Answer:
This is a direct variation where the constant of variation is 5/9
Step-by-step explanation:
The equation for direct variation is y = kx
5x-9y =0
Lets try to get this equation in the above form
Add 9y to each side
5x-9y +9y = 9y
5x = 9y
Divide each side by 9
5/9 x = 9y/9
5/9x = y
This is in the form y = k x where k =5/9
Answer:
First piece = 6 inches
Second piece = 12 inches
Third piece = 18 inches
Step-by-step explanation:
Length of the first piece = x
Length of the second piece = 2x
Length of the third piece = 3x
Total length is 36 inches:
x + 2x + 3x = 36
6x = 36
x = 6
Therefore, the lengths are:
First piece = 6 inches
Second piece = 12 inches
Third piece = 18 inches
Answer: She will need 36 yards of material.
Step-by-step explanation:
16 × 2¹/₄ can be done different ways,
First multiply ¹/₄ times 16. that is the same as dividing 16/4 = 4
Then multiply 2 times 16 2×16 = 32
Add 32 + 4 = 36
Another way is to change 2¹/₄ to an improper fraction and multiply
⁹/₄ × 16
16
<u> ×9</u>
54
<u> +9 </u>
144
144/4 = 36
<u />
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:

Step-by-step explanation:
The standard form for the equation of a circle is
where r is the radius, and the center is (h, k).
(h, k) = (-1, 2), r = 7
