Add the top and bottom together, divide by 2, then multiply by the height:
Area = (7.5 + 2.5)/2 x 2.5
Area = 10/2 x 2.5
Area = 5 x 2.5
Area = 12.5 square units.
Triangle Perimeter: Add up the sides of the triangle.
26 + 24 + 10 = 60
The triangles perimeter is 60.
Triangle Area: height * base divided by 2
10 * 24 = 240
240/2 = 120
The triangles area is 120.
x=2 is only solution while x=1 is extraneous solution
Option C is correct.
Step-by-step explanation:
We need to solve the equation
and find values of x.
Solving:
Find the LCM of denominators x-1,x and x-1. The LCM is x(x-1)
Multiply the entire equation with x(x-1)
![\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}\\\frac{1}{x-1}*x(x-1)+\frac{2}{x}*x(x-1)=\frac{x}{x-1}*x(x-1)\\Cancelling\,\,out\,\,the\,\,same\,\,terms:\\x+2(x-1)=x^2\\x+2x-2=x^2\\3x-2=x^2\\x^2-3x+2=0](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx-1%7D%2B%5Cfrac%7B2%7D%7Bx%7D%3D%5Cfrac%7Bx%7D%7Bx-1%7D%5C%5C%5Cfrac%7B1%7D%7Bx-1%7D%2Ax%28x-1%29%2B%5Cfrac%7B2%7D%7Bx%7D%2Ax%28x-1%29%3D%5Cfrac%7Bx%7D%7Bx-1%7D%2Ax%28x-1%29%5C%5CCancelling%5C%2C%5C%2Cout%5C%2C%5C%2Cthe%5C%2C%5C%2Csame%5C%2C%5C%2Cterms%3A%5C%5Cx%2B2%28x-1%29%3Dx%5E2%5C%5Cx%2B2x-2%3Dx%5E2%5C%5C3x-2%3Dx%5E2%5C%5Cx%5E2-3x%2B2%3D0)
Now, factoring the term:
![x^2-2x-x+2=0\\x(x-2)-1(x-2)=0\\(x-1)(x-2)=0\\x-1=0\,\,and\,\, x-2=0\\x=1\,\,and\,\, x=2](https://tex.z-dn.net/?f=x%5E2-2x-x%2B2%3D0%5C%5Cx%28x-2%29-1%28x-2%29%3D0%5C%5C%28x-1%29%28x-2%29%3D0%5C%5Cx-1%3D0%5C%2C%5C%2Cand%5C%2C%5C%2C%20x-2%3D0%5C%5Cx%3D1%5C%2C%5C%2Cand%5C%2C%5C%2C%20x%3D2)
The values of x are x=1 and x=2
Checking for extraneous roots:
Extraneous roots: The root that is the solution of the equation but when we put it in the equation the answer turns out not to be right.
If we put x=1 in the equation,
the denominator becomes zero i.e
which is not correct as in fraction anything divided by zero is undefined. So, x=1 is an extraneous solution.
If we put x=2 in the equation,
![\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx-1%7D%2B%5Cfrac%7B2%7D%7Bx%7D%3D%5Cfrac%7Bx%7D%7Bx-1%7D)
![\frac{1}{2-1}+\frac{2}{2}=\frac{2}{2-1}\\\frac{1}{1}+1=\frac{2}{1}\\1+1=2\\2=2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2-1%7D%2B%5Cfrac%7B2%7D%7B2%7D%3D%5Cfrac%7B2%7D%7B2-1%7D%5C%5C%5Cfrac%7B1%7D%7B1%7D%2B1%3D%5Cfrac%7B2%7D%7B1%7D%5C%5C1%2B1%3D2%5C%5C2%3D2)
So, x=2 is only solution while x=1 is extraneous solution
Option C is correct.
Keywords: Solving Equations and checking extraneous solution
Learn more about Solving Equations and checking extraneous solution at:
#learnwithBrainly
The answer is 150 because you first find the area of the square which is 10x10=100 and then you find the area of the triangle which is 10x10=100 divide by 2 will give you 50 so 100+50=150 hope this helps :)
Answer:
35 1/12 gallons of gasoline
Step-by-step explanation:
so what you're going to do is take both of the fractions (3/4 and 1/3) and convert them into two fractions with the same denominator so you can add them easily. the closest number that you can convert them to would be a denominator of 12, so we would turn 3/4 into its equivalent of 9/12 and 1/3 would now be 4/12. now we add them and get 13/12, which is an improper fraction, so we would change that to 1 and 1/12. and finally, we add 1 1/12 + 1 + 33 and we would get 35 and 1/12 as our final answer :)