Molly has sketched a design for her new kite on a coordinate grid. The sides of her quadrilateral kite design are given by the equations y = (2/3)x + 30, y = (−2/3)x + 50, y = −2x + 30 and y = 2x – 30. How many square units are in the area of Molly’s design?
Based on the previous problem, what is the perimeter of Molly’s kite design, in units? Express your answer in simplest radical form.
The radius of circle N is 3 inches, and the radius of circle O is 4 inches. What is the radius of circle P whose area is the sum of the areas of circles N and O?
Space junk is debris orbiting Earth that, for the most part, has been abandoned or has broken off spacecrafts and rockets. Some of these items are far enough from Earth that they will remain in orbit forever; however, much of this “junk” will be pulled into Earth’s atmosphere by gravity. On average, one item per day falls victim to gravity. At this rate, in what year will 2500 pieces of space junk enter the atmosphere if we begin counting on February 18th?
On some graph paper, graph the following segments:
y = x, for 0 ≤ x ≤ 2
y = 2x − 2, for 2 ≤ x ≤ 3
x = 3, for 4 ≤ y ≤ 6
y = −x + 9, for 2 ≤ x ≤ 3
y = 7, for 1 ≤ x ≤ 2
y = x + 6, for 0 ≤ x ≤ 1
Now reflect each of the segments over the y-axis. What popular shape have you drawn?
Fall is a beautiful time of year to take a hot air balloon ride! You may not be able to take a balloon ride, but we hope you enjoy solving this week’s problems.
Melrose’s hot air balloon is a sphere of diameter 100 feet. How many cubic feet of air will Melrose’s hot air balloon hold when completely filled? Express your answer as a decimal to the nearest tenth.
The summer months are the most popular time to move to a new home. Janet’s family is moving, and she suddenly realizes just how much stuff they have in their current home. Once the moving company finishes packing everything in boxes, they begin the task of numbering them. A sticker is placed on every box and on every item that is too large to fit in a box. Janet notices that stickers in three distinct colors are used. There are blue stickers numbered 239 through 262, green stickers numbered 163 through 178 and yellow stickers numbered 453 through 492.
A construction crew places orange barrels on both sides of a particular road to indicate a work zone. On each side of the road, the distance between the centers of consecutive barrels is 15 feet. If this work zone is 1.5 miles long, what is the total number of barrels that will be used?