Download GEOMETRY QUIZ 1.1 (Part I)

GEOMETRY QUIZ 1.1 (Part I)
1. Construct a copy of the line segment AB from the triangle. The copy should have one endpoint at P.
(2 points)
2. Construct a copy of DAC .
3. Bisect all 4 angles.
(3 points)
(4 points)
4. Construct the four perpendicular bisectors of the sides of the rectangle below. (4 points)
5.
Construct a triangle with a 30o angle and a 45o angle. What is the measure of the third angle?
(5 points)
6. (a)Construct a line parallel to AB through Q, and another line parallel to CD also through Q.
(b)What is the name of the resulting 4-sided shape?
(5 points)
7. Construct a line perpendicular to the one below that passes through the point P
(4 points)
8. Construct a line perpendicular to the one below that passes through the point P
(3 points)
GEOMETRY QUIZ 1.1 (Part II)
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
____
1. ____ two points are collinear.
A. Any
(½ point)
B. Sometimes
C. No
Short Answer
2. Are O, N, and P collinear? If so, name the line on which they lie.
(½ point)
O
N
M
3. (a)
(b)
P
Name the plane represented by the front of the box.
(½ point)
Are points A, and C collinear or noncollinear?
(½ point)
4. (a) Name the line shown in the diagram.
(b) Name the plane shown in the diagram in two different ways.
(½ point)
(2 points)
5. (a)
(b)
6. (a)
What is the intersection of plane TUY and plane VUZ?
(1 point)
Name a fourth point in plane TUW.
(1 point)
Name the ray in the figure below.
(½ point)
A
(b)
B
Name the ray in the figure that is opposite
.
(½ point)
D
C
B
A
(c)
If
is opposite
and
is opposite
, what can you conclude? Explain. (2 points)
7. (a)
Name all segments that are skew to
(2 points)
(b)
Name all labeled segments that are parallel to
(1 point)
(c)
Which plane is parallel to plane DEF?
(½ point)
Use the diagram below to answer questions 8-10.
8. Name two different planes that contain the points C and G.
9. Name the intersection of plane AED and plane HEG.
10. How many planes contain the points A, F, and H?
(1 point)
(1 point)
(1 point)
Use the diagram below to answer questions 11-12.
11. Name a pair of parallel planes.
12. Name a line that is skew to line XW.
(1 point)
(1 point)
Use the diagram below to answer questions 13-14.
13. If XZ = 3x, XT = x + 3, and TZ = 13, find XZ.
(1 point)
14. Suppose that T is the midpoint of XZ. If XT = 2x + 11 and XZ = 5x + 8, find the value of x.
(2 points)
15. Find AC.
(½ point)
A
B
C
D
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
16. If
find the values of x, EF, and FG. The drawing is not to scale.
E
F
G
(2 points)
17. If T is the midpoint of
S
find the values of x and ST. The diagram is not to scale.
T
9x
U
4x + 25
(1 point)
18. Which point is the midpoint of
A
B
C
(½ point)
D
–8 –7 –6 –5 –4 –3 –2 –1
19. If
?
0
1
E
2
and
3
4
5
6
7
8
, then what is the measure of
The diagram is not to scale.
(1 point)
20. (a) If
and
then what is the measure of
(b) Use a protractor to find the exact measure of
mAOC .
The diagram is not to scale.
Classify the angle.
(2 points)
21. If
then what are
and
The diagram is not to scale.
(2 points)
22. A circle is drawn on the coordinate plane. The end points of a diameter are shown. What are the
coordinates of the center of the circle and what is the length of the radius (in simplest radical form)?(5
pts)
GEOMETRY QUIZ 1.2
Questions 1-4 are multiple choice.
____
____
1. Which diagram shows plane PQR and plane QRS intersecting only in
a.
c.
b.
d.
2. How are the two angles related?
52°
128°
Drawing not to scale
a. vertical
c. complementary
?
b. supplementary
____
d. adjacent
3. Two angles whose sides are opposite rays are called ____ angles. Two coplanar angles with a common
side, a common vertex, and no common interior points are called ____ angles.
a. vertical; adjacent
b. adjacent; vertical
c. vertical; supplementary
d. adjacent; complementary
____
4. In the figure shown,
. Which of the following statements is false?
Not drawn to scale
a.
b.
BEC and
CED are adjacent angles.
