Expert answer:Pre calculus multiple choice quiz
Expert answer:I have Pre-cal 30 question multiple choice quiz needed in about two hours. Please help. I need a fast but accurate tutor to help me.
precal_quiz_1_2.docx
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Question 1 (3.33 points)
Graph the solution set of the system of inequalities or indicate that the system has no solution.
y ≥ 2x – 4
x + 2y ≤ 7
y ≥ -2
x≤1
Question 1 options:
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Question 2 (3.33 points)
A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours to
prepare, 2 hours to paint, and 9 hours to fire. A tree takes 14 hours to prepare, 3 hours to paint, and 4
hours to fire. A sleigh takes 4 hours to prepare, 15 hours to paint, and 7 hours to fire. If the workshop
has 116 hours for prep time, 64 hours for painting, and 110 hours for firing, How many of each can be
made?
Question 2 options:
6 wreaths, 2 trees, 8 sleighs
9 wreaths, 7 trees, 3 sleighs
8 wreaths, 6 trees, 2 sleighs
2 wreaths, 8 trees, 6 sleighs
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Question 3 (3.33 points)
Solve the system of equations
Question 3 options:
(19, -6)
(-6, -19)
none of these
(6, 19)
(19, 6)
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Question 4 (3.33 points)
Graph the solution set of the system of inequalities or indicate that the system has no solution.
x2 + y2 ≤ 49
5x + 4y ≤ 20
Question 4 options:
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Question 5 (3.33 points)
Graph the solution set of the system of inequalities or indicate that the system has no solution.
y > x2
10x + 6y ≤ 60
Question 5 options:
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Question 6 (3.33 points)
Write the partial fraction decomposition of the rational expression.
Question 6 options:
+
+
+
+
+
+
+
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Question 7 (3.33 points)
Solve by the method of your choice.
x3 + y = 0
11×2 – y = 0
Question 7 options:
{(-1, 1), (-11, 1331)}
{(0, 0), (-11, 1331)}
{(0, 0), (-11, 121)}
{(0, 0), ( 11, -1331)}
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Question 8 (3.33 points)
A flat rectangular piece of aluminum has a perimeter of 70 inches. The length is 11 inches longer than
the width. Find the width.
Question 8 options:
34 inches
23 inches
35 inches
12 inches
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Question 9 (3.33 points)
Solve the system of equations
Question 9 options:
x = –2, y = 2, z = -1
x = –1, y = 4, z = 1
x = –3, y = 7, z = 0
x = 4, y = 0, z = 0
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Question 10 (3.33 points)
Graph the inequality.
(x-1)2 + (y-5)2 > 9
Question 10 options:
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Question 11 (3.33 points)
Solve the system
Question 11 options:
(45, -9)
(9, 45)
(45, 9)
(-45, -9)
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Question 12 (3.33 points)
An objective function and a system of linear inequalities representing constraints are given. Graph the
system of inequalities representing the constraints. Find the value of the objective function at each
corner of the graphed region. Use these values to determine the maximum value of the objective
function and the values of x and y for which the maximum occurs.
Objective Function
z = 21x – 25y
Constraints
0≤x≤5
0≤y≤8
4x + 5y ≤ 30
4x + 3y ≤ 20
Question 12 options:
Maximum: 105; at (5, 0)
Maximum: 0; at (0, 0)
Maximum: -98.75; at (1.25, 5)
Maximum: -150; at (0, 6)
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Question 13 (3.33 points)
Solve the system by the method of your choice. Identify systems with no solution and systems with
infinitely many solutions, using set notation to express their solution sets.
