Basic Math Questions and Answers

Simplify the given equation. 5x + 2(x - 3) = +2(x - 1) 7x-6=-2x-2 7x-6=-2x+2 7x-3 = -2x-1

Which of the following is the complete factorization of the polynomial below x³+x²-17x+15 A. (x+5)(x-3)(x-1) B. (x-5)(x+3)(x-1) C. (x+5)(x+3)(x+1) D. (x-5)(x-3)(x+1)

A rectangular patio measures 20 feet by 30 feet. By adding x feet to the width and x feet to the length, the area is doubled. Find the new dimensions of the patio.

Simplify (assuming all positive exponents): √60a¹¹ 2a5√15a 4a55 √15 2a5√8a

A person buys a phone for $83 and signs up for a single-line phone plan with 2000 monthly anytime minutes. The plan costs $112.95 per month. Write an equation that can be used to determine the total cost, C(t), of this phone plan for t months Then, find the cost for 24 months, assuming that the number of minutes the person uses does not exceed 2000 per month. An equation that can be used to determine the total cost, C(t), of the phone plan for t months is C(t) = (Use integers or decimals for any numbers in the expression.)

y = x² y = 1,002 x -2,000 If (x1, y1) and (x2, y2) are distinct solutions to the system of equations shown above, what is the sum of the x ₁ and x ₂?

What is the complete factorization of the polynomial below? x^3+x^2 + 4x + 4 A. (x + 1)(x+2i)(x+2i) B. (x-1)(x + 2i)(x-2i) C. (x + 1)(x + 2i)(x-2i) D. (x-1)(x + 2i)(x+2i)

What are the zeros of the function f(x) = (x+5)(2x-8) ? A. x= -5 and x = 8 B. x = -5 and x = 4 C. x = 5 and x = -4 D. x = 5 and x = -8

Which of the following are not polynomials? A. x² +0x²+2x+√2 B.2/x3 +1/2 C. x2/3+√3x+1 D.2/3+x-2+1 E. x-2+x+1

Simplify (assuming all variables are positive): √16a²b³ 4a²b² √b ab√16b 4avb 4ab√b

Simplify: 48x^4−72x^3+44x/24x^2 48x^2 + 41x 48x^5 – 72x^3 + 11/6x 2x^3-3x + 11/6x 2x^3 - 72x^3 +44x

If P = (2, -1), find the image of P under the following rotation. 90° counterclockwise about the origin ([?], [])

A group of friends went to lunch. The bill, before sales tax and tip, was $37.50. A sales tax of 8% was added. The group then tipped 18% on the amount after the sales tax was added What was the amount, in dollars of the sales tax?

Which of the following represents "ten times the sum of a number and fourteen is equal to nine times the number"? 10(N+14) = 9N 10(N +9N) = 14 10(9N+14) = N

A student submitted the following work that is not correct. Can you find the mistake? Explain the mistake the student made. Simplify (assuming all variables are positive): √32x^3y^2z^7 Step 1: √8.4.x^2.x.y^2.z^6. z Step 2: 2xyz^3√8xz

If the zeros of a quadratic equation are -2 and 4, what would be the factors? (x + 2)(x+4) (x + 2)(x-4) (x-2)(x+4)

Select all that describe the graph of y = -2/3(4)^x+3 - 4 as compared to y = 4^x (Choose 4) horizontal shift to the left 3 vertical stretch vertical shift up 4 vertical shift down 4 horizontal shift to the right 3 reflection over the y-axis vertical compression reflection over the x-axis

Find the vertex: f(x) = -3x² + 18x - 25 (-2,-73) (-3,-106) (2.3) (3,2)

Solve the equation by taking square roots: -3(x - 2)² +33 = 0 x = -2+√30 or x = -2-√30 x = 2+√11 or x = 2-√11 x = 2+√30 or x = 2-√/30 x = -2+√11 or x = -2-√11

A scalene triangle has symmetry with respect to a line containing a median of the triangle. True False

Select all that describe the graph of f(x) = -3. 2x as compared to the graph of f (x) = 2x exponential growth vertical stretch reflected over the x-axis vertical compression exponential decay reflected over the y-axis

Solve by completing the square: x² - 6x = 22 x=3+√31 or x = 3-√31 x=-3+√√31 or x = -3-√3 x=3+√13 or x = 3-√13 x=-3+√13 or x = -3-√13

Simplify (assuming all variables are positive): √75x³y³ 5xy √3xy 25x²y²√3xy 25xy √3xy 5x²y²√3xy

In the polynomial function below, what is the leading coefficient? F(x) = x² +8-5x³-19x A. 1/2 B. 8 C. -19 D. 2 E. -5

Japan became a major economic power after World War II due to 1. the support of the Soviet Union and Warsaw Pact nations 2. a focus on the production and exportation of consumer goods 3. spoils of war brought home by Japanese soldiers 4. the acquisition of new markets through military conquest

Solve for x. 16x - 5 = 18x - 2 x = 1 1/2 x = -3 1/2 x = -1 1/2 x = 3 1/2

Which of the following describe the graph of y=1/3(3/2)^x compared to y = (3/2)^x. (Choose 2) Reflection across the x-axis Reflection across the y-axis Vertical Compression Exponential Decay Vertical Stretch Exponential Growth

Select all that describe the graph of f(x) = 1/3(1/5)* as compared to the graph of f(x) = (1/5) (Choose 2) reflected over the x-axis vertical compression exponential growth reflected over the y-axis Oexponential decay vertical stretch

Given quadrilateral RSTU, tell which sides (if any) are parallel and which are perpendicular for the coordinates of the vertices. R(-1, 1), S(1, -2), T(4, 0), U(3, 3) Click on the graphic to complete the answer RS ST

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. (-2, -1), (-5, -1), (0, 4), (5, -1), (2, -1), (2, 1), (-2, 1), (0, 5), (0, 1).

Factor, if possible. y²+y-2 Select the correct choice below and fill in any answer boxes within your choice. A. y²+y-2= (Type your answer in factored form. Factor completely.) B. The polynomial is prime.

Solve the equation b factoring: b² = -4b+ 21 Ob=7 or b=3 Ob=-7 or b=3 Ob= 7 or b=-3 Ob=-7 or b=-3

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.