AED and
BEC are adjacent angles.
c.
d.
(4 points)
5. Name an angle supplementary to
(1 point)
6. Name an angle complementary to
7.
8.
and
of each angle.
and
(1 point)
are complementary angles. m
are a linear pair.
, and
=
, and m
=
. Find the measure
(2 points)
. Find the measure of each angle.
(2 points)
9.
bisects
and
Solve for x and find
(2 points)
10. M(9, 8) is the midpoint of
The coordinates of S are (10, 10). What are the coordinates of R?
(1 point)
11. Noam walks home from school by walking 8 blocks north and then 6 blocks east. How much shorter
would his walk be if there were a direct path from the school to his house? Assume that the blocks are
square.
(2 points)
12. A high school soccer team is going to Columbus, Ohio to see a professional soccer game. A coordinate
grid is superimposed on a highway map of Ohio. The high school is at point (3, 4) and the stadium in
Columbus is at point (7, 1). The map shows a highway rest stop halfway between the cities. What are
the coordinates of the rest stop? What is the approximate distance between the high school and the
stadium? (One unit 6.4 miles.)
(3 points)
13. Find the area of the figure:
(3 points)
14. Find the perimeter of the figure below. Leave your answer in simplest radical form if necessary. (2
points)
9 cm
8 cm
13 cm
9 cm
11 cm
15. Ken is adding a ribbon border to the edge of his kite. Two sides of the kite measure 9.5 inches, while the
other two sides measure 17.8 inches. How much ribbon does Ken need?
(1 point)
16. If the perimeter of a square is 72 inches, what is its area?
points)
17. Classify the figure below. Find the perimeter and area of the figure.
y
10
5
A
–10
–5
C
B
D
–5
–10
5
10 x
(2
(4 points)
18. Find the area of the shaded portion of the figure. Each vertex of square ABCD is at the center of a circle.
Leave your answer in terms of
.
19. Find the surface area and volume of the cylinder in terms of
(3 points)
.
(3 points)
20. Find the surface area & volume of the square pyramid shown, to the nearest whole number.
(3 points)
21. Find the surface area & volume of the cone to the nearest tenth.
(3 points)
____ 22. Find the surface area & volume of the given prism. Round to the nearest tenth if necessary.
(3 points)
23. Find the surface area & volume of the sphere shown. Give each answer rounded to the nearest whole
number.
(3 points)
24. Construct
the bisector of
(2 points)
GEOMETRY QUIZ 1.3
1. Find the area of the figure below:
(1 point)
2. Find the perimeter and area of the given figure.
(2 points)
3. Find the area of the figure below.
(2 points)
4. Find the area of the un-shaded region in the figure below.
(1 point)
4 ft
14 ft
6 ft
15 ft
5. Determine the area of a circular region, in terms of
6. Find the height of the cylinder.
 , if its circumference is 42 units.
(1 point)
(2 points)
7. Find the surface area and volume of the figure below. Leave your answer in simplest radical form.
(3 points)
8. Find the surface area in terms of .
(2 points)
9. Find the surface area and volume to the nearest whole number.
(3 points)
10. Find the surface area and volume to the nearest whole number.
(3 points)
For questions 11-13 identify the letter of the choice that best completes the statement or answers the question.
____ 11. Which statement is a counterexample for the following conditional?
(1 point)
If you live in Springfield, then you live in Illinois.
A. Sara Lucas lives in Springfield.
B. Jonah Lincoln lives in Springfield, Illinois.
C. Billy Jones lives in Chicago, Illinois.
D. Erin Naismith lives in Springfield, Massachusetts.
____ 12. Which choice shows a true conditional with the hypothesis and conclusion identified correctly?(1 pt)
A. Yesterday was Monday if tomorrow is Thursday.
Hypothesis: Tomorrow is Thursday.
Conclusion: Yesterday was Monday.
B. If tomorrow is Thursday, then yesterday was Tuesday.
Hypothesis: Yesterday was Tuesday.
Conclusion: Tomorrow is not Thursday.
C. If tomorrow is Thursday, then yesterday was Tuesday.
Hypothesis: Yesterday was Tuesday.
Conclusion: Tomorrow is Thursday.
D. Yesterday was Tuesday if tomorrow is Thursday.
Hypothesis: Tomorrow is Thursday.
Conclusion: Yesterday was Tuesday.
