A rectangular tabletop will be made of maple wood that weighs 43 pounds per cubic foot. The tabletop will have a length of eight feet, a width of three feet, and a thickness of one inch.
Determine and state the weight of the tabletop, in pounds.
A rectangular fish tank measures 24 inches long, 12 inches wide, and 16 inches high, as modeled in the diagram below. If the empty tank weighs 25 pounds and the fish tank is filled with water to a height of 14 inches, what is the approximate weight of the tank and water? [27.7 in. pound of water]
Answer all 7 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil.
Triangle is the image of triangle after a dilation with a scale factor of and centered at point . Is triangle congruent to triangle ? Explain your answer.
Determine and state the area of triangle , whose vertices have coordinates , and .
A support wire reaches from the top of a pole to a clamp on the ground. The pole is perpendicular to the level ground and the clamp is 10 feet from the base of the pole. The support wire makes a angle with the ground. Find the length of the support wire to the nearest foot.
In the diagram below, circle has a radius of 10 .
If , find the area of shaded sector , in terms of .
On the set of axes below, .
Describe a sequence of rigid motions that maps onto .
In right triangle , altitude is drawn to hypotenuse , and .
Determine and state, to the nearest tenth, the length of .
Given circle with radius , use a compass and straightedge to construct an equilateral triangle inscribed in circle . [Leave all construction marks.]
A jewelry company makes copper heart pendants. Each heart uses of copper and there is pound of copper per cubic inch. If copper costs per pound, what is the total cost for 24 copper hearts?
A walking path at a local park is modeled on the grid below where the length of each grid square is 10 feet. The town needs to submit paperwork to pave the walking path. Determine and state, to the nearest square foot, the area of the walking path.
Determine and state, to the nearest square foot, the area of the walking path.
A shipping container is in the shape of a right rectangular prism with a length of 12 feet, a width of 8.5 feet, and a height of 4 feet. The container is completely filled with contents that weigh, on average, 0.25 pound per cubic foot. What is the weight, in pounds, of the contents in the container?
A walking path at a local park is modeled on the grid below, where the length of each grid square is 10 feet. The town needs to submit paperwork to pave the walking path. Determine and state, to the nearest square foot, the area of the walking path.
Determine and state, to the nearest square foot, the area of the walking path.
In the model below, a support wire for a telephone pole is attached to the pole and anchored to a stake in the ground 15 feet from the base of the telephone pole. Jamal places a 6 -foot wooden pole under the support wire parallel to the telephone pole, such that one end of the pole is on the ground and the top of the pole is touching the support wire. He measures the distance between the bottom of the pole and the stake in the ground.
Jamal says he can approximate how high the support wire attaches to the telephone pole by using similar triangles. Explain why the triangles are similar.
A walking path at a local park is modeled on the grid below, where the length of each grid square is 10 feet. The town needs to submit paperwork to pave the walking path. Determine and state, to the nearest square foot, the area of the walking path.
Determine and state, to the nearest square foot, the area of the walking path.
A gas station has a cylindrical fueling tank that holds the gasoline for its pumps, as modeled below. The tank holds a maximum of 20,000 gallons of gasoline and has a length of 34.5 feet. A metal pole is used to measure how much gas is in the tank. To the nearest tenth of a foot, how long does the pole need to be in order to reach the bottom of the tank and still extend one foot outside the tank? Justify your answer. [ gallons]
Calculate the length of the pole needed to reach the bottom of the tank and extend one foot outside.