Mason is getting quotes from two different landscaping companies to put river rock along one side of his house at a depth of 0.5 foot. The surface area of the space he wishes to install rock in is rectangular and has a length that is eight times its width.The first company charges $3.50 per cubic foot of rock and $80 for delivery. The second company charges $2.50 per cubic foot of rock and $120 for delivery.Which system of equations can be used to determine the value of the width, x, at which the cost of the two companies, y, is the same? A. 𝑦=28⁢𝑥3+80𝑦=29⁢𝑥3+120 B. 𝑦=3.5⁢𝑥3+80𝑦=2.5⁢𝑥3+120 C. 𝑦=28⁢𝑥2+80𝑦=20⁢𝑥2+120 D. 𝑦=14⁢𝑥2+80𝑦=10⁢𝑥2+120

Matt is writing an estimate for a client who would like to have a patio built from interlocking blocks. The landscaper has provided two designs that would fit in the yard:Plan 1 is for a patio 3 yards long and 4 yards wide.Plan 2 is for a patio 5 yards long and 2.5 yards wide.The client wants to know how much each plan will cost. Matt will use rectangular bricks that measure 8" by 4" and cost $5.00 a square foot. Matt's labor charge is $8.50 per square foot.1) What is the total cost of plan 2?(Enter your dollars and cents with no dollar symbol.)2) Which plan is the least expensive? Enter plan 1 or plan 2

Andrea is making a sandbox for her children. She has made a wooden frame for her backyard that is 11 feet long, 8 feet wide, and 2 feet deep. She can purchase sand for the sandbox for $30 per cubic meter. How much will it cost Andrea to purchase sand? (Hint: 1 foot = 0.3048 meters.)(Round your answer to the nearest dollar.)

A school is planning to construct two rectangular play areas in the playground.The length of play area A must be 1 foot longer than four times its width. The width of play area B must be 2 feet longer than the width of play area A, and the length must be 2 feet longer than three times its own width. In addition, the areas of the two play areas must be equal.Write a system of equations to represent this situation, where y is the area of the play areas and x is the width of play area A. Which statement describes the number and viability of the system’s solutions? A. The system has two solutions, but only one is viable because the other results in a negative width. B. The system has only one solution, but it is not viable because it results in a negative width. C. The system has only one solution, and it is viable because it results in a positive width. D. The system has two solutions, and both are viable because they result in positive widths.

A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $20 per square meter. Material for the sides costs $12 per square meter. Find the cost of materials for the cheapest such container. (Round your answer to the nearest cent.)$

ProblemAdam wants to buy a surfboard that costs $249$249. He was given a birthday present of $50$50 and he has a summer job that pays him $6.50$6.50 per hour. To be able to buy the surfboard, how many hours does he need to work? SolutionStep 1:We know the following.The surfboard costs $249$249.Adam has $50$50.His job pays $6.50$6.50 per hour.We want to know how many hours Adam needs to work to buy the surfboard.Let x=𝑥= the time expressed in hours.Let y=𝑦= Adam earningsThe equation of this line is: y=6.50x+50𝑦=6.50𝑥+50Step 2: We can solve this problem by making a graph that shows the number of hours spent working on the horizontal axis and Adam’s earnings on the vertical axis.Adam has $50$50 at the beginning. This is the Answer 1 Question 5: (0,50)(0,50).He earns $6.50$6.50 per hour. This is the Answer 2 Question 5 of the line.We can graph this line using the slope-intercept method. We graph the y𝑦−intercept of (0,50)(0,50), and we know that for each unit in the horizontal direction, the line rises by Answer 3 Question 5 units in the vertical direction. Here is the line that describes this situation.Step 3: The question was: “How many hours does Adam need to work to buy the surfboard?”We find the answer from reading the graph - since the surfboard costs $249$249, we draw a horizontal line from $249$249 on the vertical axis until it meets the graph and then we draw a vertical line downwards until it meets the horizontal axis. We see that it takes approximately 3131 hours to earn the money.Step 4: To check if this correct, let’s think of the problem again. We know that Adam has $50$50 and needs $249$249 to buy the surfboard. So, he needs to earn $249−$50=$$249−$50=$ Answer 4 Question 5 from his job.His job pays $6.50$6.50 per hour. To find how many hours he need to work we divide:$199$6.50perhour=30.6$199$6.50𝑝𝑒𝑟ℎ𝑜𝑢𝑟=30.6 hoursThis is very close to the answer we got from reading the graph.The domain of this function would be Answer 5 Question 5 Answer 6 Question 5 Answer 7 Question 5.The range of this function would be Answer 8 Question 5 Answer 9 Question 5 Answer 10 Question 5.CheckQuestion 5