System of Linear Equations and Equations Questions

SHOW WORK IF NEEDED. 40 question multi choice and assignment question. show work if needed.

The Washington Monument, in Washington, D.C., is 555 feet 5 ⅛ inches tall and weighs 90,854 tons. The monument is topped by a square aluminum
pyramid. The sides of the pyramid’s base measure 5.6 inches, and the pyramid is 8.9 inches tall. Estimate the slope that a face of the pyramid makes with
its base. Round to the nearest tenth.
163.7
3.2
1.6
0.3
Mr. and Mrs. Wellman are taking their daughter to college.The table shows their distance from home after Various amounts of time.
During which hours was the family most likely stopped?
between 0-1 hours
between 1-2 hours
between 2-3 hours
between 3-4 hours
Mary Sue is training for a 5k run. She ran for 24 minutes a shown on the graph below.
During which range did Mary Sue run the fastest?
between 0-4 minutes
between 8-14 minutes
between 14-16 minutes
between 16 and 24 minutes
Find the set of points that are part of a line that is perpendicular to the line y = -3x
(-3, -3), (3, -5)
(-6, -1), (3, 2)
(-1, -1), (1, 5)
(3, -6), (-1, 6)
Determine the value of r such that the line through (5, r) and (2, 3) is perpendicular to the line y = 2x – 4
r = 1.5
r=9
r=-3
r = 4.5
Which line set of points are part of a line that is parallel to the line y = (-⅔)x + 1
(5, 0), (-1, 4)
(2, 0), (2, -1)
(2, -2), (6, 4)
(3, -2), (6, 0)
Which line is parallel to the line that passes through the points (4, 9), (11, 9)?
x=4
y=3
y=x+4
y=x-3
Find the slope of the line that passes through the points (4, 2) and (-3, -5)
-3
1
-⅓
9/5
Find the slope of the line that passes through the points (-8, -3) and (2, 3)
0
1
3/5
5/3
What is the slope of the line shown in the graph?
-⅔
2/3
3/2
Which equation is shown in the graph?
y = [[x]]
y = [[x + 3]]
y = [[x]] – 3
y = |x – 3|
Which function is shown in the graph?
y=|x|+4
y=|x+4|
y=|x|-4
y=|x-4|
Given the function: f(x) = -½ | x+4| Describe the transformations to the function
A. moves to the right 4 units and is wider than the parent function
B. moves to the left 4 units and is wider than the parent function
C. moves to the right 4 units, is wider than the parent function, and is flipped over the x-axis
D. moves to the left 4 units, is wider than the parent function, and is flipped over the x-axis
Given the function: f(x) = 2|x-2| + 3 Describe how the function is transformed
A. Moves to the right by 2 and up by 3 units
B. Moves to the left by 2, up 3 units, and is steeper than the parent function
C. Moves to the right by 2, up 3 units, and is steeper than the parent function
D. Moves to the left by 2, up 3 units, and is flatter than the parent function
For which function is the range {y | y ≤ 0}?
f(x) = – x
f(x) = [[x]]
f(x) = | x |
f(x) = – | x |
Which piecewise function is equivalent to the absolute value function and its graph?
y = 2|x – 4| + 2
A.
B.
C.
D.
A
B
C
D
Which of the following situations could be graphed using a step function?
The cost for a phone plan is $25 per month and 10 cents per minute.
McDonald’s employees get paid $7.25 per hour up to 40 hours and they make $10.88 per hour if they work over $40 hours.
A t-shirt company charges a flat fee of $35 plus $4 per shirt for up to 100 shirts. If more than 100 shirts are ordered, the cost is $35 plus $2 per shirt.
A phone company charges $40 if you use less than 250 minutes, $75 if you use btween 250-450 minutes, and $100 for more than 450 minutes.
Which graph shows the piecewise function given below?
A.
B.
C.
D.
A
B
C
D
Which of the following represents a step function?
A.
B.
C.
D.
A
B
C
D
A.
B.
C.
D.
A
B
C
D
A student solves the system of equations given below. In which line is an error first made?
2x – y = 6
2x + y = 10
Line 1 2x – y = 6
– 2x + y = 10
Line 2 0 = 4
Line 3 0 ≠-4 so there is no solution
Line 1
Line 2
Line 3
There is no error
Which of the following situations would give you a system of equations that have at least 2 solutions?
Two lines are parallel and have different y-intercepts.
Two lines have the same slope and both pass through the origin.
Two lines are perpendicular and have the same y-intercept.
Two lines have negative slopes and different y-intercepts.
What is the best estimate for the solution to the system of equations shown on the graph below?
(2, 3)
(3, 2)
(2.5, 3.5)
(3.5, 2.5)
Solve the system of equations.
3x = -31 + 2y
5x + 6y = 23
x = -5, y = 8
x = – 29, y = – 28
no solution
infinite solutions
Solve the system of equations.
6d + 3f = 12
2d = 8 – f
d= 3, f = 2
d = 3, f = 14
no solution
infinite solutions
Which of the following systems is consistent and dependent?
y = x + 4; y = x – 4
x + y = 4; 2x + 2y = 6
3x + y = 3; 2y = 6x + 6
4x – 2y = 6; 6x – 3y = 9
Which graph shows a system of equations with no solution?
A.
B.
C.
D.
