8 for x. Assume a‡0. O A. x = 2/a O B. x = 1/a O C. x = 2a O D. x = a

The circumference of a sphere was measured to be 86 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.

After making twenty-sixth payment of $480.00 on your car loan, you wanted to find out how much is left of your original 5 years loan at 4.1% compounded monthly of $26,000.00. What is the amount of the remaining balance of your car loan? The remaining balance of your car loan would be $ (Round to 2 decimal places.)

Which of the following options is a 3rd degree polynomial with exactly 1 real root? A. F(x)= x+3x²-9x-27 B. F(x)= x +9x² +27x+27 C. F(x)=x²-9x² +27x-27 D. F(x)= x+3x² +9x+27

Name the kind or kinds of symmetry the following figure has: point, line, plane, or none. (Select all that apply.) 2 line point plane none

Given that f(x) = x² - 13x + 36 and g(x) = x-9, find (f+g)(x) and express the result in standard form.

Suppose a point has polar coordinates (3, π/2) with the angle measured in radians. Find two additional polar representations of the point. Write each coordinate in simplest form with the angle in [-2π, 2π].

Consider the function f(x)=√2-x+7 for the domain (-∞, 2]. Find f(x), where is the inverse of f. 1 Also state the domain off in interval notation.

Find the value of Q in the following system so that the solution to the system is (4,2). 3x - 2y = 8 2x+3y = Q A. 14 B. 10 C. 12 D. 8

When Jose installs a new app on his phone, it creates a square icon on his home screen. The square starts with side lengths of 1 cm. The side lengths grow by 2.8 cm each second until the square reaches its maximum size. What is the perimeter of the square after 1.5 seconds? Recall that the perimeter of a shape is the sum of its side lengths. 16.8 centimeters 19.2 centimeters 20.8 centimeters 29.2 centimeters

Find the maximum and minimum values of the function g(θ) = 2θ - 8 sin(θ) on the interval [0, π]

Suppose a point has polar coordinates (-4, -11π/6) with the angle measured in radians. Find two additional polar representations of the point. Write each coordinate in simplest form with the angle in [-2π, 2π].

What is the first step when factoring the trinomial ax²+bx+c? A. Look for a common factor in each term. B. Factor the simplified trinomial. C. List the factors of the leading coefficient. D. List the factors of the constant term.

Line j passes through the points (0, 0) and (c, d). Line k passes through the points (0,0) and (-d, c). Lines j and k are perpendicular neither parallel

Line m passes through the points (-4, 3) and (-4, 7). What is the slope of the line that is perpendicular to line m? -4 undefined zero

Rachel spent $24.15 on vegetables. She bought 2 lbs of onions, 3 lbs of carrots, and 1 1/2 lbs of mushrooms. If the onions cost $3.69 per lb, and the carrots cost $ 4.29 per lb, what is the price per lb of mushrooms? a. $2.60 b. $2.25 c. $2.80 d. $3.10

Solve the inequality. -3x - 5 ≥ 7 A. x ≤ 4 B. x ≥ 4 C. x ≤ -4 D. x ≥ -4

A party room costs $50 plus $6 per person. To reserve a party room, you must spend at least $98. Which inequality could help you figure out how many people you should invite so that you spend at least $98? A. 56p < 98 B. B. 50+ 6p ≥ 98 C. 50+ 6p ≤ 98 D. 50-6p ≤ 98

A car rental company offers two plans for renting a car. Plan A: 35 dollars per day and 10 cents per mile Plan B: 65 dollars per day with free unlimited mileage How many miles would you need to drive in one day for plan B to save you money? Enter the exact answer as an inequality using the variable m to represent the number of miles.

The circumference of a sphere was measured to be 82 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.

f(x) = √3x g(x) = √48x Find (f g)(x). Assume x ≥ 0. A. (f.g)(x) = 12√x B. (f g)(x) = √51x C. (f.g)(x) = 12x D. (f.g)(x) = 72x

John lives in Vermont and Julie lives in Florida. One January day, it was 52°F in Florida and -9°F in Vermont. What was the difference in temperatures?

