Basic Math Questions and Answers

A business estimates that the value V(t) of a certain piece of office equipment is decreasing to the function V (t) = 65(0.8)^6 according where t represents the number of years that have elapsed since it was purchased, and V(t) is in dollars. Find this piece of equipment's value after 6 years. Round the answer to the nearest cent. $

Use the quadratic formula to solve the equation: x² + 15x + 24 = 0 x = 15+√129/2 or x = 15-√129/2 x = 15+√321/2 or x = 15-√321/2 x = -15+√129/2 or x = -15-√129/2 x = -15+√321/2 or x = -15-√321/2

You are asked to solve the following quadratic equation using either quadratic formula or by factoring. What method would you chose and explain why. 6x² + 20x + 5 = 0

(x − 2)(-5x² + x) = (x)(−5x²) + (x)(x) + (−2)(-5x²)+(-2)(x) is an example of: A. Dividing two binomials B. Vertical multiplication C. Complex conjugates D. FOIL

One of the games at a carnival involves trying to ring a bell with a ball by hitting a lever that propels the ball into the air. The height of the ball is modeled by the equation h (1) = -16t² + 39t. If the bell is 25 ft above ground will it be hit by the ball? Not enough information given. Yes No

The vertices of PQR have coordinates P(2,3), Q(3,8), and R(7,3). Under which transformation of POR are distance and angle measure preserved? 1) (x,y) → (2xy + 3) 2) (x,y) → (x+2y+3) 3)(x,y) → (2x,3y) 4) (x,y) → (x-2y) O 1 O 2 O 3 O 4

Three of the vertices of a rectangle have coordinates (-1, -1), (6, -1), and (-1, 2). What are the coordinates of the fourth vertex? (-1,2) (2,6) (6,2)

The length of the rectangle is 4 more than the width. The area of the rectangle is 45 square centimeters. Identify the length and width of this rectangle. The width is 5 cm and the length is 9 cm The width is 9 cm and the length is 13 cm The width is 9 cm and the length is 5 cm The width is 5 cm and the length is 20 cm

Which of the two functions below has the smallest minimum y-value? f(x) = x^5 - 2 g(x) = 3x^2 + 1 A. f(x) B. The y-values for f(x)and g(x) both go to - C. There is not enough information to determine D. g(x)

Solve for x. 4(x + 2) = 48 x = 14 x= 10 x=6 1/2 x= 7 1/2

Solve the quadratic equation using completing the square: x2 = -2x + 21 x=-1+ √21 or x = -1- √21 x=1+ √21 or x = 1 - √21 x=-1+ √22 or x = -1 - √22 x = 1 + √22 or x = 1 - √/22

Which of the following represents the divisor and the dividend for the synthetic division problem below? -1√2 9 7 A. x+1 and 2x² +9x+7 B. x+1 and -2x² -9x-7 C. x-1 and -2x² -9x-7 D. x-1 and 2x² +9x +7

Choose the answer based on the most efficient method as presented in the lesson. If the first step in the solution of the equation 2x - 8 = 5x + 3 is "subtract 2x," then what should the next step be? subtract 5x add 8 subtract 3

Indicate the equation of the line through (2, -4) and having slope of 3/5.

In finding the solution of the equation 5 - 3x = 2x + 9, 3x is added to both sides of the equation first. Which of the following should be done next? add-9 add-5 add-2x

A book editor was proofreading a draft of a novel. She found that the number of errors on each page of the book was normally distributed, with the mean number of errors on a page as 15 and a standard deviation of 2. If 102 pages had between 11 and 15 errors, what was the approximate total number of pages in the book?

Solve for x. 7(x + 1) = 21 x = 4 Ox=22/7 Ox=2 Ox=20/7

Find the average rate of change of the function f(x)=x² + 3x from x₁ = 4 to x₂ = 6.

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 =