Answer: See Annex
z (max) = 190
x = 10
y = 20
Step-by-step explanation:
z = 5*x + 7*y to maximize
Subject to:
x + y ≤ 30
2*x + y ≤50
2*x - y ≥ 0
x≥= y ≥0
1. Ethan is using his compass and straightedge to complete a construction of a polygon inscribed in a circle. Which polygon is h
e in the process of constructing?
A. An equilateral triangle
B. A square
C. A regular pentagon
D. A regular hexagon
2. What construction does the image below demonstrate?What construction does the image below demonstrate?
A. The circumcenter of a regular hexagon
B. The incenter of a regular hexagon
C. A regular hexagon circumscribed about a circle
D. A regular hexagon inscribed in a circle
3. An architect plans to draw a rectangular patio with segment LM representing one side of the rectangle. He wants to construct a line passing through Q and parallel to side LM. He uses a straightedge and compass to complete some steps of the construction, as shown below:
Which of these is likely to be his next step in constructing the parallel line?
A. Without changing the width of the compass, place the compass at Q and draw an arc similar to the one drawn.
B. Place the compass at N and adjust the width to the widest point on arc PS.
C. Without changing the width of the compass, place the compass at S or P and draw an arc similar to the one drawn.
D. Place the compass at N and adjust the width to a length that is greater than the length of segment NS.
4. Mike constructed a quadrilateral POQS. He used a compass and straightedge to accurately construct line segment OS, as shown in the figure below:
Which could be the measures of angle POS and angle POQ?
A. Measure of angle POS is 30 degrees, measure of angle POQ is 50 degrees
B. Measure of angle POS is 30 degrees, measure of angle POQ is 65 degrees
C. Measure of angle POS is 25 degrees, measure of angle POQ is 65 degrees
D. Measure of angle POS is 25 degrees, measure of angle POQ is 50 degrees
5. The figure below shows a partially completed set of steps to construct parallelogram PQRS:
The next step is to construct side RS of the parallelogram so that side RS is congruent to side PQ.
The chart below shows the steps each of the four students took to draw side RS of the parallelogram:
Student 1 Fix the compass at L and adjust its width to point M. Without changing the width of the compass, move the compass to R and draw an arc. Draw a line segment from R that passes through T and intersects the arc at S.
Student 2 Fix the compass at Q and draw an arc that intersects side QP. Without changing the width of the compass, move the compass to R and draw an arc. Draw a line segment from R that passes through T and intersects the second arc at S.
Student 3 Fix the compass at Q and adjust its width to point P. Without changing the width of the compass, move the compass to R and draw an arc. Draw a line segment from R that passes through T and intersects the arc at S.
Student 4 Fix the compass at L and adjust its width to point P. Without changing the width of the compass, move the compass to R and draw an arc. Draw a line segment from R that passes through T and intersects the arc at S.
Which student used the correct steps to construct parallelogram PQRS?
A. An equilateral triangle
B. A square
C. A regular pentagon
D. A regular hexagon
2. What construction does the image below demonstrate?What construction does the image below demonstrate?
A. The circumcenter of a regular hexagon
B. The incenter of a regular hexagon
C. A regular hexagon circumscribed about a circle
D. A regular hexagon inscribed in a circle
3. An architect plans to draw a rectangular patio with segment LM representing one side of the rectangle. He wants to construct a line passing through Q and parallel to side LM. He uses a straightedge and compass to complete some steps of the construction, as shown below:
Which of these is likely to be his next step in constructing the parallel line?
A. Without changing the width of the compass, place the compass at Q and draw an arc similar to the one drawn.
B. Place the compass at N and adjust the width to the widest point on arc PS.
C. Without changing the width of the compass, place the compass at S or P and draw an arc similar to the one drawn.
D. Place the compass at N and adjust the width to a length that is greater than the length of segment NS.
4. Mike constructed a quadrilateral POQS. He used a compass and straightedge to accurately construct line segment OS, as shown in the figure below:
Which could be the measures of angle POS and angle POQ?
A. Measure of angle POS is 30 degrees, measure of angle POQ is 50 degrees
B. Measure of angle POS is 30 degrees, measure of angle POQ is 65 degrees
C. Measure of angle POS is 25 degrees, measure of angle POQ is 65 degrees
D. Measure of angle POS is 25 degrees, measure of angle POQ is 50 degrees
5. The figure below shows a partially completed set of steps to construct parallelogram PQRS:
The next step is to construct side RS of the parallelogram so that side RS is congruent to side PQ.
The chart below shows the steps each of the four students took to draw side RS of the parallelogram:
Student 1 Fix the compass at L and adjust its width to point M. Without changing the width of the compass, move the compass to R and draw an arc. Draw a line segment from R that passes through T and intersects the arc at S.
Student 2 Fix the compass at Q and draw an arc that intersects side QP. Without changing the width of the compass, move the compass to R and draw an arc. Draw a line segment from R that passes through T and intersects the second arc at S.
Student 3 Fix the compass at Q and adjust its width to point P. Without changing the width of the compass, move the compass to R and draw an arc. Draw a line segment from R that passes through T and intersects the arc at S.
Student 4 Fix the compass at L and adjust its width to point P. Without changing the width of the compass, move the compass to R and draw an arc. Draw a line segment from R that passes through T and intersects the arc at S.
Which student used the correct steps to construct parallelogram PQRS?
2 answers:
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