____ 13. Which conditional has the same truth value as its converse?
A. If x = 7, then
.
B. If a figure is a square, then it has four sides.
(1 point)
C. If x – 17 = 4, then x = 21.
D. If an angle has measure 80, then it is acute.
____ 14. A conditional can have a ____ of true or false.
A. hypothesis
B. truth value
(1 point)
C. counterexample
D. conclusion
In questions 15-20 if the converse of the given conditional is true, write true; if not true, provide a
counterexample.
15. If a circle’s radius is 2 m, then its diameter is 4 m.
(1 point)
16. If a point is in the first quadrant, then its coordinates are positive.
(1 point)
17. If an angle is a right angle, then its measure is 90.
(1 point)
18. If x = 4, then x2 = 16.
(1 point)
19. If lines are parallel then they do not intersect.
(1 point)
20. If a number is divisible by 10 then the number contains the digit 0.
(1 point)
21. Write a statement for each Venn diagram:
(1 point each)
A.
B.
Quadrilaterals
Squares
C.
For questions 22-25 identify the type of argument, determine the argument’s validity using a Venn diagram, and
discuss whether the argument is sound.
(3 points each)
22.
All islands are tropical
Iceland is an island.
Therefore, Iceland is tropical.
23.
All salty foods cause high blood pressure.
Apples do not cause high blood pressure.
Therefore, apples are not salty foods.
24.
Doctors know anatomy.
Cardiologists know anatomy.
Therefore, cardiologists are doctors.
25.
If you are a movie star then you do not do your own laundry.
You are not a movie star.
Therefore, you do your own laundry.
26.
Make a truth table for
(5 points)
GEOMETRY QUIZ 1.4
1. Find x given:
(1 point)
2. Find x given:
(1 point)
3. Find surface area of the cone. Round the answers to the nearest tenth.
(2 points)
4. Find the volume of the sphere shown. Give your answer rounded to the nearest cubic unit.(2 points)
5. Find the surface area of the figure below.
(2 points)
6. The figure represents the overhead view of a deck surrounding a hot tub. What is the area of the deck?
Round to the nearest tenth.
(3 points)
7. Find the area of an equilateral triangle with a side of 12, in simplest radical form.
(3 points)
8. Two square pyramids have the same volume. For the first pyramid, the side length of the base is 20 in.
and the height is 21 in. The second pyramid has a height of 84 in. What is the side length of the base of
the second pyramid?
(2 points)
____
9. Which conditional has the same truth value as its converse?
A. If x = 7, then
(1 point)
.
B. If a figure is a square, then it has four sides.
C. If x – 17 = 4, then x = 21.
D. If an angle has measure 80, then it is acute.
____ 10. Which statement provides a counterexample to the following faulty definition?
A square is a figure with four congruent sides.
A. A six-sided figure can have four sides congruent.
(1 point)
B. Some triangles have all sides congruent.
C. A square has four congruent angles.
D. A rectangle has four sides.
____ 11. Which biconditional is NOT a good definition?
(1 point)
A. A whole number is odd if and only if the number is not divisible by 2.
B. An angle is straight if and only if its measure is 180.
C. A whole number is even if and only if it is divisible by 2.
D. A ray is a bisector of an angle if and only if it splits the angle into two angles.
____ 12. Which statement is the Law of Detachment?
(1 point)
A. If
is a true statement and q is true, then p is true.
B. If
is a true statement and q is true, then
C. If
and
D. If
is a true statement and p is true, then q is true.
are true, then
is true.
is a true statement.
____ 13. Which statement is the Law of Syllogism?
(1 point)
A. If
is a true statement and p is true, then q is true.
B. If
is a true statement and q is true, then p is true.
C. if
and
are true statements, then
is a true statement.
D. If
and
are true statements, then
is a true statement.
14. What is the converse and the truth value of the converse of the following conditional?
(1 point)
If an angle is a right angle, then its measure is 90.
15. For the following true conditional statement, write the converse. If the converse is also true, combine the
statements as a biconditional.
(1 point)
If x = 3, then x2 = 9.
16. Determine whether the conditional and its converse are both true. If both are true, combine them as a
biconditional. If either is false, give a counterexample.
(1 point)
If two lines are parallel, they do not intersect.
If two lines do not intersect, they are parallel.
