Answer:
it should be c or d
Step-by-step explanation:
Answer:
Standard Form
Step-by-step explanation:
Vertex form would be: (x-1)^2- 36
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:
![f(x)=\sqrt[3]{x} \\a=5](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%5B3%5D%7Bx%7D%20%5C%5Ca%3D5)
Step-by-step explanation:
Answer:
51 and -27
Step-by-step explanation:
The sum of two numbers is 24 and their difference is 78. What are the two numbers? Let's start by calling the two numbers we are looking for x and y.
The sum of x and y is 24. In other words, x plus y equals 24 and can be written as equation A:
x + y = 24
The difference between x and y is 78. In other words, x minus y equals 78 and can be written as equation B:
x - y = 78
Now solve equation B for x to get the revised equation B:
x - y = 78
x = 78 + y
Then substitute x in equation A from the revised equation B and then solve for y:
x + y = 24
78 + y + y = 24
78 + 2y = 24
2y = -54
y = -27
Now we know y is -27. Which means that we can substitute y for -27 in equation A and solve for x:
x + y = 24
x + -27 = 24
X = 51
Summary: The sum of two numbers is 24 and their difference is 78. What are the two numbers? Answer: 51 and -27 as proven here:
Sum: 51 + -27 = 24
Difference: 51 - -27 = 78
