Jolene is creating a model of a pyramid. The model created will need to be scaled up from the blueprint. triangle ACB, point D is on segment AC between points A and C, point E is on segment BC between points B and C If segments DE and AB are parallel, which of the following expressions will help Jolene determine the length of segment AC? AC equals CB times CD all over CE AC = AB AC equals CB times AC all over CE AC = BC

AC equals CB times CD all over CE (option A)

Step-by-step explanation:

To determine length of segment AC, we would draw the diagram obtained from the given information.

Find attached the diagram.

The diagram gives two similar triangles: ∆ACB and ∆DCE

Using similar triangles theorem, ratio of corresponding sides are equal.

There are two ways to get AC using the theorem

1st: AC/AB = DC/DE

AC = AB × (DC/DE)

2nd: AC/CB = DC/CE

AC = CB × DC/CE

Let's compare with the options to find out which one was used.

a) AC equals CB times CD all over CE b) AC = AB

c) AC equals CB times AC all over CE d) AC = BC

The correct option from the workings  we derived is AC equals CB times CD all over CE (option A)

It is same as: AC = CB × DC/CE

CD = DC

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11