Solve for x 2/x+2 + 1/5 = 6/x+5 x = 0 x = –13 x = 13 x = 0 and x = 13

1 answer:

5 0

$\dfrac{2}{x+2}+\dfrac{1}{5}=\dfrac{6}{x+5}\qquad\text{multiply both sides by 5}\\\\\dfrac{10}{x+2}+1=\dfrac{30}{x+5}\\\\\dfrac{10}{x+2}+\dfrac{x+2}{x+2}=\dfrac{30}{x+5}\\\\\dfrac{10+x+2}{x+2}=\dfrac{30}{x+5}\\\\\dfrac{x+12}{x+2}=\dfrac{30}{x+5}\qquad\text{cross multiply}\\\\(x+12)(x+5)=30(x+2)\qquad\text{use distributive property}\\\\(x)(x)+(x)(5)+(12)(x)+(12)(5)=(30)(x)+(30)(2)\\\\x^2+5x+12x+60=30x+60\qquad\text{subtract 60 from both sides}\\\\x^2+17x=30x\qquad\text{subtract 30x from both sides}$

$x^2-13x=0\\\\x(x-13)=0\iff x=0\ \vee\ x-13=0\qquad\text{add 13 to both sides}\\\\\boxed{x=0\ \vee\ x=13}$

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An advertising company is designing a new logo that consists of a shaded triangle inside a parallelogram.What is the area, in sq

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<h2>Explanation:</h2><h2 />

The complete question is shown in the figure below. As you can see one square units is well shown in the graph. So we can conclude that the distance between two consecutive points is 1 unit. If so, then we can calculate the area of the parallelogram as follows:

$A=b\times h \\ \\ A:Area \\ \\ b:Base \\ \\ h:Height \\ \\ \\ CB=b \\ \\ AB=h$