7/9/23, 2:11 Week 9 Quiz -
PM Knewton
Week 9 Quiz
Attempts
Attempt 1: 95% (19/20 points), Jul 09 at 2:09pm PDT
Questions to show:
All (20)
QUESTION 1 · 1/1 POINTS
Solve the following equation.
4x5 = 144x3
List all the solutions, separated by commas. Do not type "x =" in
your answer.
That is correct!
https://nightingale.instructure.com/courses/3430680/assignments/ 1/40
35291329
,7/9/23, 2:11 Week 9 Quiz -
PM Knewton
0, − 6, 6
Answer Explanation
Correct answers:
−6,0,6
If we move everything to the left side of the equation, we find
4x5 − 144x3 = 0
Now, there is a common factor of 4x3 , which we can factor out:
4x3 (x2 − 36) = 0
x = 0 or x2 = 36, which implies
From this, we can see that either
x = −6, 6. So the solutions are −6, 0, 6.
Content attribution
QUESTION 2 · 1/1 POINTS
Find the domain of the following function.
f(x) = √4x − 28
Give your answer in interval notation.
https://nightingale.instructure.com/courses/3430680/assignments/ 2/40
35291329
,7/9/23, 2:11 Week 9 Quiz -
PM Knewton
That is correct!
[ 7,∞)
Answer Explanation
Correct answers:
[7,∞)
Remember that the radicand under a square root sign must be
greater than or equal to 0. Therefore,
4x − 28 ≥ 0
4x ≥ 28
x≥7
For interval notation, a bracket, [ ] , indicates that the endpoint is
included and a parenthesis, ( ) , indicates that the endpoint is
excluded. Therefore, in interval notation, the domain is [7, ∞) .
Content attribution
https://nightingale.instructure.com/courses/3430680/assignments/ 3/40
35291329
, 7/9/23, 2:11 Week 9 Quiz -
PM Knewton
QUESTION 3 · 1/1 POINTS
Use the square roots property to solve the quadratic equation
(a − 78) 2 + 60 = 80. If there are multiple answers, list them
separated by a comma, e.g. 1, 2. If there is no solution, enter ∅.
That is correct!
a = 2√ 5 + 78, − 2√ 5 + 78
Answer Explanation
Correct answers:
a = √ 20 + 78, − √ 20 + 78
Isolate the quadratic term and use the square root property to find
(a − 78) 2 + 60 = 80
(a − 78) 2 = 20
a − 78 = ±√20 .
Solving for a we find
a − 78 = ±√20
a = 78 ± √20 .
https://nightingale.instructure.com/courses/3430680/assignments/ 4/40
35291329
PM Knewton
Week 9 Quiz
Attempts
Attempt 1: 95% (19/20 points), Jul 09 at 2:09pm PDT
Questions to show:
All (20)
QUESTION 1 · 1/1 POINTS
Solve the following equation.
4x5 = 144x3
List all the solutions, separated by commas. Do not type "x =" in
your answer.
That is correct!
https://nightingale.instructure.com/courses/3430680/assignments/ 1/40
35291329
,7/9/23, 2:11 Week 9 Quiz -
PM Knewton
0, − 6, 6
Answer Explanation
Correct answers:
−6,0,6
If we move everything to the left side of the equation, we find
4x5 − 144x3 = 0
Now, there is a common factor of 4x3 , which we can factor out:
4x3 (x2 − 36) = 0
x = 0 or x2 = 36, which implies
From this, we can see that either
x = −6, 6. So the solutions are −6, 0, 6.
Content attribution
QUESTION 2 · 1/1 POINTS
Find the domain of the following function.
f(x) = √4x − 28
Give your answer in interval notation.
https://nightingale.instructure.com/courses/3430680/assignments/ 2/40
35291329
,7/9/23, 2:11 Week 9 Quiz -
PM Knewton
That is correct!
[ 7,∞)
Answer Explanation
Correct answers:
[7,∞)
Remember that the radicand under a square root sign must be
greater than or equal to 0. Therefore,
4x − 28 ≥ 0
4x ≥ 28
x≥7
For interval notation, a bracket, [ ] , indicates that the endpoint is
included and a parenthesis, ( ) , indicates that the endpoint is
excluded. Therefore, in interval notation, the domain is [7, ∞) .
Content attribution
https://nightingale.instructure.com/courses/3430680/assignments/ 3/40
35291329
, 7/9/23, 2:11 Week 9 Quiz -
PM Knewton
QUESTION 3 · 1/1 POINTS
Use the square roots property to solve the quadratic equation
(a − 78) 2 + 60 = 80. If there are multiple answers, list them
separated by a comma, e.g. 1, 2. If there is no solution, enter ∅.
That is correct!
a = 2√ 5 + 78, − 2√ 5 + 78
Answer Explanation
Correct answers:
a = √ 20 + 78, − √ 20 + 78
Isolate the quadratic term and use the square root property to find
(a − 78) 2 + 60 = 80
(a − 78) 2 = 20
a − 78 = ±√20 .
Solving for a we find
a − 78 = ±√20
a = 78 ± √20 .
https://nightingale.instructure.com/courses/3430680/assignments/ 4/40
35291329
