Answer:
0≤y≤5
Step-by-step explanation:
The range is the values of the output, or in this case the y values
The y values go from 0 to 5
0≤y≤5
Answer:
![\boxed{-3xy^{2}\sqrt [3] {2x^{2}}}](https://tex.z-dn.net/?f=%5Cboxed%7B-3xy%5E%7B2%7D%5Csqrt%20%5B3%5D%20%7B2x%5E%7B2%7D%7D%7D)
Step-by-step explanation:
Your expression is
![\sqrt [3] {-54x^{5}y^{6}}](https://tex.z-dn.net/?f=%5Csqrt%20%5B3%5D%20%7B-54x%5E%7B5%7Dy%5E%7B6%7D%7D)
Here's how I would simplify it.
![\begin{array}{rcll}\sqrt [3] {-54x^{5}y^{6}} & = & \sqrt [3] {(-1)^{3}\times 2 \times 27 \times x^{2} \times x^{3} \times y^{6}} & \text{Factored the cubes}\\& = & \sqrt [3] {(-1)^{3} \times 3^{3}\times x^{3} \times y^{6}\times 2 \times x^{2}} & \text{Grouped the cubes}\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcll%7D%5Csqrt%20%5B3%5D%20%7B-54x%5E%7B5%7Dy%5E%7B6%7D%7D%20%26%20%3D%20%26%20%5Csqrt%20%5B3%5D%20%7B%28-1%29%5E%7B3%7D%5Ctimes%202%20%5Ctimes%2027%20%5Ctimes%20x%5E%7B2%7D%20%5Ctimes%20x%5E%7B3%7D%20%5Ctimes%20y%5E%7B6%7D%7D%20%26%20%5Ctext%7BFactored%20the%20cubes%7D%5C%5C%26%20%3D%20%26%20%5Csqrt%20%5B3%5D%20%7B%28-1%29%5E%7B3%7D%20%5Ctimes%203%5E%7B3%7D%5Ctimes%20x%5E%7B3%7D%20%5Ctimes%20y%5E%7B6%7D%5Ctimes%202%20%5Ctimes%20x%5E%7B2%7D%7D%20%26%20%5Ctext%7BGrouped%20the%20cubes%7D%5C%5C%5Cend%7Barray%7D)
![\begin{array}{rcll}& = & \sqrt [3] {(-1)^{3} \times {3^{3}\times x^{3} \times y^{6}}} \times\sqrt [3] { 2 \times x^{2}} & \text{Separated the cubes}\\&=& \mathbf{-3xy^{2}\sqrt [3] {2x^{2}}} & \text{Took cube roots}\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcll%7D%26%20%3D%20%26%20%5Csqrt%20%5B3%5D%20%7B%28-1%29%5E%7B3%7D%20%5Ctimes%20%7B3%5E%7B3%7D%5Ctimes%20x%5E%7B3%7D%20%5Ctimes%20y%5E%7B6%7D%7D%7D%20%5Ctimes%5Csqrt%20%5B3%5D%20%7B%202%20%5Ctimes%20x%5E%7B2%7D%7D%20%26%20%5Ctext%7BSeparated%20the%20cubes%7D%5C%5C%26%3D%26%20%5Cmathbf%7B-3xy%5E%7B2%7D%5Csqrt%20%5B3%5D%20%7B2x%5E%7B2%7D%7D%7D%20%26%20%5Ctext%7BTook%20cube%20roots%7D%5C%5C%5Cend%7Barray%7D)
![\text{The simplified expression is $\boxed{\mathbf{-3xy^{2}\sqrt [3] {2x^{2}}}}$}](https://tex.z-dn.net/?f=%5Ctext%7BThe%20simplified%20expression%20is%20%24%5Cboxed%7B%5Cmathbf%7B-3xy%5E%7B2%7D%5Csqrt%20%5B3%5D%20%7B2x%5E%7B2%7D%7D%7D%7D%24%7D)
Answer:
c) The given expression represents Addition Property of Equality.
Step-by-step explanation:
Here, the given expression is j = k
Now by ADDITION PROPERTY OF EQUALITY:
The property that states that if you add the same number to both sides of an equation, the sides remain equal.
So, <u> if A = B ⇒ A + </u><u>x </u><u> = B + </u><u>x</u>
<u></u>
Now, here given that j = k
If we add the same number 9 on both the sides, the equation remains undisturbed.
⇒ j + 9 = k + 9
Hence, the above expression represents Addition Property of Equality.
1/3 and 2/5 --> what we need is a least common denominator
(1/3)x5 (2/5)x3
5/15 and 6/15
so he needs to paint his room two more times which will make the 5/15 become 15/15
you start with 5/15 and you need to add "5/15" two more times which will make 15/15
so you do that to 6/15
6/15+6/15+6/15=18/15=1 3/15 or 1 1/5 cans of paint ANSWER
Answer:
(1.0025ⁿ)² + 3.7124×(1.0025ⁿ) - 5.3124 = 0
Step-by-step explanation:
Nina will have saved the enough money to pay off the remaining balance on the loan when the functions are the same. So
f(x) = g(x)
86248 - 74248(1.0025)ⁿ = 20000(1.005)ⁿ - 20000
we sum 20000 on each side of the equation
106248 - 74248(1.0025)ⁿ = 20000(1.005)ⁿ
then we divide by 2000 each side of the equation
5.3124 - 3.7124(1.0025)ⁿ = 1.005ⁿ
the square root of 1.005 is aproximately 1.0025, so
1.005 ≈ 1.0025²
5.3124 - 3.7124(1.0025)ⁿ = (1.0025²)ⁿ
Since (1.0025²)ⁿ = 1.0025²ⁿ = (1.0025ⁿ)² we can write:
(1.0025ⁿ)² + 3.7124(1.0025ⁿ) - 5.3124 = 0
