Basic Math Questions and Answers

Determine whether (1, 1) and (-1, 4) are solutions to 2x + 5y ≤ 7. Both (1, 1) and (-1, 4) are solutions. (1, 1) is a solution, but (-1, 4) is not. (-1, 4) is a solution, but (1, 1) is not. Neither (1, 1) nor (-1, 4) is a solution.

A rectangular lot whose perimeter is 290 ft is fenced along three sides. An expensive fencing along the lot's length cost $15 per foot. An inexpensive fencing along the two side widths costs only $3 per foot. The total cost of the fencing along the three sides comes to $1635. What are the lot's dimensions? *****

Use a linear approximation to estimate the number (27.07) 2/3. Make sure that your answer is correct to at least 9 decimal places. Answer:

- A connected graph G without multiple edges or loops has five vertices: A, B, C, D, and E. Vertices B, C, D have degrees of 3 and Vertex A has a degree of 1. What is the degree of the vertex E if the maximum possible numbers of paths in G from A to B is 5? 1 2 I need to learn this.

Trina's paycheck earnings varies directly as the number of hours she works. If she works 19 hours and earns $187.15, what should she earn if she worked 40 hours? $394 $440 $472.80 $512.20

Juliet is trying to increase her savings account and she decides that she is going save an additional $700 every month. If her monthly take home pay is $5,430, what proportion of her monthly take home pay is she saving?

13. Randy and Mico work in a car station. The time that Randy takes in washing a car alone is 10 minutes less than the time that Mico takes in washing the same car. Which of the equations represent the time randy takes in washing the car. A. x-10 B. x(x- 10) X-10 D.

19) Avia Company sells a product for $120 per unit. Variable costs are $80 per unit, and fixed costs are $1200 per month. The company expects to sell 670 units in September. The unit contribution margin is A) $40 per unit B) $80 per unit C) $200 per unit D) $120 per unit Answer:

Diana has 520 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area? (a) A(W) = 260w-w² (b) The area is largest for W = 130 yards. (Simplify your answer.) (c) The maximum area is 16900 square yards. (Simplify your answer.)

Solve the following equation for on the interval [0, 2π). csc (θ) + 3.35 = 0 Select all correct answers. Select all that apply: 0.272 2.191 5.980 3.137 3.445 0.973

A bag contains 12 yellow and 8 purple marbles. Joe pays $2 for the opportunity to pick a marble from the bag. If he picks a yellow marble, he does not get anything. If he picks a purple marble, he gets $k. The game is fair. Find the value of k. Give an exact answer. Do not include the dollar sign in your answer.

A movie rental company charges a monthly fixed membership fee of $12 plus $6 per movie that the user rents in that month. If M represents the number of movies that the user rents, and C represents the user's total charge for the month, find the relationship between M and C. Select the correct answer below: M= 6C + 12 C= 12M + 6 M 12C+6 C=6M + 12

A commuter plane provides transportation from an international airport to surrounding cities. One commuter plane averaged 280 mph flying to a city and 140 mph returning to the international airport. The total flying time was 3 h. Find the distance between the two airports.

Use the long division method to find the result when 8x³ + 18x² + 11x + 2 is divided by 2x + 1.

After descending for 8 minutes, an airplane is at an altitude of 24800 feet. After descending for 20 minutes, the plane's altitude is 12800 feet. Assuming a linear function, write an equation in the form a(t) = mt+b that shows the altitude, a, after t minutes of descent. Provide your answer below: a(t) =

Ernie deposited $4000 between two savings accounts. One account paid 4% simple interest and the other paid 2%. At the end of one year, Ernie had earned $140 in interest for both accounts. How much money did Ernie deposit in the account that paid 4% interest?

Given that the degree of the polynomial f(x) is 5, which of the following most accurately describes the number of x- intercepts that f(x) has? Select the correct answer below: f(x) has at most 4 x-intercepts. f(x) has at least 4 x-intercepts. f(x) has at least 5 x-intercepts. f(x) has at least 6 x-intercepts. f(x) has at most 5 x-intercepts. f(x) has at most 6 x-intercepts.

