"a student made the following chart to prove that ab2 + bc2 = ac2.
statement justification
1. triangle abc is similar to triangle bdc 1. angle abc = angle bdc and angle bca = angle bcd
2. bc2 = ac × dc 2. bc ÷ dc = ac ÷ bc because triangle abc is similar to triangle bdc
3. triangle abc is similar to triangle abd 3. angle abc = angle bad and angle bac = angle abd
4. ab2 = ac × ad 4. ab ÷ ad = ac ÷ ab because triangle abc is similar to triangle abd
5. ab2 + bc2 = ac × ad + ac × dc
= ac (ad + dc)
6. adding statement 1 and statement 2
7. ab2 + bc2 = ac2
which of the first four steps is the error? "

Solution:

Given : In triangle ABC right angled at B.

To Prove :

Construction: Draw B D perpendicular AC.

Proof: 1. Triangle ABC is similar to triangle BDC 1. Angle ABC = Angle BDC and Angle BCA = Angle BCD  

2. = AC × DC 2. BC ÷ DC = AC ÷ BC because triangle ABC is similar to triangle BDC  

3. Triangle ABC is similar to triangle ABD 3. Angle ABC = Angle BAD and Angle BAC = Angle ABD  

4.  = AC × AD 4. AB ÷ AD = AC ÷ AB because triangle ABC is similar to triangle ABD  

5.

= AC (AD + DC)  

6. Adding Statement 1 and Statement 2  

7.

→→→Statement 3 is incorrect.It should be replaced by, Angle ABC = Angle ADB and Angle B AC = Angle BAD .

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).