Basic Math Questions and Answers

Simplify the expression to a + bi form: 36+√-12-√64-√-147

The perimeter of a rectangle is 78 cm. The length is 7 more than the width. Write two equations that would be used to solve the system.

The perimeter of a geometric figure is the sum of the lengths of its sides. If the perimeter of the pentagon (five-sided figure) to the right is 60 meters, find the length of each side. Note that the figure is not to the scale.

A sphere fits inside a cube with the sphere's diameter equal to the width of the cube, 20 centimeters. What is the approximate volume of the cube not filled by the sphere? A. 4189 cm³. B. 3811 cm³ C. 8000 cm³ D. 5644 cm³

Which best describes her prediction? interpolation, because a key that is 12 keys from middle C is within the data set interpolation, because a key that is 12 keys from middle outside the data set extrapolation, because a key that is 12 keys from middle C is within the data set extrapolation, because a key that is 12 keys from middle C is outside the data set

Perform the operation. (-10x²-10x + 3) - (-4x²-x)

The formula F = 1.8C + 32 gives the temperature in degrees Fahrenheit (F) for a given temperature in degrees Celsius (C). There is one temperature for which the number of degrees Fahrenheit is equal to the number of degrees Celsius. Complete the equation you can solve to find that temperature and then use it to find the temperature. Use the variable C to represent the number of degrees Celsius where degrees Fahrenheit and degrees Celsius are the same.

The product of two consecutive even numbers is 624. Find the numbers. Enter your responses surrounded by brackets [] and in order from least to greatest. So, if the numbers were 9 and 4, you would enter [4,9]. If there are multiple sets of numbers that solve the problem, separate the responses with commas, for example enter [4,9],[5,10] .

Sally bought an item and the dealer told her that its change in value is modeled by the function V(t) = 10000 (0.985)t where V(t) is the value in dollars t years after its purchase. If values continue at that rate, calculate how long will it take until the item is worth only half of what Sally paid for it. Round your answer to the nearest whole year when the value is no more than half of what she paid. It will be worth about half of its original value after about years.

In the diagram, a right circular cylinder with a radius of 3 inches is intersected vertically by a plane passing through points A and B, the centers of the circular bases. What is the perimeter of the figure formed by the intersection of the plane and the cylinder? 17 inches 20 inches 26 inches 40 inches

Select the equivalent expression. x-1.x-8/x7

Tony Ring wants to attend Northeast College. If he deposits $66,969 today, how much will he have 5 years from now at 6% interest compounded semiannually? (Use the Table provided.) (Do not round intermediate calculations.

Give the measure of the supplement of the angle. yº The measure of the supplement of the angle yº is (Type an expression using y as the variable.)

Read this passage: Amendment III No Soldier shall, in time of peace be quartered in any house, without the consent of the Owner, nor in time of war, but in a manner to be prescribed by law. What is the main idea of this amendment from the Bill of Rights? A. Soldiers cannot enter a private home unless the owner allowsh B. Soldiers can lawfully enter a private home during times of war. C. Homeowners have the right to remove any soldiers in their home. D. A private home becomes the property of the state during times of war.

Use synthetic division to find the result when 4x³ + 25x² - 24x - 30 is divided by x + 7. If there is a remainder, express the result in the form q(x) + r(x)/b(x).

A baseball is thrown vertically upward at a rate of 60 feet per second from an initial height of 3 feet. Use the projectile formula h = - 16t² + vot + ho to determine when the height of the ball will be 39 feet. [Recall that vo is the initial velocity of the object and he is the inital height of the object.]

Eliot is simplifying a radical. His work is shown √64-√4-16 √4-16-2√16 √64-2√16 Which statement best applies to Eliot's mathematical work? The equality √64= √4-16 is incorrect of invalid Removing the 4 from under the radical in the second step is incorrect or invalid The work shown above is correct, however, 2√16 may be simplified further The work shown above is correct, and 2√16 may not be simplified further

Manny has $4.90 in dimes and quarters. He has 7 more dimes than quarters. Write two equations that would be used to solve the system.

Write √-12 in simplest radical form.

Select the equivalent expression. x8/ x-3.x-6

A pet toy manufacturer is designing a plastic ball for dogs that will float in water. In order for the ball to float it must have a density that is less than 1 gram per milliliter (the density of water). The approved design has a mass (m) of 115 grams and a density (d) of 0.600 g/mL.

Write √-27 in simplest radical form.

Factor the expression completely. 63x² +18

A candle that is 11 inches tall burns 1/4 inch every hour. A 13-inch candle burns 2/3 inch every hour. After how many hours will the candles be the same height? Round to the nearest hour.

Write √-200 in simplest radical form.

Write the explicit equation for the table of values. Please enter the answer in f (x) = mx + b x f(x)

While visiting Crimson Lake, Sally decided to go kayaking. The rangers charge $8.50 per hour in addition to a $25.00 deposit to rent the kayak. If she rented the kayak from 11:30 a.m. until 2:30 p.m., write and solve a linear equation to find the total cost to rent the kayak.

For a project in his Geometry class, Magan uses a mirror on the ground to measure the height of his school building. He walks a distance of 7.95 meters from the school, then places a mirror on flat on the ground, marked with an X at the center. He then steps 1.8 meters to the other side of the mirror, until he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.15 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.