17. Write the two conditional statements that make up the following biconditional.
(1 point)
I drink juice if and only if it is breakfast time.
18. Decide whether the following definition of perpendicular is reversible. If it is, state the definition as a
true biconditional.
(1 point)
Two lines that intersect at right angles are perpendicular.
19. Is the statement a good definition? If not, find a counterexample.
(1 point)
A square is a figure with two pairs of parallel sides and four right angles.
20. Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write
not possible.
(1 point)
If two angles are congruent, then they have equal measures.
and
are congruent.
21. Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not
possible.
(1 point)
I can go to the concert if I can afford to buy a ticket.
I can go to the concert.
22. Use the Law of Syllogism to draw a conclusion from the two given statements.
(1 point)
If a number is a multiple of 64, then it is a multiple of 8.
If a number is a multiple of 8, then it is a multiple of 2.
23. Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the three given
statements.
If an elephant weighs more than 2,000 pounds, then it weighs more than Jill’s car.
If something weighs more than Jill’s car, then it is too heavy for the bridge.
Smiley the Elephant weighs 2,150 pounds.
(1 point)
24. Assume that the following statements are true.
(3 points)
I. If Cecil makes his bed, then it is morning.
II. If it is 8 p.m., then Tami brushes her teeth.
III. If it is morning, then Ted listens to the radio.
IV. If it is afternoon, then Jeanette takes her daily swim.
V. Cecil makes his bed.
For each statement below, write must be true, may be true, or not true. Use only the information given
above.
A. Ted listens to the radio.
B. Tami does not brush her teeth.
C. Jeanette takes her daily swim.
(a) Identify the type of argument in # 25-29. (b) Determine the argument’s validity. (c) State whether the
argument is sound.
(3 points each)
25. All dairy products contain protein.
Soybeans contain protein.
Soybeans are dairy products.
26. All opera singers can whistle a Mozart tune.
Pavarotti is an opera singer.
Pavarotti can whistle a Mozart tune.
27. If an animal is a bird, then it flies.
If a vehicle is a plane, then it flies.
If an animal is a bird, then it is not a plane.
28. All residents of Minnesota know how to drive in freezing temperatures.
Wendy doesn’t know how to drive in freezing temperatures.
Wendy doesn’t live in Minnesota.
29. All U.S. presidents have been men.
Dave was not a US president.
Dave is not a man.
30. Construct a valid argument based on the diagram shown.
(1 point)
GEOMETRY EXAM 1.1
Use the following information to answer questions 1-5.
A has coordinates (3,8). B has coordinates (0,-4). C has coordinates (-5,-6).
1. Find the distance between A and B in simplest radical form.
(1 point)
2. Find BC in simplest radical form.
(1 point)
3. Find the midpoint M of AC .
(1 point)
4. B is the midpoint of AD . Find the coordinates of endpoint D.
(1 point)
5. An airplane flies from Stanton to Mercury in a straight flight path. Mercury is 300 miles east and 400 miles south
of Stanton. How many miles is the flight?
(1 point)
Use the figure below for questions 6-7.
6. Find x.
7. Find m DNB .
point)
8. If m 1 is twice m 2 , find m 1 .
NQ bisects DNB
(1 point)
(1
(2 points)
9. The radius of the bull’s-eye of the dartboard is 8 inches. The radius of each concentric circle is 8 inches more than
the radius of the circle inside it. Find the area of the shaded region. Leave your answer in terms of π. (3 points)
10. Jason designed an arch made of wrought iron for the top of a mall entrance. The wrought iron used to make the
11 line segments between the two concentric circles are each 1.25 m long. Find the total length of wrought iron
used to make the structure. Round the answer to the nearest meter.
11. Find the volume of the figure below:
(4 points)
(2 points)
12. The radius of the base of a cylinder is 28 cm and its height is 48 cm. Find the volume of the cylinder in
terms of
(2 points)
13. Find the surface area of the figure to the nearest tenth.
points)
(3
14. Find the surface area & volume of the cone to the nearest whole number.
points)
(3
15. The volume of a sphere is 3000 m . What is the surface area of the sphere to the nearest square
meter?(2 points)
16. Write a conjecture given that ∆ABC is an equilateral triangle.
(1
point)
17. Give a counterexample for the following statement:
(1 point)
“If  A and  B are complementary, then  A is 45.”