A
B
C
D
The caterer at a brunch bought several pounds of chicken salad and several pounds of tuna salad. The chicken
salad cost $9 per pound, and the tuna salad cost $6 per pound. He bought a total of 14 pounds of salad and
paid a total of $111. How much chicken salad did he
buy?
6 pounds
7 pounds
8 pounds
9 pounds
In order to practice at home, Tadeo purchased a basketball and a volleyball that cost a total of $67, not including tax. If the price of the basketball b is $4
more than twice the cost of the volleyball v. Which system of linear equations could be used to determine the price of each ball?
b + v = 67; b = 2v – 4
b + v = 67; b = 2v + 4
b + v = 4; b = 2v – 67
b + v = 4; b = 2v + 67
Which of the following best describes the graph of the equations?
4y = 3x + 8
-6x = -8y + 24
The lines are parallel
The lines have the same x-intercept
The lines are perpendicular
The lines have the same y-intercept
A student is solving the system of equations below. In which line is a mistake first made?
2x + y – 2z = 23
3x + 2y + z = 11
x – y + z = -2
Line 1 z = 11 + 3x + 2y
Line 2 2x + y – 2(11 + 3x + 2y) = 23
Line 3 -4x – 3y = 45
Line 4 x – y + (11 + 3x + 2y) = – 2
Line 5 4x + y = – 13
Line 6 -2y = 32
Line 7 y = 16, x = ¾, z = -11/4
Line 1
Line 3
Line 5
Line 6
What is the solution to the system of equations shown below?
2x + 5y + 3z = 10
3x – y + 4z = 8
5x – 2y + 7z = 12
(7, 1, -3)
(7, -1, -3)
(7, 1, 3)
(-7, 1, -3)
Which ordered triple represents all of the solutions to the system of equations shown below?
2x – 2y – z = 6
-x + y + 3z = -3
3x – 3y + 2z = 9
(-x, x + 2, 0)
(x, x – 3, 0)
(x + 2, x, 0)
(0, y, y + 4)
What is the solution to the system of equations shown below?
2x – y + z = 4
4x – 2y + 2z = 8
-x + 3y – z = 5
(5, 4, -2)
(0, -5, -1)
No Solution
Infinite Solutions
What is the solution to the system of equations shown below?
2x + y – 3z = 11
-x + 2y + 4z = -3
x – 5y + 2z = – 18
(-1, 1, -4)
(1, 3, -2)
(3, 8, 1)
(2, -3, 0)
A student is solving the system of equations below. What would be best next step in order to solve the system?
3x + y + z = 4
2x + 2y + 3z = 3
x + 3y + 2z = 5
6x + 2y + 2z = 8
3x + y + z = 4
→ (-)x + 3y + 2z = 5
x + 3y + 2z = 5
5x – 1y = 3
9x + 3y + 3z = 12
3x + y + z = 4
B.
→ (-)x + 3y + 2z = 5
2x + 2y + 3z = 3
8x +1z = 7
9x + 3y + 3z = 12
3x + y + z = 4
C.
→ (-)x + 3y + 2z = 5
x + 3y + 2z = 5
8x + 1z = 17
3x + y + z = 4
x+y+z=4
D.
→ (-)3x + 9y + 6z = 15
x + 3y + 2z = 5
-8y – 5z = -9
A.
A
B
C
D
Which image shows a system of equations with infinite solutions?
A.
B.
C.
D.
A
B
C
D
What is the solution to the system of equations shown below?
x- y + z = 0
-5x + 3y – 2z = -1
2x – y + 4z = 11
(0, 3, 3)
(2, 5, 3)
no solution
infinitely many solutions
Which answer correctly shows the first step that can be used to correctly solve the
system of equations?
5x + 2y = 4
3x + 4y + 2z = 6
7x + 3y + 4z = 29
3x + 4y + 2z = 6 → 3x + 4y + 4z = 6
7x + 3y + 4z = 29 → (-)7x + 3y + 4z = 29
A.
-4x – y =- 23
3x + 4y + 2z = 6 → 6x + 8y + 4z = 12
7x + 3y + 4z = 29 → (-)7x + 3y + 4z = 29
B.
-x + 5y = -17
3x + 4y + 2z = 6 → 6x + 8y + 4z = 6
7x + 3y + 4z = 29 → (-)7x + 3y + 4z = 2
C.
-x + 5y =- 23
3x + 4y + 2z = 6 → 6x + 8y + 4z = 12
7x + 3y + 4z = 29 → (-)7x + 3y + 4z = 29
D.
-x + 8y = 41
A
B
C
D
Complete the sentence.
A system of equations in 3 variables always has infinite solutions if _________.
the planes intersect in one point
the planes have no common point
the planes intersect in a line.
the planes are parallel.
.
Let c be the distance between Carlisle and Wellesley, let b be the distance between Carlisle and Stonebridge,
and let a be the distance between Wellesley and Stonebridge.
•
If you did a circuit, traveling from Carlisle to Wellesley to Stonebridge and back to Carlisle, you would
travel 73 miles.
•
Stonebridge is 12 miles farther than Wellesley is from Carlisle.
•
If you drove from Stonebridge to Carlisle and back to Stonebridge, and then continued to Wellesley then
back to Stonebridge, you would travel 102 miles.
a. Write a system of linear equations to represent the situation.
b. Solve the system of equations. Explain the meaning of the solution in the context of the situation.
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