You work as a nurse. One of your patients has a fluid limit of 20 ounces per day. Each IV bag contains 3 ounces of fluid. How many IV bags can the patient have in a day before going over his fluid limit?

If you want to earn 2% annual simple interest on an investment, how much should you pay for a note that will be worth $19,500 in 10 months? (Round your answer to two decimal places.)

The ratio of white socks to black socks in Terry's drawer is 4/5. Which of the following combinations could NOT be the actual numbers of white and black socks in Terry's drawer? A 25 black socks; 20 white socks B 35 black socks; 28 white socks C 24 black socks; 30 white socks D 15 black socks; 12 white socks

Suppose that the functions r and s are defined for all real numbers x as follows. r(x) = x-4 s(x)=2x-6 Write the expressions for (r+s) (x) and (r-s) (x) and evaluate (r.s)(1).

Solve the quadratic by factoring. 5x² - 39x - 4 = 4

Given the polynomial function, f(x) = (x² + 2)(x + 5)(x-3)². Which statement must be true about this polynomial? A. It has 5 distinct roots that are all real numbers. B. It has 5 distinct roots that are real and complex numbers. C. It has 4 distinct roots that are all real numbers. D. It has 4 distinct roots that are real and complex numbers.

Fully simplify using only positive exponents. 4x²y/2x8y4

Ava is required to take at least 200 shots at basketball practice each week. During the first practice this week, Ava took 80 shots. She has three remaining practices this week, and she plans to take an equal number of shots at each of those practices. Let s represent the number of shots taken at each of the remaining three practices. a. Type an inequality to represent the situation. b. What is the smallest number of shots she needs to take at each of the remaining practices to meet the weekly requirement? The smallest number of shots Ava needs to take at each remaining practice is

Solve the quadratic by factoring. x² = 4x +32

You and a friend are heading to the movies. You each buy a ticket and you also want to buy some refreshments. The total cost of admission per person, a, is $7.50 and you spent $15.50 on refreshments. Write an expression to represent the total cost of the trip. Then, find the total cost. Total Cost: $

Which of the following is NOT true of the graph y = x³ - 6x² + 11x - 6? As x → ∞o, f(x) - -0. As x +∞o, f(x) → +00. For values of x > 3, the function will be positive. The graph will have no x intercepts.

A fan of trigonometry is building a right triangular pool in his backyard. The hypotenuse of the right triangle is 30 feet long and the height of the right triangle is 24 feet long. If the fan of trigonometry wants to purchase a pool cover, how many square feet of material should he purchase?

Suppose a part inside a computer chip has been measured to be 0.0000266m wide, 0.0000014m long and 0.000284m high. The part has the shape of a rectangular box. What is its volume? Write your answer in scientific notation.

A gas station sells regular gas for $2.10 per gallon and premium gas for $2.60 a gallon. At the end of a business day 290 gallons of gas had been sold, and receipts totaled $639. How many gallons of each type of gas had been sold?

The manager of a 90-unit apartment complex knows from experience that at a rent of $1500 per month, all units will be rented. However, for each increase of $30 ir[ rent, he can expect one unit to be vacated. Let x represent the number of $30 increases over $1500. Complete parts (a) through (e) below. (a) Express, in terms of x, the number of apartments that will be rented if x increases of $30 are made. (For example, with three such increases, the number of apartments rented will be 90-3=87.) The number of apartments that will be rented if x increases of $30 are made is 90-x. (b) Express the rent per apartment if x increases of $30 are made. (For example, if he increases rent by $90=3-$30, the rent per apartment is given by 1500+3 (30) = $1590.) The rent per apartment if x increases of $30 are made is 1500 + 30x. (c) Determine a revenue function R in terms of x that will give the revenue generated as a function of the number of $30 increases. A revenue function R in terms of x that will give the revenue generated as a function of the number of $30 increases is R(x) = -30x² +1200x + 135,000. (Simplify your answer.) (d) For what number of increases will the revenue be $142,680? The number of increases is (Use a comma to separate answers as needed.)

If the radius of a right circular cylinder is 4x and the height of the cylinder is 3y, which of the following represents the volume of the cylinder? 12π* 2y 24π* 2y 48π*2y 144π* 2y .

Find the second derivative of the function. (Simplify your answer completely.) g(x) = ex In x g" (x). = (Express your answer as a single fraction. Factor the numerator, if possible.

A farmer classifies his carrots as 'small', 'medium' or 'large'. His harvest follows a normal distribution, with a mean length of 15 cm and standard deviation 5 cm. If 18% of his carrots are classified as small, what is the longest carrot in the small classification? Give your answer correct to 3 significant figures.

Eric determines that the length of a bus journey is normally distributed with mean 20 minutes and standard deviation 5 minutes. He wants to calculate the probability that the journey lasts at least 25 minutes. Which of the following curves shows the area of the normal distribution he needs to determine?

Express the following fraction in simplest form, only using positive exponents. 3x10c10/-4(x³ c²)-4

A sun in a distant galaxy has an estimated Mass of 1.67216 x 1030 kg and the earth has a mass of 5.972 x 1024 kg, how many earths would it take to equal the mass of the sun? Write your answer in scientific notation. It would take earths to equal the mass of the sun.

The random variable X is normally distributed with mean µ = 7.4 and standard deviation o = 2.1. Find the value of k if P(X > k) = 0.32. Give your answer as a decimal, rounded to three significant figures.