Answer:
Step-by-step explanation:
Hi there!
<u>What we need to know:</u>
- Linear equations are typically organized in slope-intercept form:
where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)
- Parallel lines will always have the same slope but different y-intercepts.
<u>1) Determine the slope of the parallel line</u>
Organize 3x = 2y into slope-intercept form. Why? So we can easily identify the slope, m.
Switch the sides
Divide both sides by 2 to isolate y
Now that this equation is in slope-intercept form, we can easily identify that 
is in the place of m. Therefore, because parallel lines have the same slope, the parallel line we're solving for now will also have the slope . Plug this into :
<u>2) Determine the y-intercept</u>
Plug in the given point, (4,0)
Subtract both sides by 6
Therefore, -6 is the y-intercept of the line. Plug this into as b:
I hope this helps!
When we multiply a whole number with a fraction, we can think of the whole numbers as "over one"...
5 3 5 15
3 * --- = --- * ---- = ----
6 1 6 6
We can further simplify the fraction, by dividing numerator and denominator by 3...
15 15 / 3 5
--- = ------- = ----
6 6 / 3 2
Since this is an improper fraction, we need to turn it into a mixed number...
5 2 + 2 + 1 2 2 1 1 1
---- = -------------- = --- + ---- + --- = 1 + 1 + ---- = 2 --- or 2.5
2 2 2 2 2 2 2
48 inches to 30 inches is a decrease.
percent decrease = change/original value x 100%
= (48 - 30)/48 x 100%
= 18/48 x 100%
= 37.5% decrease
Answer:
755 or more
Step-by-step explanation:
The profit is the difference between revenue and costs. We want the profit to be $2000 or more, and we have both fixed and variable costs.
Let x represent the number of puppets sold. Then the costs are ...
... 76.25 + 2.25x
The revenue is 5x.
The above-described relationship can then be written as
... 5x -(76.25 +2.25x) ≥ 2000
... 2.75x ≥ 2076.25 . . . . . add 76.25, collect terms
... x ≥ 2076.25/2.75 . . . . divide by the coefficient of x
... x ≥ 755
755 or more puppets must be sold to earn $2000 or more.