4x – 3y = 6
-12x + 9y = -24
Question 13 options:
{( 3, 4)}
∅
{(x, y) | 4x – 3y = 6 }
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Question 14 (3.33 points)
In the town of Milton Lake, the percentage of women who smoke is increasing while the percentage of
men who smoke is decreasing. Let x represent the number of years since 1990 and y represent the
percentage of women in Milton Lake who smoke. The graph of y against x includes the data points (0,
15.9) and ( 13, 19.67). Let x represent the number of years since 1990 and y represent the percentage of
men in Milton Lake who smoke. The graph of y against x includes the data points (0, 29.7) and ( 15,
26.85). Determine when the percentage of women who smoke will be the same as the percentage of
men who smoke. Round to the nearest year. What percentage of women and what percentage of men
(to the nearest whole percent) will smoke at that time? [Hint: first find the slope-intercept equation of
the line that models the percentage, y, of women who smoke x years after 1990 and the slope-intercept
equation of the line that models the percentage, y, of men who smoke x years after 1990]
Question 14 options:
2023; 23%
2019; 24%
2021; 24%
2017; 25%
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Question 15 (3.33 points)
Solve the system
Question 15 options:
x = 3, y = 2
x = 2, y = 5
x = 1, y = 2
All real solutions.
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Question 16 (3.33 points)
Solve the system of equations using matrices. Use Gauss-Jordan elimination.
3x – 7 – 7z = 7
6x + 4y – 3z = 67
-6x – 3y + z = -62
Question 16 options:
{( 7, 7, 1)}
{( -7, 7, 14)}
{( 7, 1, 7)}
{( 14, 7, -7)}
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Question 17 (3.33 points)
Use Cramer’s rule to solve the system. 2x + 4y – z = 32 x – 2y + 2z = -5 5x + y + z = 20
Question 17 options:
{( 1, -9, -6)}
{( 1, 9, 6)}
{( 2, 7, 6)}
{( 9, 6, 9)}
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Question 18 (3.33 points)
Find the product AB, if possible.
A=
,B=
Question 18 options:
AB is not defined.
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Question 19 (3.33 points)
Find the inverse of the matrix.
Question 19 options:
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Question 20 (3.33 points)
Find the product AB, if possible.
A=
,B=
Question 20 options:
AB is not defined.
Save
Question 21 (3.33 points)
Find the product AB, if possible.
A=
,B=
Question 21 options:
AB is not defined.
Save
Question 22 (3.33 points)
Find the determinant of the matrix.
Question 22 options:
D = -277
D = -279
D = -272
D = -278
D = -276
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Question 23 (3.33 points)
Find the inverse of the matrix.
Question 23 options:
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Question 24 (3.33 points)
Let B = [-1 3 6 -3]. Find -4B.
Question 24 options:
[4 -12 -24 12]
[4 3 6 -3]
[-4 12 24 -12]
[-3 1 4 -5]
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Question 25 (3.33 points)
Evaluate the determinant.
Question 25 options:
-60
30
-30
60
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Question 26 (3.33 points)
Solve the system of equations using matrices. Use Gaussian elimination with back-substitution.
3x + 5y – 2w = -13
2x + 7z – w = -1
4y + 3z + 3w = 1
-x + 2y + 4z = -5
Question 26 options:
{(
,-
, 0,
)}
{(-1, –
, 0,
)}
{(1, -2, 0, 3)}
{(
, -2, 0,
)}
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Question 27 (3.33 points)
Find the products AB and BA to determine whether B is the multiplicative inverse of A.
A=
,B=
Question 27 options:
B = A-1
B ≠ A-1
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Question 28 (3.33 points)
Find the determinant of the matrix if it exists.
Question 28 options:
7
27
-9
-7
47
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Question 29 (3.33 points)
Determinants are used to show that three points lie on the same line (are collinear). If
= 0,
then the points ( x1, y1), ( x2, y2), and ( x3, y3) are collinear. If the determinant does not equal 0, then
the points are not collinear. Are the points (-2, -1), (0, 9), (-6, -21) and collinear?
Question 29 options:
Yes
No
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Question 30 (3.33 points)
Solve the matrix equation for X.
Let A =
and B =
Question 30 options:
X=
X=
X=
X=
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; 4X + A = B
…
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