In the diagram below, \triangle ABC with sides of 13, 15, and 16, is mapped onto \triangle DEF after a clockwise rotation of 90° about point P .
If DE = 2x - 1 , what is the value of x ?
In the diagram below,
If
Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For each statement or question, choose the word or expression that, of those given, best completes the statement or answers the question.
After a dilation with center (0,0), the image of
In the diagram below,
If
On the set of axes below,
Which sequence of transformations will map
The figure below shows a rhombus with noncongruent diagonals.
Which transformation would not carry this rhombus onto itself?
In the diagram below of circle
Which statement about
In right triangle
If
In rhombus
Given right triangle ABC with a right angle at C,
Which proportion in relation to
A vendor is using an 8-ft by 8-ft tent for a craft fair. The legs of the tent are 9 ft tall and the top forms a square pyramid with a height of 3 ft.
What is the volume, in cubic feet, of space the tent occupies?
In the diagram below of right triangle
If
Which three-dimensional figure will result when a rectangle 6 inches long and 5 inches wide is continuously rotated about the longer side?
Which statement about parallelograms is always true?
From a point on the ground one-half mile from the base of a historic monument, the angle of elevation to its top is 11.87°. To the nearest foot, what is the height of the monument?
The area of a sector of a circle with a radius measuring
Point
In the diagram below of triangle
Which equation is always true?
In the diagram below of right triangle
Which equation would determine the value of angle
Francisco needs the three pieces of glass shown below to complete a stained glass window. The shapes, two triangles and a trapezoid, are measured in inches.
Glass can be purchased in rectangular sheets that are 12 inches wide. What is the minimum length of a sheet of glass, in inches, that Francisco must purchase in order to have enough to complete the window?
In the diagram of quadrilateral
Which segment has the shortest length?
What is an equation of a circle whose center is (1,4) and diameter is 10?
On the set of axes below,
Which expression represents the area of
In right triangle
As shown in the diagram below, the radius of a cone is 2.5 cm and its slant height is 6.5 cm.
How many cubic centimeters are in the volume of the cone?
What is an equation of the image of the line
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.
Write an equation of the line that is parallel to the line whose equation is
Parallelogram
If
As shown in the diagram below, secants
If
On the set of axes below,
Describe a sequence of transformations that would map
Given points
[Leave all construction marks.]
On the set of axes below,
Is Owen correct? Explain why.
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.
Answer all 3 questions in this part. Each correct answer will receive 4 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.
A triangle has vertices
Prove that
[The use of the set of axes below is optional.]
Theresa has a rectangular pool 30 ft long, 15 ft wide, and 4 ft deep. Theresa fills her pool using city water at a rate of $3.95 per 100 gallons of water.
Nancy has a circular pool with a diameter of 24 ft and a depth of 4 ft. Nancy fills her pool with a water delivery service at a rate of $200 per 6000 gallons.
If Theresa and Nancy both fill their pools 6 inches from the top of the pool, determine and state who paid more to fill her pool. [1 ft3 water = 7.48 gallons]
Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for the question to determine your answer. Note that diagrams are not necessarily drawn to scale. For the question in this part, a correct numerical answer with no work shown will receive only 1 credit.
In the diagram of quadrilateral
Prove:
