Answer:
The equivalent expression for the given expression ![\sqrt[3]{256x^{10}y^{7} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B256x%5E%7B10%7Dy%5E%7B7%7D%20%7D)
is
![4x^{3} y^{2}(\sqrt[3]{4xy} )](https://tex.z-dn.net/?f=4x%5E%7B3%7D%20y%5E%7B2%7D%28%5Csqrt%5B3%5D%7B4xy%7D%20%29)
Step-by-step explanation:
Given:
Solution:
We will see first what is Cube rooting.
![\sqrt[3]{x^{3}} = x](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E%7B3%7D%7D%20%3D%20x)
Law of Indices
Now, applying above property we get
![\sqrt[3]{256x^{10}y^{7} }=\sqrt[3]{(4^{3}\times 4\times (x^{3})^{3}\times x\times (y^{2})^{3}\times y )} \\\\\textrm{Cube Rooting we get}\\\sqrt[3]{256x^{10}y^{7} }= 4\times x^{3}\times y^{2}(\sqrt[3]{4xy}) \\\\\sqrt[3]{256x^{10}y^{7} }= 4x^{3}y^{2}(\sqrt[3]{4xy})](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B256x%5E%7B10%7Dy%5E%7B7%7D%20%7D%3D%5Csqrt%5B3%5D%7B%284%5E%7B3%7D%5Ctimes%204%5Ctimes%20%28x%5E%7B3%7D%29%5E%7B3%7D%5Ctimes%20x%5Ctimes%20%28y%5E%7B2%7D%29%5E%7B3%7D%5Ctimes%20y%20%20%20%29%7D%20%5C%5C%5C%5C%5Ctextrm%7BCube%20Rooting%20we%20get%7D%5C%5C%5Csqrt%5B3%5D%7B256x%5E%7B10%7Dy%5E%7B7%7D%20%7D%3D%204%5Ctimes%20x%5E%7B3%7D%5Ctimes%20y%5E%7B2%7D%28%5Csqrt%5B3%5D%7B4xy%7D%29%20%5C%5C%5C%5C%5Csqrt%5B3%5D%7B256x%5E%7B10%7Dy%5E%7B7%7D%20%7D%3D%204x%5E%7B3%7Dy%5E%7B2%7D%28%5Csqrt%5B3%5D%7B4xy%7D%29)
∴ The equivalent expression for the given expression is
M(slope) = Δy/Δx = 8-(-6)/-4-(-3) = 14/-1 = -14
Answer:
I think your functions are 
,
and 
If yes then then the third function which is .
Step-by-step explanation:
The function 
where c is a constant has
Domain : 
Range : ( 0 , ∞ )
The above range is irrespective of the value of c.
I have attached the graph of each of the function, you can look at it for visualization.
- <em> ⇒ </em>This function is same as so its range is <em>( 0 , ∞ )</em>.
- <em> ⇒ </em>If we double each value of the function
, which has range ( 0 , ∞ ), but still the value of extremes won't change as 0*2=0 and ∞*2=∞. Therefore the range remains as <em>( 0 , ∞ )</em>.
- <em></em> ⇒ If we add 2 to each value of the function , which has range ( 0 , ∞ ), the lower limit will change as 0+2=2 but the upper limit will be same as ∞. Therefore the range will become as <em>( 2 , ∞ )</em>.
Ex 2) -27 + 28w
Ex 4) -13m + 21
Ex 6) 9(3x + y)
Ex 8) -6(3a + 5)
Ex 10) c - 17= 3
Ex 12) n= -27
Ex 14) v= 5
Ex 16)
equation: 24= 1/4x
Answer: x= 96% decimal form .96
Ex 18)
a) 7w+ 6 = 9w+2
b)
You sold 62 magazine subscriptions and your friend sold 74. Therefore your friend sold 12 more subscriptions than you after 8 weeks.
Ex 20)
Equation: 1/3a = 5
Answer: 15 years old
