Answer:
Varies directly uses the formula: y/x = k
22/3 = 7.33
105/x = 7.33
105/x (7.33/x) = 7.33(x/7.33)
105/7.33 = x
x = 14.32
<span>We can safely assume that 1212 is a misprint and the number of seats in a row exceeds the number of rows by 12.
Let r = # of rows and s = # of seats in a row.
Then, the total # of seats is T = r x s = r x ( r + 12), since s is 12 more than the # of rows.
Then
r x (r + 12) = 1564
or
r**2 + 12*r - 1564 = 0, which is a quadratic equation.
The general solution of a quadratic equation is:
x = (-b +or- square-root( b**2 - 4ac))/2a
In our case, a = 1, b = +12 and c = -1564, so
x = (-12 +or- square-root( 12*12 - 4*1*(-1564) ) ) / 2*1
= (-12 +or- square-root( 144 + 6256 ) ) / 2
= (-12 +or- square-root( 6400 ) ) / 2
= (-12 +or- 80) / 2
= 34 or - 46
We ignore -46 since negative rows are not possible, and have:
rows = 34
and
seats per row = 34 + 12 = 46
as a check 34 x 46 = 1564 = total seats</span>
To find the equation of the line, we need to figure out the slope and y-intercept.
To find the y-intercept, look at the number where the line intersects the y-axis. The number is 5. The equation so far is y = ?x + 5.
We still didn't figure out the slope yet. To figure out the slope, pick two points. Use the rise over run method. It is in the image below. The line is going up to the left, so the slope will be negative. Now we know the slope is -1/3. The equation now that we figured out the slope is y = -1/3x + 5.
I hope this helps you! Let me know if I got something wrong.
Answer:
y = - 2(x - 1)² + 18
Step-by-step explanation:
- 2x² + 4x + 16 ← factor out - 2 from the first 2 terms
= - 2(x² - 2x) + 16
using the method of completing the square
add/subtract ( half the coefficient of the x- term)² to x² - 2x
= - 2(x² + 2(- 1)x + 1 - 1) + 16
= - 2(x - 1)² + 2 + 16
= - 2(x - 1)² + 18 ← in vertex form
Answer:
$1003.84615
Step-by-step explanation:
130.5 = x * 0.13
130.5/0.13 = x
x = 1003.84615