18. Find the truth value of  p  q  r .
(1 point)
2
p: (-4) > 0
q: An isosceles triangle has two congruent sides.
r: Two angles, whose measure have a sum of 90, are supplements.
19. Suppose p and q are both false. What is the truth value of  p ~ q ~ p ?
(1
point)
20. Use the method of successive differences to find the next term in the sequence 1, 5, 12, 22, 35. (2
points)
21. Use the law of detachment and a Venn diagram to tell whether the following reasoning is valid and/or
sound.
If you drive more than 65 miles per hour you will always get a ticket.
(3
points)
Joe got a ticket.
Joe drove over 65 miles per hour.
22. Write three statements that illustrate the Law of syllogism soundly.
23. Determine which statement follows logically from statements (1) and (2).
point)
(1) If a triangle is equilateral, then it has three congruent sides.
(2) If all the sides of a triangle are congruent, then each of its angles measures 60.
A. If a triangle is not equilateral, then it cannot have congruent angles.
B. A figure with three congruent sides is always an equilateral triangle.
C. If a triangle is not equilateral, then none of the angles equals 60.
D. If a triangle is equilateral, then each of its angles measures 60.
(1 point)
(1
24. Which of the following illustrates the Law of Detachment?
A.  p  q  q  r    p  r 
C.
 p  q  q  p
B.  p  q  q  r    p  r 
D.
 p  q  p  q
(1 point)
25. Determine the intersection of lines l and p.
(1 point)
26. Give another name for plane K.
point)
(1
For questions 27-29 name the definition, property, postulate or theorem that justifies each statement.
27. If x = 2, then 2 = x.
28. If x + 3 = y, then x = y – 3.
29. If m  A = 10 and m  B = 10, then m  A = m  B.
(1 point)
(1 point)
(1 point)
For questions 30-31, use the statement ‘If a ray bisects an angle then it divides the angle into two congruent angle’
and the given choices.
A.
B.
C.
D.
If a ray divides an angle into two congruent angles, then it bisects the angle.
A ray bisects an angle if and only if it divides it into two congruent angles.
If a ray does not bisect an angle, then it does not divide the angle into two congruent angles.
If a ray does not divide an angle into two congruent angles, then it does not bisect the angle.
30. Which choice is the inverse of the given statement?
31. Which choice is the contrapositive of the given statement?
(1 point)
(1 point)
For questions 32-35 write whether each sentence is true or false. If false, replace the underlined word to make a
true sentence.
32. A postulate is a statement that has been proved.
(1
point)
33. A statement that has opposite meaning and truth value of the original statement is called the negation. (1
point)
34. Deductive reasoning uses facts, rules, definitions, or properties to reach logical conclusions.
(1
point)
35. Kamran lives in Dallas or Kamran lives in Houston is an example of a conjunction.
(1
point)
36. Complete the proof of the statement If x + 3 = 15x – 53, then x = 4.
points)
Proof:
Statements
a. x + 3 = 15x – 53
b. x – x + 3 = 15x – x – 53
c. 3 = 14x – 53
d. 3 + 53 = 14x – 53 + 53
e. 56 = 14x
f. 56 = 14x
14 14
g. 4 = x
h. x = 4
Use the figure below for questions 37-40.
(4
Reasons
a. Given
b.
c.
d.
e.
f.
g.
h.
NQ bisects DNB
37. Construct AC so that AC  NB .
(2 points)
38. Construct the perpendicular bisector of AC .
39. Construct RST  QNB .
40. Construct the bisector of RST .
(2 points)
(3 points)
(2 points)
GEOMETRY EXAM 1.2
1. Jason designed a mall entrance made of wrought iron. The wrought iron used to make the 16 line
segments between the two concentric circles are each 1.5 m long. Find the total length of wrought iron
used to make the structure. Round the answer to the nearest meter.
(4 points)
2. Find the volume of the composite space figure to the nearest whole number.
3. Which biconditional is NOT a good definition?
point)
A. A whole number is odd if and only if the number is not divisible by 2.
B. An angle is straight if and only if its measure is 180.
C. A whole number is even if and only if it is divisible by 2.
D. A ray is a bisector of an angle if and only if it splits the angle into two angles.
(4 points)
(1
4. Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, state
not possible.
(1
point)
Statement 1: If two lines intersect, then they are not parallel.
Statement 2:
do not intersect.
