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:
The length of the segment is 10.
Step-by-step explanation:
Think of the segment as the hypotenuse of a right triangle.
Draw the legs and label the lengths.
See the picture below.
The length of the hypotenuse is c.
c^2 = a^2 + b^2
c^2 = 6^2 + 8^2
c^2 = 36 + 64
c^2 = 100
c = 10
Answer: 10
Answer:
Down below.
Step-by-step explanation:
Use Pythagorean’s Theron
9 + 16 = c squared
25 = c squared
c = 5
Answer:
x -intercepts are x = -3 and x = 1
y-intercept at y = -3
The line of symmetry is x = -1
vertex is (h,k) = (-1,-4)
Step-by-step explanation:
Given a quadratic equations: h(x) = (x + 1)^2 - 4
The vertex for is :
h(x) = a(x - h)² + k
where,'h' is the axis of symmetry and (h,k) is the vertex.
So from the given equation we will rewrite the equation as:
h(x) = (x - (-1))^2 - 4
Hence,h = -1 and k = -4
The line of symmetry is x = -1 and vertex is (h,k) = (-1,-4)
Now, we have to find the x intercepts,
using the equation,
(x + 1)² = 4
Taking the square root on both sides,
√(x + 1)² = √4
x + 1 = ± 2
x = 1 or x = -3
So x -intercepts are x = -3 and x = 1
For y-intercept put x = 0 into the real equation:
h(x) = (0 +1)^2 - 4
y = 1 - 4
y = -3
So y-intercept at y = -3
Here with I have attached the graph.
Thank you.
Areas B and D have buckeyes and monarchs in the same proportion
