Basic Math Questions and Answers

Consider the following system of equations -2x+y=8 -6x-8y=24 A. Which method would you use to solve the system of equations? Explain your reasoning B. Show work, find the solution to the system. C. Sketc the graph of the above system. Tell how the graph verifies your answer.

Find the horizontal asymptote of f(x) =-5x +4x³-4 / -x³-2x²-3

Given the function h(x) below, select the answer choice that correctly decomposes h(x) into component functions f(x) and g(x) so that h(x) = f(g(x)). Select the correct answer below: h(x) = (8x - 14)^5 h(x) = f(g(x)), where f(x) = 8x - 14 and g(x)=x^5 h(x) = f(g(x)), where f(x) = x - 14 and g(x) = 8x^5 h(x) = f(g(x)), where f(x) = 8x^5 and g(x) = x - 14 h(x) = f(g(x)), where f(x) = 8x and g(x) = (x - 14)^5 h(x) = f(g(x)), where f(x) = x^5 and g(x)= 8x - 14

Graph the function. h(x)=x² Plot five points on the graph of the function: one point with x=0, two points with negative x-values, and two points with positive x-values. Then click on the graph-a-function button.

A small child is climbing up a slide angled at 27.0° above the horizontal. They only make it 0.800 m up the slide before they give up, stop, and then slide back down. When the child reaches the bottom of the slide how fast will they be going? 2.67 m/s 3.74 m/s 3.96 m/s 1.21 m/s

Find (a) the solution to the equation f(x) = 0, (b) the x-intercept of the graph of y = f(x), and (c) the zero of f(x). f(x) = 92 +4.6x (a) What is the solution to f(x)=0? X= (Simplify your answer.)

Brandon has a jar of quarters and dimes with a total value of $10.40. The number of quarters is 4 less than twice the number of dimes. How many quarters and how many dimes does Brandon have?

On two examinations, you have grades of 87 and 88. There is an optional final examination, which counts as one grade. You decide to take the final in order to get a course grade of A, meaning a final average of at least 90. a. What must you get on the final to earn an A in the course? b. By taking the final, if you do poorly, you might risk the B that you have in the course based on the first two exam grades. If your final average is less than 80, you will lose your B in the course. Describe the grades on the final that will cause this to happen. a. You must get at least a

Initially there were 3 liters of blue paint and 3 liters of crimson paint. A paint job uses 20% of the blue and 80% of the crimson paint. a. What percentage of the total combined amount of paint is used during the job? Answer: % b. What percentage of the total combined amount of paint remains after the job is finished? Answer: %

In the fall of 2017, there were 43 thousand more female undergraduate students enrolled at a college than male undergraduate students. If the total undergraduate enrollment was 431 thousand that fall, find the numbers of female undergraduate students and male undergraduate students who were enrolled The number of female undergraduate students was thousand.

Mr. Hall had some money in his bank earning 5.5% simple interest. He had $6000 more deposited in a credit union earning 7% simple interest. If his total interest for 1 yr was $1250, how much did he deposit in each account?

Select the statement that is equivalent to I saw Robin Hood or Bourne Supremacy. Choose the correct statement below. A. If I saw Bourne Supremacy, I did not see Robin Hood. B. I saw both Robin Hood and Bourne Supremacy C. If I saw Robin Hood, I did not see Bourne Supremacy. D. If I did not see Robin Hood, I saw Bourne Supremacy.

In 2005, there were 15,300 students at college A, with a projected enrollment increase of 1000 students per year. In the same year, there were 35,550 students at college B, with a projected enrollment decline of 1250 students per year. According to these projections, when will the colleges have the same enrollment? What will be the enrollment in each college at that time? In the year , the enrollment at both colleges will be the same.

Hannah has to make 105 gallons of punch for a big party. The punch is made of soda and fruit drink. The cost of the soda is $2.55 per gallon and the cost of the fruit drink is $2.90 per gallon. Hannah's budget requires that the punch cost $2.74 per gallon. How many gallons of soda and how many gallons of fruit drink does she need?