For questions 5-7, create a simple deductive argument of the given form. Use a Venn diagram to illustrate
whether or not the argument is valid and/or sound.
(3
points each)
5.
Affirming the conclusion
6. Denying the hypothesis
7. A chain of conditionals
8. Each unit on the map represents 5 miles. What is the actual distance from Oceanfront to Seaside?(2 pts)
y
8
6
Seaside
4
2
–8 –6 –4 –2
–2
Landview
–4
2
4
6
8
x
Oceanfront
–6
–8
9. Find the coordinates of the midpoint of the segment whose endpoints are H(8, 2) and K(6, 10). (1
point)
10. Write an equation in point-slope & slope-intercept form of the line through J(–5, 6) with slope –4. (2
pts)
11. Write an equation of the line through point S(–10, –3) and perpendicular to the line with equation
-4x + 7y = -28.
points)
(2
12. Which two lines are parallel?
point)
(1
I.
II.
III.
A. I and II
C. II and III
B. I and III
D. No two of the lines are parallel.
____ 13. Complete the statement. If a transversal intersects two parallel lines, then ____.
point)
(1
A. corresponding angles are supplementary
B. same-side interior angles are complementary
C. alternate interior angles are congruent
D. none of these
____ 14. Complete the statement. If a transversal intersects two parallel lines, then ____ angles are
supplementary.
A. Acute
C. same-side interior
B. alternate interior
D. Corresponding
15. In the figure below, which lines, if any, can you conclude are parallel given that
Justify your conclusion with a theorem or postulate.
(1 point)
( 1 point)
?
g
1
2
j
h
k
A.
, by the Converse of the Same-Side Interior Angles Theorem
B.
, by the Converse of the Alternate Interior Angles Theorem
C.
, by the Converse of the Alternate Interior Angles Theorem
D.
, by the Converse of the Same-Side Interior Angles Theorem
16. Find the values of x and y. The diagram is not to scale.
points)
(x – 3)°
(3
41°
(y + 8)°
74°
17. Find
points)
The diagram is not to scale.
Q
(2
R
70°
50°
18. Complete the two-column proof.
points)
Given:
Prove:
are supplementary.
(3
For Questions 19-20 use the diagram below. Suppose m 1 = 3x + 10, m 2 = 3x + 14, and m 6 = x + 58.
19. Find the value of x for which a || b.
points)
20. Find the value of x for which m || n.
points)
(2
(2
21. You are given that 2c2 = 2bc + ac with c ≠ 0. Justify each step of the proof that 4b = 4c – a.
2
(2 points)
2c2 = 2bc + ac
a. Given
2
2
4c = 4bc + ac
b.
4c = 4b + a
c.
4c – a = 4b
d.
4b = 4c – a
e.
22. What can you conclude from the information in the diagram?
A. 1.
2.
3.
are vertical angles
B. 1.
2.
3.
C. 1.
are adjacent angles
(1 point)
2.
is a right angle
3.
are vertical angles
D. 1.
2.
is a right angle
3.
are adjacent angles
23. In the figure shown,
. Which of the following statements is false?
(1 point)
Not drawn to scale
A.
B.
BEC and
CED are adjacent angles.
AED and
BEC are adjacent angles.
C.
D.
24. How are the two angles related?
point)
(1
52°
128°
Drawing not to scale
A. Vertical
C. complementary
B. Supplementary
25. If
and
D. adjacent
are supplementary angles and
, find
and
(2 point)
26. What is a correct name for the polygon?
point)
(1
A
B
E
C
D
A. EDCAB
27.
B. ABCDA
C. CDEAB
Which figure is a convex polygon?
point)
A.
D. BAEAB
(1
C.
B.
28. Solve the following system of equations by graphing.
y = 3x + 3
D.
(3 points)
y = -x – 3
29.
Sharon has some one-dollar bills and some five-dollar bills. She has 14 bills. The value of the bills is $30.
Solve a system of equations to find how many of each kind of bill she has.
(3 points)
30.
An ice skating arena charges an admission fee for each child plus a rental fee for each pair of ice skates.
John paid the admission fees for his six nephews and rented five pairs of ice skates. He was charged
$32.00. Juanita paid the admission fees for her seven grandchildren and rented five pairs of ice skates.
She was charged $35.25. What is the admission fee? What is the rental fee for a pair of skates?
(3 points)