As modeled in the diagram below, an access ramp starts on flat ground and ends at the beginning of the top step. Each step is 6 inches tall and 8 inches deep. If the angle of elevation of the ramp is , determine and state the length of the ramp, to the nearest tenth of a foot. Determine and state, to the nearest tenth of a foot, the horizontal distance, , from the bottom of the stairs to the bottom of the ramp.
Determine and state the length of the ramp, to the nearest tenth of a foot.
Determine and state, to the nearest tenth of a foot, the horizontal distance, , from the bottom of the stairs to the bottom of the ramp.
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.
As shown in the diagram below, a symmetrical roof frame rises 4 feet above a house and has a width of 24 feet.
Determine and state, to the nearest degree, the angle of elevation of the roof frame.
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?
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. [14]
Triangle is the image of triangle after a translation of 2 units to the right and 3 units up. Is triangle congruent to triangle ? Explain why.
Triangle and point are graphed on the set of axes below. Graph and label , the image of , after a dilation of scale factor 2 centered at point .
Quadrilaterals BIKE and GOLF are graphed on the set of axes below. Describe a sequence of transformations that maps quadrilateral BIKE onto quadrilateral GOLF.
In the diagram below, secants and , drawn from point , intersect circle at , and . If , and , what is the length of ?
Using a compass and straightedge, construct the median to side in below. [Leave all construction marks.]
Skye says that the two triangles below are congruent. Margaret says that the two triangles are similar. Are Skye and Margaret both correct? Explain why.
Randy's basketball is in the shape of a sphere with a maximum circumference of 29.5 inches. Determine and state the volume of the basketball, to the nearest cubic inch.
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.