SOPHIA| College Algebra - Final Milestone with Answers!!|
SPRING 2021
You passed this Milestone
23 questions were answered
correctly. 2 questions were
answered incorrectly. 1
Which of the following equations is correctly calculated?
•
-2 × -7 = -14
•
81 ÷ -9 = -9
•
-36 ÷ 4 = 9
•
4 × 12 = -48
RATIONALE
This is correct. The quotient of a positive and
negative number is always negative.
This is incorrect. The product of two negative
numbers is always positive. The correct product
is 14.
, This is incorrect. The quotient of a positive and a
negative number is always negative. The correct
quotient is -9.
This is incorrect. The product of two positive
numbers is always positive. The correct product
is 48.
CONCEPT
Multiplying and Dividing Positive and Negative Numbers
2
Select the solution to the following system of equations:
•
•
correct
•
•
RATIONALE
,Before you can add equations, sometimes
you must multiply entire equations by a
scalar value for the method to work as
intended. For this system, we can multiply
the second equation by .
Here, by multiplying by , the
result contains a term, which will cancel
when combined with the second equation.
Now, we can add the two equations
together.
When we add the two equations, the term
will cancel, leaving . Now we can solve for
by dividing both sides by .
Once we divide both sides by , we get a
solution of . We can solve for by
plugging in for in either
equation.
Let's use the second equation .
Once is plugged in for ,
evaluate and solve for .
Subtracting a negative is the same as
adding a postive . Next, subtract
from both sides.
On the right side, minus equals .
Now we can solve for by dividing both
sides by .
Dividing by gives a solution of .
, This is the solution to the system of
equations.
CONCEPT
Solving a System of Linear Equations using the Addition Method
3
Perform the following operations and write the result as
a single number.
[4 + 8 × (5 – 3)] ÷ 5 + 6
•
10 correct
•
10.8
•
2
•
1.8
RATIONALE
Following the Order of Operations, we must
first evaluate everything in parentheses and
grouping symbols. When there are brackets or
braces, evaluate the innermost operations first.
Here, we must evaluate 5 minus 3 first.
5 minus 3 is 2. There are still operations inside
grouping symbols to evaluate. Multiplication
comes before addition, so we must evaluate 8
times 2 next.
SPRING 2021
You passed this Milestone
23 questions were answered
correctly. 2 questions were
answered incorrectly. 1
Which of the following equations is correctly calculated?
•
-2 × -7 = -14
•
81 ÷ -9 = -9
•
-36 ÷ 4 = 9
•
4 × 12 = -48
RATIONALE
This is correct. The quotient of a positive and
negative number is always negative.
This is incorrect. The product of two negative
numbers is always positive. The correct product
is 14.
, This is incorrect. The quotient of a positive and a
negative number is always negative. The correct
quotient is -9.
This is incorrect. The product of two positive
numbers is always positive. The correct product
is 48.
CONCEPT
Multiplying and Dividing Positive and Negative Numbers
2
Select the solution to the following system of equations:
•
•
correct
•
•
RATIONALE
,Before you can add equations, sometimes
you must multiply entire equations by a
scalar value for the method to work as
intended. For this system, we can multiply
the second equation by .
Here, by multiplying by , the
result contains a term, which will cancel
when combined with the second equation.
Now, we can add the two equations
together.
When we add the two equations, the term
will cancel, leaving . Now we can solve for
by dividing both sides by .
Once we divide both sides by , we get a
solution of . We can solve for by
plugging in for in either
equation.
Let's use the second equation .
Once is plugged in for ,
evaluate and solve for .
Subtracting a negative is the same as
adding a postive . Next, subtract
from both sides.
On the right side, minus equals .
Now we can solve for by dividing both
sides by .
Dividing by gives a solution of .
, This is the solution to the system of
equations.
CONCEPT
Solving a System of Linear Equations using the Addition Method
3
Perform the following operations and write the result as
a single number.
[4 + 8 × (5 – 3)] ÷ 5 + 6
•
10 correct
•
10.8
•
2
•
1.8
RATIONALE
Following the Order of Operations, we must
first evaluate everything in parentheses and
grouping symbols. When there are brackets or
braces, evaluate the innermost operations first.
Here, we must evaluate 5 minus 3 first.
5 minus 3 is 2. There are still operations inside
grouping symbols to evaluate. Multiplication
comes before addition, so we must evaluate 8
times 2 next.