A woman decides to invest $4000 in an IRA CD at the end of each year for 10 years. If she makes these payments and the certificates all pay 6%, compounded annually, how much will she have at the end of the 10 years?

Given that the degree of the polynomial f(x) is 4, which of the following most accurately describes the number of x- intercepts that f(x) has? Select the correct answer below: f(x) has at least 4 x-intercepts. f(x) has at most 3 x-intercepts. f(x) has at least 5 x-intercepts. f(x) has at most 4 x-intercepts. f(x) has at least 3 x-intercepts. f(x) has at most 5 x-intercepts.

I can break apart unknown facts into known facts and solve multiplication problems. Madison broke up a large array into a 3 x 4 array and a 5 x 4 array. What was the large array that Madison started with? Use evidence to justify your thinking.

The number x of printer cartridges that a store will sell per week and their price p (in dollars) are related by the equation x² = 7000 - 5p². If the price is falling at the rate of $1 per week, find how the sales will change if the current price is $30.

Each day a small business owner sells 200 pizza slices at $3.00 per slice and 85 sandwiches at $3.00 each. Business expenses come to $70 per day. What is the owner's profit for a ten-day period?

A toy shop sells baby rattles in green and yellow. For every two green rattles the toy shop sells, it sells 7 yellow rattles. If the company sells 108 rattles, how many yellow rattles did they sell?

Allistair throws a biased six-sided dice. The probability of getting a 6 with this dice is 0.4. The other numbers are equally probable. If he throws the dice 3 times, what is the probability that he gets 5, 3 and 2 in this order?

Let a and b be positive constants. If a > b, then which of the following is true? It is not possible to tell anything about the relationship between a³ and b³. a³ > b³ a³ = b³ b³ > a³

g(x)=3x²-18x+22 (a) Write the equation in the form g (x)= a (x-h)²+k. Then give the vertex of its graph. (b) Graph the function. To do this, plot five points on the graph of the function: the vertex, two points to the left of the verte of the vertex. Then click on the graph-a-function button.

The graph to the right shows that the three components of love, namely passion, intimacy, and commitment, progress differently over time. Passion peaks early in a relationship and then declines. By contrast, intimacy and commitment build gradually. What is the maximum level of intensity for passion? After how many years in a relationship does this occur?

Which description lists Earth's layers from most superficial to deepest? a Lithosphere, lower mantle, asthenosphere, outer core, inner core b Asthenosphere, Lithosphere, lower mantle, inner core, outer core c Inner core, outer core, lower mantle, ästhenosphere, lithospherea d Lithosphere, asthenosphere, lower mantle, outer core, inner core

5. A French toast recipe uses 2 eggs to make 14 slices of French toast, Brenda wants to make 98 slices of French toast to feed her family and friends. How many eggs will Brenda need to make 98 slices?

John is going to the amusement park, where he has to pay a set price of admission and another price for tickets to go on each of the rides. The total amount of money John will spend is given by the equation y = 18 + 1.5x, where represents the total amount of money, in dollars and cents, and art represents the number of rides John goes on. What could the number 1.5 represent in the equation? The total amount of money John will spend if he goes on o rides. The change in the total amount of money for every one additional ride he goes on. The total amount of money John will spend if he goes on a ride. The total amount of money John will spend if he goes on 100 rides.

If $8000 is invested at 3% interest, compounded annually, then after n years the investment is worth an = 8000(1.03)" dollars. Find the first five terms of the sequence {a}. Step 1 For an = 8000(1.03), we have a₁ = 8000(1.03)¹ = a2 = 8000(1.03)² = and

Suppose that an object is dropped from a height of h meters and hits the ground with a velocity of v meters per second. Then v= 19.6h. If an object hits the ground with a velocity of 18.3 meters per second, from what height was it dropped? Carry your intermediate computations to at least four decimal places, and round your answer to the nearest tenth.