Scientists are conducting an experiment with a gas in a sealed container. The mass of the gas is measured, and the scientists realize that the gas is leaking at a constant rate of 9 grams per minute. Ten minutes after the experiment started, the gas in the container has a mass of 342 grams. Let a be the number of minutes that have passed since the experiment started, and let f(x) be the mass of the gas, in grams, at that moment. a. Write an equation for f: f(x) = b. 33 minutes after the experiment started, there would be__ grams of gas left. c. If a linear model continues to be accurate, __ minutes since the experimentstarted, all gas in the container will be gone.

Solve the following equation analytically. Check it analytically by direct substitution, and then support your solution graphically. 3x +1/2 + x-1/3 = 15/2 The solution set of this equation is (Simplify your answer.)

Find the following for the function f(x) = 3x² + 3x-3. (a) f(0) (b) f(4) (c) f(-4) (d) f(-x) (e) - f(x) (f) f(x + 2) (g) f(3x) (h) f(x + h) (a) f(0) = (Simplify your answer.) (b) f(4) = (Simplify your answer.) (c) f(-4)= (Simplify your answer.) (d) f(-x) = (Simplify your answer.) (e) -f(x)= (Simplify your answer.)

Car A leaves San Diego at noon driving at 60 mph along a route which is 400 miles long to San Francisco. Car B leaves San Francisco 2 hours later traveling along the same route at 80 mph. How far from the midpoint of the route are they when they meet? Are they closer to San Diego (answer "y" for yes or "n" for no)? How far from the midpoint? Are they closer to San Diego?

The number of counties in state A and the number of counties in state B are consecutive even integers whose sum is 102. If state A has more counties than state B how many counties does each state have? State A has counties.

After four years in college, Josie owes $64000 in student loans. The interest rate on the federal loans is 2.4% and the rate on the private bank loans is 4%. The total interest she owes for one year was $2,176.00. What is the amount of each loan? Federal loan at 2.4% account = $ Private bank loan at 4% account = $

Solve the equation using a graphical method. 3t/4-1=3t-3/3 +1

Brandon has a cup of quarters and dimes with a total value of $56.9. The number of quarters is 10 less than five times the number of dimes. How many quarters and how many dimes does Brandon have? Number of quarters: Number of dimes:

Stanley's weekly allowance is $5. He can also earn $2 each time he walks the family dog. Write an equation that shows how the amount of money Stanley gets in a week, y, depends on the number of times he walks the dog, X.

A motorboat travels 153 kilometers in 3 hours going upstream. It travels 225 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?

Julia and her husband own a coffee shop. They experimented with mixing a City Roast Columbian coffee that cost $7.80 per pound with French Roast Columbian coffee that cost $8.50 per pound to make a 7-pound blend. Their blend should cost them $8.20 per pound. How much of each type of coffee should they buy? Pounds of City Roast coffee = Pounds of French Roast coffee =

A cashier has 60 bills, all of which are $1 or $10 bills. The total value of the money is $231. How many of each type of bill does the cashier have? Number of $1 bills: Number of $10 bills:

A shop order calls for 1000 steel pins each 1 5/8-inches long. If 3/16 inch is allowed for cutting off and facing each pin, how many complete 8-foot lengths of stock are needed for the order? a. 19 b. 18 d. 10 c. 15

In 2002, 330 teenagers underwent gastric bypass surgery. In 2007, 780 teenagers underwent gastric bypass surgery. Use t years since 2000 and V (teenagers underwent gastric bypass surgery) and assume the above information is linear. According to your model, what is the number of teenagers having gastric bypass surgery in 2010? {final answer will be number only}

Tickets for an Amtrak train cost $23 for children and $50 for adults. Josie paid $3,440 for a total of 85 tickets. How many children tickets and how many adult tickets did Josie buy?

Julia has saved $91 from last year and would like to babysit enough hours to buy a new bike. She makes $8 per hour babysitting, and she needs at least $300 for a good quality bike. How many hours must Julia babysit in order to meet her goal?

