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3 years ago

What is the length of AC

Mathematics

2 answers:

IgorLugansk [536]3 years ago

8 0

Answer:

The correct answer is D. 126

Step-by-step explanation:

In order to solve this exercise, we need to know that two straight triangles that are sharing a vertex like in this picture are considered similar triangles. One property of the similar triangles is that exist a linear relationship between its sides. In this exercise, one triangle is ABC and the other CDE.

The relationship that we can write is between the length of its sides.

The relationship is a division between the length of the sides :

$\frac{AC}{AB}=\frac{CE}{DE}$ ⇒

$\frac{140-x}{81}=\frac{x}{9}$

Solving the equation

$x=\frac{(140-x)}{81}.(9)$

$x=\frac{(140-x)}{9}$

$9x=140-x$

$10x=140$

$x=14$ ⇒

If the side AC is $140-x$ the length is

$140-14=126$

The correct option is D. 126

Arte-miy333 [17]3 years ago

3 0

Answer:

126

Step-by-step explanation:

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3 years ago

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Roman55 [17]

Answer:

$(x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}$

$(x,y)=\left(\; \boxed{5,16} \; \right)\quad \textsf{(larger $x$-value)}$

Step-by-step explanation:

Given system of equations:

$\begin{cases}y=x^2-9\\y=4x-4\end{cases}$

To solve by the method of substitution, substitute the first equation into the second equation and rearrange so that the equation equals zero:

$\begin{aligned}x^2-9&=4x-4\\x^2-4x-9&=-4\\x^2-4x-5&=0\end{aligned}$