70 POINTS FOR CORRECT ANSWER.
Use the following matrices to answer the questions below. Make sure you write in complete sentences, and use correct grammar and punctuation.

1. What does element LaTeX: B_{2,1}B 2 , 1 represent?

2. What does element LaTeX: A_{_{3,2}}A 3 , 2 represent?

3. How many vehicles did Sydney sell?

4. Who had the highest bonus? How do you know this? (Hint: Find AB).

1) It is a code for a formula.

2) Same thing as number 1

3) 17 total vehicles

4) Sydney had the highest bouns

Step-by-step explanation:

4)

Justin

Cars: 140 x 7 = 980

Trucks: 130 x 2 = 260

Vans: 180 x 6 = 1,080

Bonus:  980 + 260 + 1080 = 2320

Sydney

Cars: 140 x 5 = 700

Trucks: 130 x 8 = 1040

Vans: 180 x 4 = 720

Bonus: 700 + 1040 + 720 = 2460

Timothy

Cars: 140 x 10 = 1400

Trucks: 130 x 0 = 0

Vans: 180 x 2 = 360

Bonus: 1400 + 360 = 1760

Step-by-step explanation:

1. means element present at the intersection of second row and first column, which is $130.

2. means element present at the intersection of third row and second column, which is 0.

3.

Number of vehicles sold by Sydney = 5 + 8 + 4= 17

4.

Bonus of Justin

= 7*140 + 2*130 + 6*180

= 980 + 260 +1080

= $2320

Bonus of Sydney

= 5*140 + 8*130 + 4*180

= 700 + 1040 + 720

= $2460

Bonus of Timothy

= 10*140 + 0*130 + 2*180

= 1400 + 0 + 360

= $1760

Hence, Sydney had highest bonus.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.