Kayla wants to find the distance, ab, across a river. she walks along the edge of the river 100 ft and marks point c. then she walks 100 ft further and marks point d. she turns 90° and walks until her location, point a, and point c are collinear. she marks point e at this location, as shown. (a can kayla conclude that abc and edc are congruent? why or why not?
(b) suppose de=175 ft. what can kayla conclude? explain.

You are given Kayla's walking distance along the edge of the river 100 ft and marks point C, then she walks 100 ft further and marks point D and she turns 90° and walks until her location, point A, and point C are collinear. She marks point E at this location. ABC and EDC are congruent.

The triangles ABC and EDC are congruent by ASA rule.

Step-by-step explanation:

Given Kayla walks along the edge of the river 100 ft and marks point C. Then she walks 100 ft further and marks point D. She turns 90° and walks until her location, point A, and point C are collinear. She marks point E at this location. we have to find the distance AB.

In ΔABC and ΔEDC

∠EDC=∠ABC    (each 90)

CD=CB              (given)

∠DCE=∠BCA    (vertical angles)

By ASA rule, ΔABC≅ΔEDC

Now, given DE=175 ft

If two triangles are congruent then these are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent

By triangle proportionality,

⇒

⇒ AB=175 ft.

Length of DE is same as AB

Given that the value of a car that costs $17900 depreciates at 12.25% per year, the value of the car in 10 years time will be:
The depreciation follows exponential decay:
V(t)=Pe^(-rt) or P(1+r/100)^(-nt)
where:
principle,P=17900
rate,r=12.25=0.1225
time,t=10 years
therefore the value after 10 years will be:
V(10)=17900*e^(-0.1225×10)
=$5258.30