Solve 3x + 3 = 21. A. x = 6 and x = -8 B. x= -6 and x = -8 C. x= 6 and x = -6 D. x=-6 and x = 8

Solve the triangle BQK where b=3.43, q = 6.51, and Q = 90°. Which of the following statements are true about BQK? There is at least one correct response. Choose all correct responses. Rounded to the nearest degree, the measure of angle K = 53° The perimeter of BQK is approximately 17.3 The perimeter of BQK is approximately 15.47 Rounded to the nearest degree, the measure of angle B = 32° None of these statements are true about AABQK

Which of the following is a validation of congruency between two polygons? if by applying only rotation you can make them coincide if by applying only translation you can make them coincide if by applying rigid motions you can make them coincide if by applying dilation you can make them equal

Define the sets A, B and C as: A = {-7, 4, 0, 3} B = {-7, 0, 4, 6} C = {-5, 4, 0, 2, 4, 6} List all values of a that satisfy each statement. - x is in A and x is in B: x is in A or x is in C: x is not in B and is in C:

A school board wants to implement a new lunch program, but wants to know how the students feel about it. Which sample is the best predictor of how the students feel? A. Select 7th graders at random. B. Select the first 10 students that show up to lunch. C. Ask the other members of the school board. D. Select random students from every grade.

a. When 50.19 and 50.67 are multiplied, the answer should have Enter the answer, using the correct number of significant figures: 50.19 x 50.67 = b. When 50.19 and 50.67 are summed, the answer should have Enter the answer, using the correct number of decimal places: 50.19 +50.67: =

Rosario and Enrique are in the same mathematics class. On the first five tests, Rosario received scores of 78, 77, 64, 86, and 70. Enrique received scores of 90, 61, 79, 73, and 87. How much higher was Enrique's average than Rosario's average? 15 points 2 points 3 points 4 points

a. When 28.40 and 27.6 are divided, the answer should have ____ Enter the answer, using the correct number of significant figures: 28.40/27.6 = b. When 27.6 is subtracted from 28.40, the answer should have ___ Enter the answer, using the correct number of decimal places: 28.40 27.6 =

The number 1.464163 rounded to 4 significant figures is: The number 418.308 rounded to 3 significant figures is: The number 43.94754 rounded to 5 significant figures is:

f(x) = 3x + 8. Find the inverse of f(x). A. f ¹ (x) = 3x - 8 B. ƒ ¹ (x) = x - 3 / 8 c. f ¹ (x) = x - 3 / 3 D. f¹(x)= 8 - 3x

You want to solve the following system of equations by addition. What should you do first, so that one variable is eliminated when you add the equations? -2x+4y=10 3x-2y=-7 A. Multiply the top equation by -3. B. Multiply the top equation by 3 and the bottom equation by -2. C. Multiply the top equation by 2 and the bottom equation by 3. D. Multiply the bottom equation by 2.

Amy is thinking of a number that is 2 times the value of Jake's number. Amy's number is also 2 more than 3 times the value of Jake's number. What is Amy's number? Write and solve a system of equations to answer the question. A. -2 B. -4 C. 4 D. 2

Solve 4|x + 5| + 8 = 24. A. x = -1 and x = 9 B. x = -1 and x = -9 C. x = 1 and x = -9 D. = 1 and x = -1

Which of these is a factor in this expression? 7z^4 - 5+10 (y³+5) A. 10 (y³ + 5) B. −5+10 (y³ + 5) c. (y³ + 5) D. 7z^4 - 5

The expression below is the factorization of which of the following trinomials? (2x+7)(x+5) A. 2x²+2x+35 B. 2x² +10x+35 C. 2x² +12x+35 D. 2x² +17x+35

You know that this statement is true: If A is true then B is true. Which of the following statements might also be true? If B is false then A is false If A is false then B is true If A is false then B is false If A is true then B is false

Construct a polynomial of degree two that has the numbers-2, 4 as its zeros and has y intercept 12. The result is an expression in the form y-Ax² + Bx+C. Which one of the following statement(s) is(are) true? There may be more than one correct answer. (x-2) is a factor A=1.5 A=-1.5 When x=-3, y=-11.5

Use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x) = 8 + 9/x f'(x)= f(1) = f(2)= f(3) =

The negation of the statement "Sophie is wearing white shoes" is: Maria is wearing white shoes Sophie is wearing shoes Sophie is not wearing shoes Sophie is not wearing white shoes Sophie is wearing black shoes

The number 38.99011 rounded to 3 significant figures is: The number 347.0067 rounded to 5 significant figures is: The number 3533.620 rounded to 3 significant figures is:

Using the discriminant, how many real solutions does the following quadratic equation have? x^2+6x+10=0 A. Three real solutions B. Two real solutions C. One real solution D. No real solutions

Solve |x + 6| = 8. A. x = -2 and x = 14 B. x =2 and x = -14 C. x = 2 and x = -2 D. x = 2 and x = -14

a. When 15.039 and 11.523 are divided, the answer should have ________ Enter the answer, using the correct number of significant figures: 15.039/11.523 = b. When 11.523 is subtracted from 15.039, the answer should have _____ Enter the answer, using the correct number of decimal places: 15.039 11.523 =.

The number of hours worked, x, and the total dollars earned, y, have a strong positive relationship. Explain what it means to have a strong positive relationship in this situation.