The rate of depreciation dv/dt of a machine is inversely proportional to the square of t + 1, where Vis the value of the machine t years after it was purchased. The initial value of the machine was $900,000, and its value decreased $200,000 in the first year. Estimate its value after 6 years. (Round your answer to the nearest whole number.)

Peter has half of his investments in stock paying a 9% dividend and the other half in a stock paying 11% interest. If his total annual interest is $470, how much does he have invested?

An island has 12 fur seal rookeries (breeding places). To estimate the fur seal pup population in Rookery A, 4416 fur seal pups were tagged in early August. In late August, a sample of 500 pups was observed, and 350 of these were found to have been previously tagged. Use a proportion to estimate the total number of fur seal pups in Rookery A. The estimated total number of fur seal pups in Rookery A is

Patsy's's Pizza sells one 14-inch cheese pizza or two 10-inch cheese pizzas for $11.99. Determine which size gives more pizza. (A = πr²)

Which describes the end behavior of the function f(x) = -x² + 4x +37? Select the correct answer below: rising to the left and to the right falling to the left and to the right rising to the left and falling to the right falling to the left and rising to the right

Let f(x) = 4x + 2 and g(x) = 4x² + 4x. After simplifying, (fg)(x) =

Factor. x6+5x5-50x4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x6 +5x5 - 50x4= (Factor completely.) B. The polynomial is prime.

Tickets for an Amtrak train cost $22 for children and $42 for adults. Josie paid $3,026 for a total of 83 tickets. How many children tickets and how many adult tickets did Josie buy?

Determine the following estimate without using a calculator. Then use a calculator to perform the computation necessary to obtain an exact answer. How reasonable is your estimate when compared to the actual answer? Estimate the total cost of six grocery items if their prices are $4.62, $7.62, $2.15, $9.35, $8.01, and $1.84, by rounding each price to the nearest dollar and then adding. The estimate of the total cost of the grocery items is $ (Type a whole number.) The actual total cost of the grocery items is $ How reasonable is your estimate when compared to the actual answer? Select the correct answer below and fill in the answer box to complete your choice. A. The estimate is a little lower than the actual result. The difference is $ B. The estimate is a little higher than the actual result. The difference is $

Given g(x)=2x-1, solve for a when g(x) = 3.

A ball is placed on the ground next to a tree at the top of a hill. The distance, in feet, the ball travels away from the tree during the first 6 seconds after it begins rolling down the hill is shown on the graph. At which interval of time is the ball traveling with the greatest average speed? A between x = 0 and x = 2 B between x = 2 and x = 4 C x = 2 and x = 6 D between x = 4 and x = 6

A recent survey showed that 50% of recent college graduates named flexible hours as their most desired employment benefit. In a graduating class of 820 college students, how many would you expect to rank flexible hours as their top priority in job benefits? (Round to the nearest whole number.) We would expect college students.

A bank account principal is $8,000 and accumulates yearly interest at 7% interest. Assuming that no withdrawals are made, use the compound interest formula to compute the amount in the account after 8 years. If interest is compounded annually, what is the amount of money after t = 8 years?

What could you divide and then multiply by to go from the first number to the second?

Find the first and second derivatives of the function. (Simplify your answer completely.) g(t) =t²/ t-7 g' (t) = g" (t) =

There are some red, green and blue counters in a box. 1/3 of the counters are red. There are 53 blue counters and 29 more green counters than red counters. How many counters are there in the box altogether?

Two integers that are opposites whose sum is zero.

A 30% antifreeze solution is to be mixed with a 70% antifreeze solution to get 16 liters of a 40% solution. How many liters of the 30% and how many liters of the 70% solutions will be used?

Shelly spent 30 minutes jogging and 50 minutes cycling and burned 880 calories. The next day, she spent 20 minutes jogging and 45 minutes cycling and burned 715 calories. How many calories were burned for each minute of jogging and how many for each minute of cycling?

Larry, Simone, Kim, Eduardo, lan, Sergio, Sarah, and Jim have all been invited to a dinner party. They arrive rand a. In how many ways can they arrive? b. In how many ways can Larry arrive first and Jim last? c. Find the probability that Larry will arrive first and Jim last.