In 2012, the population of a city was 5.91 million. The exponential growth rate was 2.48% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 9 million? d) Find the doubling time.

The formula for the surface area of a rectangular solid is: S = 2HW + 2LW + 2LH, where S, H, W, and L represent surface area, height, width, and length, respectively. Solve this formula for L.

You were offered either a simple interest note or a simple discount note with the following terms: $39,242 at 9% for 18 months. a. Calculate the effective interest rate. (Do not round intermediate calculations. Round your final answer to the nearest tenth percent.) Effective interest rate %

The lengths of the sides of a right triangle are such that the shortest side is 7 in. shorter than the middle side, while the longest side (the hypotenuse) is 1 in. longer than the middle side. Find the lengths of the sides.

Victoria counts this week's food donations at a pet shelter. There are 16 full cases of canned food. There are 4 cases of canned food that are each missing 5 cans. Victoria records a total of 220 cans of food. a. Use c to represent the number of cans in a full case. What expression could represent the number of cans in each case that is missing cans? b. Write an equation you could use to find c. c. How many cans are in a full case? How many cans are in each of the 4 other cases? Show your work.

A factory manufactures parts for a new television at a cost of $30 per part, and also has a monthly fixed cost of $600. If P represents the number of parts the factory manufactures in a month, and C is the total cost, write the linear equation that represents the relationship between P and C.

Given that the polynomial f(x) has 4 turning points, which of the following most accurately describes the degree of f(x)? Select the correct answer below: The degree of f(x) is at most 3. The degree of f(x) is at most 5. The degree of f(x) is at least The degree of f(x) is at most 4. The degree of f(x) is at least 3. The degree of f(x) is at least 5.

27 boxes of coconut creams for $14.95 each 36 boxes of pralines for $11.39 each 14 boxes of raspberry bites at $8.50 each Round the cost of each box to the nearest dollar, and then estimate the amount of money that the class earned. $927 $963 $1,025 $913

There are 240 students going on a field trip. Each school bus can hold 48 students. Complete the equation to show which operation to use and how many school buses are needed. Then complete the sentence to explain your reasoning. because 240 students need to be split into equal groups of 48 students.

For a total accumulated amount of $3687.52, a principal of $2000, and a time period of 9 years, use the compound interest formula to find r, if interest is compounded monthly.

In a race in which seven automobiles are entered and there are no ties, in how many ways can the first three finishers come in?

Andrew is watching the stock market. He recorded the changes every day, as follows: • Day 1: Opened at 4,798.68 points Day 2: Lost 125.07 points Day 3: Lost 36.5 points Day 4: Gained 52.71 points ● ● Round each number to the nearest whole number. Then, add the values to find the value on Day 5. O O 4,690 4,689 4,691 4.584

Find the vertex, focus, and directrix of the following parabola. Graph the equation. Verify your graph using a graphing utility. (y-2)² = 8(x+3) The vertex of the parabola is (-3,2). (Type an ordered pair.) The focus of the parabola is. (Type an ordered pair.)

A can of tennis balls has a diameter of 3 in. and a height of 9 in. Find the volume of the can to the nearest cubic inch.

A survey of a random sample of voters shows that 66% plan to vote for Katie and 34% plan to vote for Casey. The survey has a margin of error of ±2%. What is the range for the percentage of voters who plan to vote for Katie?

Solve the system of linear equations by graphing. (2x-y=0 3x+y=5

Points: U of 1 In triangle ABC, the angles A and B have the same measure, while the measure of angle C is 18° larger than the measure of each of A and B. What are the measures of the three angles? The measure of angle A and the measure of angle B are each (Type a whole number.)

For some particular website, the password must start with one of the letters A, B, C, D, E, or F. Then there must be 2 more charaters, and each of those characters may be a numeric digit or a letter of the alphabet. How many different passwords are possible?