-converting to a common denominator
The terms -c of the left side was converted to -4ac/4a to have the same denominator of b^2/4a.
A constant of variation is only in the form ay=bx where b/a=constant so given any point y/x=constant let us check here by substituting x=1 and x=2
when x=1---> 2y=14,y=7 here y/x=7
when x=2--->2y=19,y=9.5 here y/x=4.75
so this equation is not constant of variation
let us check an equation of the form 3y=7x
when x=1--->y=7/3--->y/x=7/3
when x=2--->y=14/3---->y/x=7/3
so 3y=7x is a constant of variation
Answer:
6.4 m
Step-by-step explanation:
We have 2 expressions here. The first one is the fact that r = y. That's one of 2 equations. The second one involves whats' left after cutting off certain lengths of each color string. We cut 2.5 m from red, we cut 3.8 m from yellow. We know that what's left of red is 1.5 times the length of what's left of yellow. What's left of red is r - 2.5; what's left of yellow is y - 3.8. We know that r = 1.5y, so filling that in with our corresponding expressions gives us
r - 2.5 = 1.5(y - 3.8)
Distribute to get
r - 25 = 1.5y - 3.2
Now from the first expression, r = y, so fill in y for r to get an equation in one variable:
y - 2.5 = 1.5y - 3.2
Combine like terms:
-.5y = -3.2 and divide to get
y = 6.4
Check it to make sure it works. What's left of red should be 1.5 times the length of what's left of yellow and y = 6.4:
What's left of red: 6.4 - 2.5 = 3.9
What's left of yellow: 6.4 - 3.8 = 2.6
1.5 x 2.6 = 3.9, just like it should!
Answer:
1653
Step-by-step explanation:
Hope it helpped.
