MILESTONE
SCORE
24/25
24/25 that's 96% RETAKE
24 questions were answered correctly.
1 question was answered incorrectly.
1
Find the solution to the following equation.
RATIONALE
To solve this equation, first re-write the term on the
right side so that both terms have a common base.
Since 8 is a power of 2, we can re-write 8 as .
The two terms now have the same base, 2. Use the
, properties of exponents to simplify by
MILESTONE
multiplying the exponents 3 and 1 – x.
SCORE
3 times 1 – x is equal to 3 – 3x. Because the bases 24/25
are the same, we can focus on the exponents and
set them equal to each other.
Since the exponents are equivalent, we can simply
solve for x. Add 3x to both sides to undo the -3x on
the right.
We know have the x term isolated on the left side.
Next, divide both sides by 6 to solve for x.
Once we divide 3 by 6, we have isolated x on the left
side. However, we can still simplify this fraction.
is equivalent to . The solution for is .
CONCEPT
Solving an Exponential Equation
2
Select the correct slope and y-intercept for the following linear
equation:
y = -3x + 8
slope = 8
y-intercept = (-3,0)
slope = -3
y-intercept = (8,0)
slope = -3
y-intercept = (0,8)
, MILESTONE
slope = 8 SCORE
y-intercept = (0,-3) 24/25
RATIONALE
Equations in the form y = mx + b allow us to
easily identify the slope and y-intercept. The
slope is given by the variable m, and the y-
intercept is given by the variable b.
The variable m is the coefficient in front of x
that represents the slope. In the equation y =
-3x + 8, the coefficient in front of x is -3, so -3 is
the slope.
The variable b represents the y-coordinate of
the y-intercept. In the equation y = -3x + 8, 8
will be the y-coordinate of the y-intercept.
Remember that the x-coordinate of the y-
intercept is always 0, so the y-intercept is (0,8).
CONCEPT
Forms of Linear Equations
3
Ashley mixes two types of soft drinks with different types of
concentration: one soft drink has 20% sugar and the other drink
has 45% sugar.
Each can has 250 milliliters of soda.
What is the sugar concentration of the mixed soft drink?
62.5%
38%
, MILESTONE
32.5%
SCORE
24/25
25%
RATIONALE
To find the concentration of the mixed
soft drink, set up an equation using
weighted averages. In the numerator,
we will multiply the concentration and
quantity of each soft drink and then add
them together. In the denominator, we
will add the quantities of each soft
drink.
The quantity of the first soft drink is
250 milliliters with a concentration of
20% sugar. Substitute 0.20 for C₁ and
250 for Q₁. The quantity of the second
soft drink is 250 milliliters with a
concentration of 45% sugar. Substitute
0.45 for C₂ and 250 for Q₂.
Once the values are substituted into
the formula, evaluate the denominator.
In this case, the denominator simplifies
to 500. Next, multiply 0.20 and 250.
When multiplying the concentration and
quantities of the first soft drink, we get
0.20 times 250, which is equal to 50.
Next, multiply 0.45 and 250.
When multiplying the concentration and
quantities of the first soft drink, we get
0.45 times 250, which is equal to 112.5.
Then, add these two values in the
numerator together.
50 plus 112.5 is equal to 162.5. Finally,
divide by 500.
162 5 divided by 500 is equal to
SCORE
24/25
24/25 that's 96% RETAKE
24 questions were answered correctly.
1 question was answered incorrectly.
1
Find the solution to the following equation.
RATIONALE
To solve this equation, first re-write the term on the
right side so that both terms have a common base.
Since 8 is a power of 2, we can re-write 8 as .
The two terms now have the same base, 2. Use the
, properties of exponents to simplify by
MILESTONE
multiplying the exponents 3 and 1 – x.
SCORE
3 times 1 – x is equal to 3 – 3x. Because the bases 24/25
are the same, we can focus on the exponents and
set them equal to each other.
Since the exponents are equivalent, we can simply
solve for x. Add 3x to both sides to undo the -3x on
the right.
We know have the x term isolated on the left side.
Next, divide both sides by 6 to solve for x.
Once we divide 3 by 6, we have isolated x on the left
side. However, we can still simplify this fraction.
is equivalent to . The solution for is .
CONCEPT
Solving an Exponential Equation
2
Select the correct slope and y-intercept for the following linear
equation:
y = -3x + 8
slope = 8
y-intercept = (-3,0)
slope = -3
y-intercept = (8,0)
slope = -3
y-intercept = (0,8)
, MILESTONE
slope = 8 SCORE
y-intercept = (0,-3) 24/25
RATIONALE
Equations in the form y = mx + b allow us to
easily identify the slope and y-intercept. The
slope is given by the variable m, and the y-
intercept is given by the variable b.
The variable m is the coefficient in front of x
that represents the slope. In the equation y =
-3x + 8, the coefficient in front of x is -3, so -3 is
the slope.
The variable b represents the y-coordinate of
the y-intercept. In the equation y = -3x + 8, 8
will be the y-coordinate of the y-intercept.
Remember that the x-coordinate of the y-
intercept is always 0, so the y-intercept is (0,8).
CONCEPT
Forms of Linear Equations
3
Ashley mixes two types of soft drinks with different types of
concentration: one soft drink has 20% sugar and the other drink
has 45% sugar.
Each can has 250 milliliters of soda.
What is the sugar concentration of the mixed soft drink?
62.5%
38%
, MILESTONE
32.5%
SCORE
24/25
25%
RATIONALE
To find the concentration of the mixed
soft drink, set up an equation using
weighted averages. In the numerator,
we will multiply the concentration and
quantity of each soft drink and then add
them together. In the denominator, we
will add the quantities of each soft
drink.
The quantity of the first soft drink is
250 milliliters with a concentration of
20% sugar. Substitute 0.20 for C₁ and
250 for Q₁. The quantity of the second
soft drink is 250 milliliters with a
concentration of 45% sugar. Substitute
0.45 for C₂ and 250 for Q₂.
Once the values are substituted into
the formula, evaluate the denominator.
In this case, the denominator simplifies
to 500. Next, multiply 0.20 and 250.
When multiplying the concentration and
quantities of the first soft drink, we get
0.20 times 250, which is equal to 50.
Next, multiply 0.45 and 250.
When multiplying the concentration and
quantities of the first soft drink, we get
0.45 times 250, which is equal to 112.5.
Then, add these two values in the
numerator together.
50 plus 112.5 is equal to 162.5. Finally,
divide by 500.
162 5 divided by 500 is equal to
