Basic Math Questions and Answers

Convert the expression x² + 12x + 27 into vertex form.

Find the intersection points of the parabola y = -x² - 2 and the line -x + y = -4. Give your answer as two ordered pairs separated by a comma. For example, if you found that the solutions were (1, 2) and (3, 4) you would enter (1, 2), (3, 4).

Compute the specified quantity. Your total payment on a 8 year loan, which charged 9% annual simple interest, amounted to $20,260. How much did you originally borrow (in dollars)? (Round your answer to the nearest cent.) $

Which inequality is true when the value of k is -1? k-3>4 -k-3<-4 -k-3>4 -k-3>4

The following passage from Julius Caesar is in reverse word order. Which answer best describes its meaning? BRUTUS: Thus must I piece it out A. Thus, I give out pieces B. Thus, I must figure it out C. Thus, I must be out of pieces

A coin is to be flipped four times, in sequence. What is the probability that the number of tails will never exceed the number of heads? The sequence HHTH satisfies the description, as does HTHT. However, in each of the sequences THHH and HTTH there is a point at which the number of tails exceeds the number of heads.

For f(x) = 9x and g(x)=x+6, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(4); d. (gof)(4)

A board is cut into 8 pieces. This requires the carpenter to make 7 cuts. Each cut produces a kerf, destroying a small amount of wood. If each kerf destroys 5/32" of the board, what total length of board will be lost to kerf once all cuts have been made?

A 6 year bond costs $20,000 and will pay a total of $2,000 in interest over its lifetime. What is its annual interest rate r (as a percent)? (Round your answer to three decimal places.)

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. We let P be any point on line 1, but different from point X. X Given: px is the bisector of YZ Prove: YP = ZP Send To Proof Send To Proof

What are the coordinates of the point of intersection of y = 5x -5 and y=2 - 2x? The coordinates of the point of intersection are (Type an ordered pair.)

Use the Segment Addition Postulate to find the missing length if the given points are collinear and appear in alphabetical order.

Write the linear equation in slope-intercept form y=b+mx. What are the values of m and b? y=100-2(x - 25) y=

Yesterday in Juneau, Alaska it was -20 degrees and in San Dieg California it was 75 degrees. What was the difference in temperature between these two cities? Select one: a. -20 degrees b. 55 degrees C. 75 degrees d. 95 degrees

You have decided to start saving for college and open up a 529 account. You invest $5,000 into the account at a 4% interest rate compounded monthly. How much money will you have after 7 years? $11,533.61 $13,482.02 $6,579.66 $6,612.57

Hurricane Bob is currently located at (18N, 53W). It is traveling at 11 knots. How far away from Galveston is it if Galveston is at (29N, 95W)? How long would it take to get there in hours and in days? You must show work to get credit.

If 4 is decreased to 1, the decrease is what percent of the original number?

In calm waters, the oil spilling from the ruptured hull of a grounded tanker spreads in all directions. Assuming that the area polluted is circular, determine how fast the area is increasing when the radius of the circle is 38 ft and is increasing at the rate of 1 ft/sec?

Assume 520,000 people line up on the streets to see the Macy's Thanksgiving Parade. If attendance is expected to increase 25% next year, what will be the number of people lined up on the street to see the parade? Number of people

Why can't first differences be used to tell if the following data is linear? (2,8), (6,11), (8,14), (11,17) Choose the correct answer below. A. The first differences are not equal. B. The difference between inputs is not constant. C. The inputs and output values are all positive. D. The difference between inputs is constant.

Which inequality is true when the value of a is-18?

What color flag signified a comedy would be shown that night? A. A black flag signified a comedy would be shown that night. B. A white flag signified a comedy would be shown that night, C. A red flag signified a comedy would be shown that night, D. A brown flag signified a comedy would be shown that night.

Consider the force exerted by a spring that obeys Hooke's law. Find where U(xf) - U(x) = - SF₁.ds, Fs = -kx i, ds == dx i, and the spring constant k is positive. Express your answer in terms of k, xo, and xf.

Solve the equation. x+6/8 x + 53 What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. The solution set is {x|x is a real number}. C. The solution set is Ø. .

The length of a new rectangular playing field is 9 yards longer than triple the width. If the perimeter of the rectangular playing field is 466 yards, what are its dimensions?

Puthina Unge bought a new Compaq computer system on sale for $1,990. It was advertised as 30% off the regular price. What was the original price of the computer? (Round to the nearest whole dollar.)

The percentage of families that were married couples with children between 1970 and 2000 is approximately where t is measured in decades, with t = 1 corresponding to 1970. (a) What percentage of families were married couples with children in 1980? (Round your answers to one decimal place.) (b) How fast was the percentage of families that were married couples with children changing in 1980? (Round your answers to

Find the domain and range of the relation Provide your answer below: domain: range: {(22, 21), (5, -16), (20, -24), (-17,4), (-9,2)).

Challenge A car is traveling at a steady speed. It travels travel in 41 minutes? In 1 hour? miles in 2 The car will travel miles in 41 minutes.

David has 3 cups of blueberries. He uses of a cup of blueberries to make a breakfast smoothie. He uses of tof the remaining blueberries to make blueberry pancakes. How many cups of blueberries does he use for the pancakes? A Write your answer as a whole number, fraction, or mixed number. Simplify any fractions.

