A number added to itself equals 5 less than the number

Mathematics

1 answer:

Nastasia [14]3 years ago

4 0

Answer:

The number is -5.

Step-by-step explanation:

x+x=x-5

2x=x-5

x-2x=5

-x=5

x=-5

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Sonbull [250]

Answer:

$x=\boxed{6.6}$

$\overline{\sf DE}=\boxed{13.2}\:\:\sf units$

Step-by-step explanation:

<u>Geometric Mean Theorem - Altitude Rule</u>

The <u>altitude</u> drawn from the vertex of the right angle perpendicular to the hypotenuse separates the <u>hypotenuse</u> into <u>two segments</u>. The ratio of one segment to the altitude is equal to the ratio of the altitude to the other segment:

$\sf \dfrac{segment\:1}{altitude}=\dfrac{altitude}{segment\:2}$

From inspection of the given diagram:

altitude = FD = 9
segment 1 = CD = 5
segment 2 = DE = $2x+3$

$\begin{aligned}\sf \dfrac{segment\:1}{altitude} & = \sf \dfrac{altitude}{segment\:2}\\\\\implies \dfrac{5}{9} & = \dfrac{9}{2x+3}\\\\5(2x+3) & = 81\\\\10x+15 & = 81\\\\10x & = 66\\\\ \implies x & = 6.6\end{aligned}$