Remember
xyz=(x)(y)(z)
if x and y and z are all perfect cubes, xyz is also a perfect cube
remmeber
(x^n)^m=x^(mn)
so if it is perfect cube it can be factored into
(x^n)^3, such taht n is a whole number
basiclaly, see if the expoent is divisble by 3
all of them should be perfect cubes
215x^18y^3z^21
split them up to see which ones need changing
215=5*43, not a perfect cube
could be changed to 6^3, which is 216
x^18=(x^6)^3
y^3=y^3
z^21=(z^7)^3
the 215 needs to be changed
Question:
The quantities x and y are proportional.
x 15 25
y 5 8⅓
Find the constant of proportionality.
Answer:
r = ⅓
Step-by-step explanation:
To find the constant of proportionality, we make use of the following formula
y = rx
Where y is the given data in the y row
r is the constant of proportionality
x is the given data in the x row.
Using the first values of x and y.
When x = 15, y = 5.
So,
y = rx becomes
5 = r * 15
5 = 15r
Divide through by 15
5/15 = 15r/15
⅓ = r
r = ⅓
Taking the second values of x and y
when x = 25, y = 8⅓
So,
y = rx becomes
8⅓ = r * 25
8⅓ = 25r
Convert mixed fraction to improper fraction
25/3 = 25r
Divide through by 25
25/3 ÷ 25 = 25r/25
25/3 * 1/25 = r
25/75 = r
⅓ = r
r = ⅓
Notice that r = ⅓ is the same for both values of x and y.
Hence, the constant of proportionality is ⅓
Y = x² + 2x – 45
y = -3x + 5
-3x + 5 = x² + 2x – 45
x² + 5x – 50 = 0
x has two values 5 and -10
x = 5 => y = -10
x = -10 => y = 35
Good luck.
1.25 is the slope 5/4 rise over run
The correct answer is 3207.
