Basic Math Questions and Answers

The coefficients in the expansion of (x + y)4 are. A. 1, 4, 6, 4, 1 B. 0, 1, 6, 4, 1,0 C. 1, 4, 6, 6, 4, 1 D. 0, 4, 6, 4,0

Fire towers A and B are located 10 miles apart. They use the direction of the other tower as 0°. Rangers at fire tower A spots a fire at 42°, and rangers at fire tower B spot the same fire at 64°. How far from tower A is the fire to the nearest tenth of a mile?

Find the image of the given point under the given translation. . P(-5, 7) T(x, y) = (x + 5, y - 4)

Which function is the inverse of y=-3x+6/7? A. y=-1/3 x+2/7 B. y = -1/3 x + 18/7 C. y=-3x-6/7 D. y=-1/3x+7/6

Simplify (assuming all variables are positive): √9x²y² 3√xy 3xy 3√3xy 9xy

An equation _______ has one solution. sometimes never always

Suppose a point has polar coordinates (2, - 3π/4),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].

Use vertical multiplication to find the product of: x³ +2x+3 x²-x+1 A. x^6+x^4+4x³ - 2x² -x +3 B. x^6+2x³-2x²+2x+1 C. x^6+ x^4 + 3x³ - 2x²-3x+3 D. x^6 -x^4 +x³ - 2x² + 2x +3

Suppose a point has polar coordinates (-5, 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].

32) Irene is on the 18th floor of a hotel. Her car is parked in the B level of the parking garage which is two floors below the main floor (ground level). Including the floor on which Irene is located and the floor on which her car is located, how many floors will Irene pass when she rides the elevator to go to her car?

The total cost (in dollars) of manufacturing x auto body frames is C(x) = 70,000+400x. (A) Find the average cost per unit if 500 frames are produced. (B) Find the marginal average cost at a production level of 500 units. (C) Use the results from parts (A) and (B) to estimate the average cost per frame if 501 frames are produced. (A) If 500 frames are produced, the average cost is $ 540 per frame. (B) The marginal average cost at a production level of 500 units is $0.8 per frame. (Round to the nearest cent as needed.)

What's the circumference of a circle with a radius of 3 inches? Use 3.14 for π.

What is the degree of this polynomial? 5y² + y +1 A. 2 B. 1 C. 5 D. 3

Question 6 of 46 Using the factor theorem, which of the following is a factor of the polynomial below? x3 +7x2 +4x-12 A. x+6 B. x+4 C. x-3 D. x-2

Which of the following points lies in quadrant III? (-1,-5) (-1,5) (1,-5)

What identity can be used to rewrite the expression 27X³ -64? A. Pythagorean Triples B. Sum of Cubes C. Difference of Squares D. Difference of Cubes

Three of the vertices of a square are the points whose coordinates are (2, 3), (2, 6), and (5, 3). What are the coordinates of the fourth vertex? (6,5) (2,5) (5,6)

To solve this system of equations, Ayana isolated y in the first equation and then substituted for y in the second equation. What was the result? 2y = 6x x² + y = 4 A. x² + 3x² = 4 B. x² + 6x = 4 C. x² + 3x = 4 D. x² + 6x² = 4

Calculate the mass percent concentration in the following solution: A sugar solution with 100 g of sugar, dissolved in 0.25 kg of water. Hint: Make sure that all of your units are in grams before doing any calculations. Round to one decimal place and do NOT include the % sign in your answer.

Simplify (assuming all variables are positive): √20x²5 2xy² √5y 2x²y4√√5y 4xy² √5y 2x²y² √5y

Solve x/3- 6 y for x. A. x= 3y - 18 B. x = y + 2 C. x = y 2 D. x= 3y + 18

Simplify: (2x²y³)4 16x8y¹2 8x6y7 8x8y¹2 16x6y7

What is the degree of the polynomial below? 2x² +3x+1 A. 0 B. 3 C. 2 D. 1

Expand the expression. 1/3 (12d + e)

What expression is represented by the factorization below? (3x+2)(3x-2) A. 9x² +12x-4 B. 9x² +12x+4 C. 9x²-4 D. 9x² +4

Which of the following is a monomial? A. 9x²+2x+4 B. √2x+1 C. 6/x D. 3x

Kristen and Martha have a company making widgets. When working alone, Kristen can make a widget in 6 minutes. When working alone, Martha can make a widget in 2 minutes. How long would it take them working together to create a widget?

Which of the following would be the most logical first step to solving this quadratic equation? x^2 - 5x+6 = 0 A. Factor the left side. B. Use the zero product rule to set up smaller equations. C. Add-6 to both sides. D. Take the square root of both sides.

What is the vertex of the quadratic function below? y = x² - 8x+1 A. (8, 1) B. (-4, 15) C. (4, -15) D. (-8, 129)

Use the sum of cubes formula to factor. Be sure to factor out any common factors. x³+27

Choose the kind(s) of symmetry. (Select all that apply.) H point line none plane

First factor out the greatest common factor from each term. Then factor the remaining polynomial. 4x² + 16x+12 4x² + 16x + 12 =

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