If f(x) = 3x + 2 and g(x)=x²-x, find each value. 14. f(4) 15. f(8) 16.)f(-2) 17.g(2) 18. g(-3). 19.f(-6) 20. f(2) + 1 21. f(1) - 1 23,g(-1) + 4 24. f(x + 1) 25. g(3b)

Jay Miller sold his ski house at Attitash Mountain in New Hampshire for $42,000. This sale represented a loss of 15% off the original price. What was the original price Jay paid for the ski house? (Round your answer to the nearest dollar.)

A rhombus is a four-sided figure with all sides the same length. Points F(-2,-2), G(-2, 3), and H(2, 6) are three vertices of rhombus FGHJ. Vertex J is directly below vertex H. a. Graph rhombus FGHJ. Label J with its coordinates. b. What is the perimeter of the rhombus? Show your work.

Riley is packing 144 pencils, 120 folders and 108 notebooks into as many boxes as possible. a. Find the greatest number of boxes that Riley could pack the items into. b. Find the number of pencils, folders and notebooks in each box.

Out of 5,600 colleges surveyed, 60% reported that SAT scores were not used as a high consideration in viewing their applications. How many schools view the SAT as important in screening applicants?

Earl Miller, a lawyer, charges Lee's Plumbing, his client, 25% of what he can collect for Lee from customers whose accounts are past due. The attorney also charges, in addition to the 25%, a flat fee of $50 per customer. This month, Earl collected $6,400 from three of Lee's past-due customers. What is the total fee due to Earl?

For the graph of a function y = f(x) shown to the right, find the absolute maximum and the absolute minimum, if they exist. Identify any local maxima or local minima. Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice. A. The absolute maximum of y=f(x) is f(1) = 4. (Type integers or simplified fractions.) B. There is no absolute maximum for y = f(x). Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice. A. The absolute minimum of y = f(x) is f() = B. There is no absolute minimum for y = f(x).

A city planning commission must determine whether or not to approve the construction of a new building. The company wants to build in an area of the city that has a height limitation of 310 feet. The plans show that the first floor of the building is 20 ft high and each of the next 15 floors have a height of 11 ft, including the space between each floor needed for electrical, plumbing, and other systems. If the plan meets all other city code requirements, should the city commission approve the building plan? Explain. According to the plan, the building will have a height of the building plan. feet, which is the height limitation for the area. So, the city commission approve

Part A: Solve the equation 5(x + 2) = 6x + 3x - 14, and show your work. Part B: Use this list of properties to justify each step of your math work. Justifications may be used more than once if needed Distributive Property Subtraction Property of Equality Combine Like Terms Multiplication Property of Equality Division Property of Equality Given Addition Property of Equality

The sides of a right triangle are given, where 3x is the base, x - 1 is the height and =40c3² 3x + 1 is the measure of the leg of the triangle. If the perimeter is 56m, calculate the pengths of the triangle and then calculate the area.

The closest distance from Venus to Earth is about 40.000.000 kilometers. The closest distance from Jupiter to Earth is about 6.0 × 108 kilometers. How many times closer to Earth is Venus than Jupiter? Write your answer in standard notation.

If total employee benefits are calculated as a percentage of their gross pay, which of the following employees recieves the largest percentage of their gross pay in employee benefits? (Must show work) Emily: Gross pay $32,600, total job benefits $33,600 Jack: Gross pay $33,700, total job benefits $34,700 Judy: Gross pay $33,400, total job benefits $33,900 Marcel: Gross pay $32,900, total job benefits $34,000

Abrar is creating a model of the Pyramid of Giza using clay. Abrar's model will have a square base with side lengths of 15 inches and the height of the pyramid 10 inches. What will be the volume of Abrar's model? 750 cubic inches 2250 cubic inches 1000 cubic inches 1500 cubic inches

The Health Club offers a silver membership and a gold membership. The table contains information about the one-time registration fee and the monthly fee for each membership. After how many months is the gold membership a better value than the silver membership? Answer in a complete sentence.

Pedro is building a spice rack with 4 shelves that are each 0.55 meter long. At the hardware store, Pedro finds that he can only buy the shelving in whole meter lengths. Exactly how many meters of shelving does Pedro need? Since he can only buy whole-number lengths, how many meters of shelving should he buy? Justify your thinking.

Barry's employer pays $1,945 in health insurance and $234 in life insurance per year. He also gets $4,213 in paid time off per year. His monthly gross pay is $5,020. What are Barry's total job benefits per year?

Which statement is true about a translation? A. A translation takes a line to a parallel line or itself. B. A translation takes a line to a perpendicular line. C. A translation requires a center of translation. D. A translation requires a line of translation. A B C D

Assume that in the year 2019, 766,300 people attended the Christmas Eve celebration at Walt Disney World. In 2020, attendance for the Christmas Eve celebration is expected to increase by 32%. What is the total number of people expected at Walt Disney World for this event? Total number of people

The brain volumes (cm³) of 20 brains have a mean of 1059.4 cm³ and a standard deviation of 127.1 cm³. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a brain volume of 1273.6 cm³ be significantly high? Significantly low values are cm³ or lower. (Type an integer or a decimal. Do not round.)

Use differentials and the graph of f to approximate the following. (Round your answers to three decimal places.)