Expert answer:multiple choice test
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mathsqs.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.
x≥0
y≥0
3x + 2y ≤ 6
3x + y ≤ 5
Question 1 options:
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Question 2 (3.33 points)
A system for tracking ships indicated that a ship lies on a hyperbolic path
described by 5×2 – y2 = 20. The process is repeated and the ship is found to lie
on a hyperbolic path described by y2 – 2×2 = 7. If it is known that the ship is
located in the first quadrant of the coordinate system, determine its exact
location.
Question 2 options:
( -3, -5)
( 5, 3)
( 3, 5)
( -5, -3)
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Question 3 (3.33 points)
Ms. Adams received a bonus check for $12,000. She decided to divide the
money among three different investments. With some of the money, she
purchased a municipal bond paying 5.8% simple interest. She invested twice
the amount she paid for the municipal bond in a certificate of deposit paying
4.9% simple interest. Ms. Adams placed the balance of the money in a money
market account paying 3.7% simple interest. If Ms. Adams’ total interest for
one year was $534, how much was placed in each account?
Question 3 options:
municipal bond: $ 2500 certificate of deposit: $ 5000 money market: $ 4500
municipal bond: $ 1500 certificate of deposit: $ 3000 money market: $ 7500
municipal bond: $ 2000 certificate of deposit: $ 4000 money market: $ 6000
municipal bond: $ 1750 certificate of deposit: $ 3500 money market: $ 6750
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Question 4 (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 4 options:
{( 3, 4)}
{(x, y) | 4x – 3y = 6 }
∅
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Question 5 (3.33 points)
Graph the inequality.
(x-1)2 + (y-5)2> 9
Question 5 options:
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Question 6 (3.33 points)
Solve the system
Question 6 options:
(-45, -9)
(45, 9)
(9, 45)
(45, -9)
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Question 7 (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 7 options:
2023; 23%
2019; 24%
2021; 24%
2017; 25%
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Question 8 (3.33 points)
Solve the system
Question 8 options:
x = 3, y = 2
x = 2, y = 5
All real solutions.
x = 1, y = 2
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Question 9 (3.33 points)
Solve the system by the substitution method.
x2 + y2 = 113
x + y = 15
Question 9 options:
{( 8, 7), ( 7, 8)}
{( -8, 7), ( -7, 8)}
{( 8, -7), ( 7, -8)}
{( -8, -7), ( -7, -8)}
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Question 10 (3.33 points)
In a 1-mile race, the winner crosses the finish line 10 feet ahead of the
second-place runner and 23 feet ahead of the third-place runner. Assuming
that each runner maintains a constant speed throughout the race, by how
many feet does the second-place runner beat the third-place runner? (5280
feet in 1 mile.)
Question 10 options:
3 ft
-13 ft
13 ft
-10 ft
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Question 11 (3.33 points)
You throw a ball straight up from a rooftop. The ball misses the rooftop on its
way down and eventually strikes the ground. A mathematical model can be
used to describe the relationship for the ball’s height above the ground, y,
after x seconds. Consider the following data:
x, seconds y, ball’s
after ball is height, in
thrown
feet, above
the ground
1
114
2
146
4
114
Find the quadratic function y = ax2 +bx + c whose graph passes through the
given points.
Question 11 options:
y = -10×2 + 60x + 64
y = -16×2 + 80x + 50
y = -12×2 + 80x + 46
y = -16×2 + 100x + 30
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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: -150; at (0, 6)
Maximum: 105; at (5, 0)
Maximum: 0; at (0, 0)
Maximum: -98.75; at (1.25, 5)
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Question 13 (3.33 points)
Solve the system by the substitution method.
xy = 12
x2 + y2 = 40
Question 13 options:
{( 2, 6), ( -2, -6), ( 6, 2), ( -6, -2)}
{( 2, 6), ( -2, -6), ( 2, -6), ( -2, 6)}
{( -2, -6), ( -6, -2), ( -2, 6), ( -6, 2)}
{( 2, 6), ( 6, 2), ( 2, -6), ( 6, -2)}
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Question 14 (3.33 points)
Solve the system by the addition method.
x2 – 3y2 = 1
3×2 + 3y2 = 15
Question 14 options:
{( 1, 2), ( -1, 2), ( 1, -2), ( -1, -2)}
{( 2, 1), ( -2, 1), ( 2, -1), ( -2, -1)}
{( 2, 1), ( -2, -1)}
{( 1, 2), ( -1, -2)}
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Question 15 (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.
x + y = -8
x – y = 14
Question 15 options:
{(x, y) | x + y = -8}
{( 3, -11)}
∅
{( 3, 11)}
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Question 16 (3.33 points)
Find the inverse of the matrix, if possible.
A=
Question 16 options:
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Question 17 (3.33 points)
Find the products AB and BA to determine whether B is the multiplicative
inverse of A.
A=
,B=
Question 17 options:
B = A-1
B ≠ A-1
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Question 18 (3.33 points)
Evaluate the determinant.
Question 18 options:
60
-30
30
-60
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Question 19 (3.33 points)
Find the product AB, if possible.
A=
,B=
Question 19 options:
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Question 20 (3.33 points)
Let A =
and B =
Question 20 options:
. Find A – 3B.
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Question 21 (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 21 options:
Yes
No
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Question 22 (3.33 points)
Give the order of the matrix, and identify the given element of the matrix.
; a12
Question 22 options:
4 × 2; -11
2 × 4; -11
2 × 4; 14
4 × 2; 14
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Question 23 (3.33 points)
Find the products AB and BA to determine whether B is the multiplicative
inverse of A.
A=
,B=
Question 23 options:
B = A-1
B ≠ A-1
Save
Question 24 (3.33 points)
Solve the matrix equation for X.
Let A =
and B =
Question 24 options:
; 4X + A = B
X=
X=
X=
X=
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Question 25 (3.33 points)
Use Gaussian elimination to find the complete solution to the system of equations, or state
that none exists.
x+y+z=9
2x – 3y + 4z = 7
x – 4y + 3z = -2
Question 25 options:
{({(
{(
+
+
+
,
,
,
–
, z)}
+
, z)}
–
, z)}
{(-
+
,
+
, z)}
Save
Question 26 (3.33 points)
Use Cramer’s rule to determine if the system is inconsistent system or
contains dependent equations.
2x + 7 = 8
6x + 3y = 24
Question 26 options:
system is inconsistent
system contains dependent equations
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Question 27 (3.33 points)
Find the determinant of the matrix if it exists.
Question 27 options:
47
-7
-9
27
7
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Question 28 (3.33 points)
Evaluate the determinant.
Question 28 options:
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Question 29 (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 29 options:
{(
,-
, 0,
)}
{(-1, –
, 0,
)}
{(1, -2, 0, 3)}
{(
, -2, 0,
)}
Save
Question 30 (3.33 points)
Use Gaussian elimination to find the complete solution to the system of
equations, or state that none exists.
3x – 2y + 2z – w = 2
4x + y + z + 6w = 8
-3x + 2y – 2z + w = 5
5x + 3z – 2w = 1
Question 30 options:
{(
, 0, –
,
)}
∅
{(1, {(2, 0, –
,
, 6)}
,
)}
…
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