Answer:
y=1
x=4
hope this helps!
if you graph these equations, they will intersect at (4,1). They look very short because they are vertical and horizontal.
Step-by-step explanation:
Answer:
-keeping a detailed record of the procedure and results of a scientific experiment
-conducting an experiment to confirm the effects of gravity on earth
-solving an expression in steps using the order of operations
Step-by-step explanation:
just did on edgenuity
Answer:
Number 1 and Number 4
Step-by-step explanation:
By factoring, you can figure out the roots (x = -2 or x = 2)...
1. x^2 - 4 = 0
--> (x + 2)(x - 2) = 0
--> x = -2, x = 2
2. x^2 + 4 = 0
--> factors weirdly, so I won't write it. You'd have to use the quadratic formula.
3. 3x^2 + 12 = 0
--> 3 (x^2 + 4) = 0
--> factors weirdly (same as above)
4. 4x^2 - 16 = 0
--> 4 (x^2 - 4) = 0
--> 4 (x+2) (x-2) = 0
--> x = -2, x = 2
5. 2 (x-2) 2 = 0
--> x = 2
Answer:
step 3 has incorrect justification.
Step-by-step explanation:
because it was combine like terms but 8 is still in left hand side. So,combine like terms 3 has incorrect justification.
<u>Methods to solve rational equation:</u>
Rational equation:
A rational equation is an equation containing at least one rational expression.
Method 1:
The method for solving rational equations is to rewrite the rational expressions in terms of a common denominator. Then, since we know the numerators are equal, we can solve for the variable.
For example,
![\frac{1}{2}=\frac{x}{2}\Rightarrow x=1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7Bx%7D%7B2%7D%5CRightarrow%20x%3D1)
This can be used for rational equations with polynomials too.
For example,
![\frac{1+x}{x-3}=\frac{4}{x-3}\Rightarrow(1+x)=4 \Rightarrow x=3](https://tex.z-dn.net/?f=%5Cfrac%7B1%2Bx%7D%7Bx-3%7D%3D%5Cfrac%7B4%7D%7Bx-3%7D%5CRightarrow%281%2Bx%29%3D4%20%5CRightarrow%20x%3D3)
When the terms in a rational equation have unlike denominators, solving the equation will be as follows
![\frac{x+2}{8}=\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B2%7D%7B8%7D%3D%5Cfrac%7B3%7D%7B4%7D)
![\Rightarrow\frac{x+2}{1}=\frac{3\times8}{4}\Rightarrow{x+2}=2\times3](https://tex.z-dn.net/?f=%5CRightarrow%5Cfrac%7Bx%2B2%7D%7B1%7D%3D%5Cfrac%7B3%5Ctimes8%7D%7B4%7D%5CRightarrow%7Bx%2B2%7D%3D2%5Ctimes3)
![\Rightarrow{x+2}=6\Rightarrow x=6-2\Rightarrow x=4](https://tex.z-dn.net/?f=%5CRightarrow%7Bx%2B2%7D%3D6%5CRightarrow%20x%3D6-2%5CRightarrow%20x%3D4)
Method 2:
Another way of solving the above equation is by finding least common denominator (LCD)
![\frac{x+2}{8}=\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B2%7D%7B8%7D%3D%5Cfrac%7B3%7D%7B4%7D)
Factors of 4: ![1\times2\times2](https://tex.z-dn.net/?f=1%5Ctimes2%5Ctimes2)
Factors of 8: ![1\times2\times2\times2](https://tex.z-dn.net/?f=1%5Ctimes2%5Ctimes2%5Ctimes2)
The LCD of 4 and 8 is 8. So, we have to make the right hand side denominator as 8. This is done by the following step,
![\Rightarrow\frac{x+2}{8}=\frac{3}{4}\times{2}{2}](https://tex.z-dn.net/?f=%5CRightarrow%5Cfrac%7Bx%2B2%7D%7B8%7D%3D%5Cfrac%7B3%7D%7B4%7D%5Ctimes%7B2%7D%7B2%7D)
we get,
![\Rightarrow\frac{x+2}{8}=\frac{6}{8}](https://tex.z-dn.net/?f=%5CRightarrow%5Cfrac%7Bx%2B2%7D%7B8%7D%3D%5Cfrac%7B6%7D%7B8%7D)
On cancelling 8 on both sides we get,
![\Rightarrow(x+2)=6\rightarrow x=6-2\rightarrow x=4](https://tex.z-dn.net/?f=%5CRightarrow%28x%2B2%29%3D6%5Crightarrow%20x%3D6-2%5Crightarrow%20x%3D4)
Hence, these are the ways to solve a rational equation.