Given that ae∥bd, identify the length of ac.

Explanation:

x = length of BC

AC = AB+BC

AC = 6 + x

CE = CD+DE

CE = 22+8

CE = 30

Triangles ACE and BCD are similar triangles (can be proven by the AA similarity theorem due to the fact that AE || BD)

Therefore the corresponding sides are proportional letting us set up the proportion below

AC/BC = CE/CD

(6+x)/x = 30/22 substitution

22(6+x) = 30x ... cross multiply

132+22x = 30x

132 = 30x-22x subtract 22x from both sides

132 = 8x

8x = 132

x = 132/8 divide both sides by 8

x = 16.5

Now use this to find the length of AC

AC = 6+x

AC = 6+16.5

AC = 22.5

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!

answer:   expression= p+p*d%

price reduction + sale price = $625

sale price: $p+$p*d%

where d% is the percentage of discount

step-by-step explanation:

original price = p

price went down by $150 price reduction $p*d%

sale price= $ 475

therefore the price before sale is: $625

and the expression that shows the price before sale is: p+p*d%