Answer:
4
Step-by-step explanation:
Answer:
8.1 , 8.2, 8.3, 8.4 , 8.5, ............. etc.
To solve this problem, you have to know these two special factorizations:

Knowing these tells us that if we want to rationalize the numerator. we want to use the top equation to our advantage. Let:
![\sqrt[3]{x+h}=x\\ \sqrt[3]{x}=y](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7Bx%2Bh%7D%3Dx%5C%5C%20%5Csqrt%5B3%5D%7Bx%7D%3Dy%20)
That tells us that we have:

So, since we have one part of the special factorization, we need to multiply the top and the bottom by the other part, so:

So, we have:
![\frac{x+h-h}{h(\sqrt[3]{(x+h)^2}+\sqrt[3]{(x+h)(x)}+\sqrt[3]{x^2})}=\\ \frac{x}{\sqrt[3]{(x+h)^2}+\sqrt[3]{(x+h)(x)}+\sqrt[3]{x^2}}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%2Bh-h%7D%7Bh%28%5Csqrt%5B3%5D%7B%28x%2Bh%29%5E2%7D%2B%5Csqrt%5B3%5D%7B%28x%2Bh%29%28x%29%7D%2B%5Csqrt%5B3%5D%7Bx%5E2%7D%29%7D%3D%5C%5C%20%5Cfrac%7Bx%7D%7B%5Csqrt%5B3%5D%7B%28x%2Bh%29%5E2%7D%2B%5Csqrt%5B3%5D%7B%28x%2Bh%29%28x%29%7D%2B%5Csqrt%5B3%5D%7Bx%5E2%7D%7D%20)
That is our rational expression with a rationalized numerator.
Also, you could just mutiply by:
![\frac{1}{\sqrt[3]{x_h}-\sqrt[3]{x}} \text{ to get}\\ \frac{1}{h\sqrt[3]{x+h}-h\sqrt[3]{h}}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B%5Csqrt%5B3%5D%7Bx_h%7D-%5Csqrt%5B3%5D%7Bx%7D%7D%20%5Ctext%7B%20to%20get%7D%5C%5C%20%5Cfrac%7B1%7D%7Bh%5Csqrt%5B3%5D%7Bx%2Bh%7D-h%5Csqrt%5B3%5D%7Bh%7D%7D%20)
Either way, our expression is rationalized.
Answer:
(-1, -2) will be the solution.
Step-by-step explanation:
System of equations has been given as,
y = 3x + 1 ---------(1)
Input-output value table for the given line will be,
x -2 -1 0 1
y -5 -2 1 4
y = -x - 3 ----------(2)
Input-output value table for the given line will be,
x -2 -1 0 1
y -1 -2 -3 -4
By plotting the given coordinates we can draw the straight lines.
And the point of intersection (common point) of these lines will be the solution of the given system of equations.
Hence, (-1, -2) will be the solution.
Let's solve this question by breaking it up into fragments.
"8 more" means something plus 8.
"product 2 and a number x" means 2x.
Therefore, "8 more than the product of 2x" means 2x + 8. Hope this helps!