SOPHIA MILESTONE
MATH 110
Final Mile Exam
Exam Elaborations Questions & Answers
,11/13/2020 Sophia :: Welcome
Score 24/25
You passed this Milestone
24 questions were answered correctly.
MILESTONE
1 question was answered incorrectly.
1
Find the solution for x if |5x – 2| = 13.
RATIONALE
To solve this equation, we will need to create two separate equations without absolute
value bars.
One equation will contain the expression exactly as it appears within the absolute value
bars. The second equation must consider the case when the expression has the opposite
value. Next, solve each equation separately, starting with 5x – 2 = 13.
To solve for x, start by adding 2 to both sides.
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,11/13/2020 Sophia :: Welcome
On the left, we have only 5x. On the right 13 plus 2 is 15. Then divide both sides by 5 to
isolate x.
The solution for the first equation is x = 3. The same process can be applied to the
second equation 5x – 2 = -13.
To solve, start by adding 2 to both sides.
On the left, we have only 5x. On the right -13 plus 2 is -11. Then divide both sides by
5 to isolate x.
The solution for second equation is .
The two solutions to |5x – 2| = 13 are x = 3 and .
CONCEPT
Absolute Value Equations
2
What is the following expression equivalent to?
81
-3
3
-81
RATIONALE
When evaluating higher-order roots, it helps to break down the number underneath
the radical into prime factors.
243 can be written as (3)(3)(3)(3)(3).
Notice that there are five factors of 3, and they are all underneath a fifth root. This
means the expression underneath the radical simplifies to 3.
Lastly, we apply the negative sign in front of the radical, so the original expression
can be simplified to -3.
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, 11/13/2020 Sophia :: Welcome
CONCEPT
Evaluating Radicals
3
In 2000, the median household income was $41,990. In 2010, it was $49,445. (Source: www.census.gov.)
What is the average rate of change in the median household income over this time period?
$745.50 per year
$7,455.00 per year
$1,341.00 per year
$3,727.50 per year
RATIONALE
The average rate of change can be
computed like slope. It is the change in
median household income divided by
the change in years. The median
household income changed from
in , to in
. Substitute these values into the
formula.
The change in median household
income is the difference between
and , or
. The change in
years is the difference between
and , or . Next,
evaluate the subtraction in the
numerator and denominator.
equals ;
equals . The average
https://strayer.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/6866326 3/36
MATH 110
Final Mile Exam
Exam Elaborations Questions & Answers
,11/13/2020 Sophia :: Welcome
Score 24/25
You passed this Milestone
24 questions were answered correctly.
MILESTONE
1 question was answered incorrectly.
1
Find the solution for x if |5x – 2| = 13.
RATIONALE
To solve this equation, we will need to create two separate equations without absolute
value bars.
One equation will contain the expression exactly as it appears within the absolute value
bars. The second equation must consider the case when the expression has the opposite
value. Next, solve each equation separately, starting with 5x – 2 = 13.
To solve for x, start by adding 2 to both sides.
https://strayer.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/6866326 1/36
,11/13/2020 Sophia :: Welcome
On the left, we have only 5x. On the right 13 plus 2 is 15. Then divide both sides by 5 to
isolate x.
The solution for the first equation is x = 3. The same process can be applied to the
second equation 5x – 2 = -13.
To solve, start by adding 2 to both sides.
On the left, we have only 5x. On the right -13 plus 2 is -11. Then divide both sides by
5 to isolate x.
The solution for second equation is .
The two solutions to |5x – 2| = 13 are x = 3 and .
CONCEPT
Absolute Value Equations
2
What is the following expression equivalent to?
81
-3
3
-81
RATIONALE
When evaluating higher-order roots, it helps to break down the number underneath
the radical into prime factors.
243 can be written as (3)(3)(3)(3)(3).
Notice that there are five factors of 3, and they are all underneath a fifth root. This
means the expression underneath the radical simplifies to 3.
Lastly, we apply the negative sign in front of the radical, so the original expression
can be simplified to -3.
https://strayer.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/6866326 2/36
, 11/13/2020 Sophia :: Welcome
CONCEPT
Evaluating Radicals
3
In 2000, the median household income was $41,990. In 2010, it was $49,445. (Source: www.census.gov.)
What is the average rate of change in the median household income over this time period?
$745.50 per year
$7,455.00 per year
$1,341.00 per year
$3,727.50 per year
RATIONALE
The average rate of change can be
computed like slope. It is the change in
median household income divided by
the change in years. The median
household income changed from
in , to in
. Substitute these values into the
formula.
The change in median household
income is the difference between
and , or
. The change in
years is the difference between
and , or . Next,
evaluate the subtraction in the
numerator and denominator.
equals ;
equals . The average
https://strayer.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/6866326 3/36
