Math Questions

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?

Point (0, 6) lies on the line y = x x-axis y-axis

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)

Which statement best describes the end behavior of the following function? F(x) = 2x²-x² +5x-9 A. The graph of the function starts low and ends low. B. The graph of the function starts high and ends low. C. The graph of the function starts high and ends high. D. The graph of the function starts low and ends high

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

What are the zeros of the polynomial function F(x) = x² +5x+6? A. x = -6 and x = 1 B. x = -3 and x = -2 C. x= -1 and x = 6 D. x = 2 and x = 3

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

Which of the following equations represents F(x) = x^4 shifted left 3 units and up 2 two units? A. F(x)=(x-3)^4 +2 B. F(x)=(x-3)^4 - 2 C. F(x) = (x+3)^4 - 2 D. F(x) = (x+3)^4 +2

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

Diameter = 18, Angle = 36°, Arc length = ? 1.8 The injury was not a stubbed toe. 1.8π Professor Delta was winding his watch in the movie theater. 3.6π The injury was not done by chemical poisoning. 32.4π Coach Omega was cooking in the kitchen.

The target temperature for a laboratory is 68° Fahrenheit. It can vary by up to 4°. If t is the temperature in the laboratory, which of the following inequalities represents this situation? A. |t + 4| ≤ 68 B. |t+ 68| ≤ 4 C. |t - 68| ≤ 4 D. |t-4| ≥ 68

Victoria was given the expression -3x+x²-8+4x-3x² -2 and asked to simplify it. How can she simplify the expression? A. 4x²+7x+6 B. -2x²+x-10 C. -4x²-7x-6 D. 2x²-x+10

Use the quadratic formula to solve the equation: 4x² - 26x - 42 = 0 Ox= 132-√337/4 or x = -13-2√//127/4 Ox= 13+√337/4 or x = -13+2√127/4 Ox= 13+2/127/4 or x = -13+2√/337/4 Ox= 13-2√//127/4 or x = -13-2√//127/4

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

A rock falls from a tower that is 102.9 m high. As it is falling, its height is given by the formula h = 102.9-4.91². How many seconds will it take for the rock to hit the ground? (h = 0) 2160.9 sec 4.6 sec 9.9 sec 10.1 sec

A rice producer fills boxes with the same weights of different rice varieties to produce rice blends. The machinery filling each box is designed to put 42 ounces of rice in each box. But the machinery is imperfect. The actual weight of each box varies by a certain number of ounces. What mathematical model could the manufacturer use to represent the weights of the boxes?

A straight highway is 100 miles long, and each mile is marked by a milepost numbered from 0 to 100. A rest area is going to be built along the highway exactly 5 miles away from milepost 63. If mis the milepost number of the rest area, which of the following equations represents the possible locations for the rest area? A. |m + 5| = 63 B. |m - 5| = 63 C. |63 + m| = 5 D. |63-m| = 5

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

What is the quotient of the synthetic division problem below, written in polynomial form? -1√264 A. -2x+8 B. 2x+8 C. 2x+4 D. -2x+4

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

Hans is planting a garden with snapdragons and daisies. The table shows some possible combina of the two plants. If Hans plants 29 daisies, how r snapdragons will he plant? The equation Hans will plant models the scenario. snapdragons.

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

Solve the triangle, if possible. Round to the nearest hundredth. a = 27 ft b = 31 ft c = 42 ft A = 39.96°, B = 47.51°, C = 92.53° A = 39.96°, B = 23.76°, C = 116.28° A= 47.51°, B = 39.96°, C.= 92.53° No solution

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).

Find all the roots. 22x² - 15x=0 x = (Use a comma to separate answers. Type repeated roots only once.)

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

The longer base of an isosceles trapezoid joins points (-3, -2) and (7, -2). One endpoint of the shorter base is (-1, 4). What are the coordinates of the other endpoint? (0, -3) (5,4) (4, 5)

A ball is thrown from the top of the school. The height of the ball (in feet) written in terms of the time (in seconds) is modeled by f(t) = -16r² + 32 + 48. What is the maximum height of the ball? 6 feet 64 feet 48 feet 112 feet

Select all that describe the graph of f(x) = 1/3 4x as compared to the graph of f(x) = 4x vertical compression exponential growth reflected over the y-axis reflected over the x-axis vertical stretch exponential decay

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