An employer provides two payment options for employees.

Option A: Receive $200 the first week. Receive an additional $50 for each of the following weeks.

Option B: Receive $200 the first week. Receive an additional 10% for each of the following weeks.

Complete the tables to show how much money would be received for both payment options, each week, for 6
weeks.
Option A: Week 1 2 3 4 5 6

Amount paid 200 250 300 350 400 450

Option B: 1 2 3 4 5 6

200 220 244 268.4 295.24 324.764

I know the answer to this part but I need help with the rest.

2. Referring to the tables in #1, suppose you are a new employee. You notice that each payment option describes a sequence and decide to use rules to help determine which option to take.

(a) Determine the rule (or formula) for each sequence. Show your work.

(b) Your friend trusts your tables in #1, but wonders if you wrote the rules correctly.
Show two calculations using week 6 to convince your friend that both your rules work.

3. Consider the formulas you wrote in Problem 2.

(a) Your friend says that because the rules are functions, they can be graphed and must have y-intercepts. Do you agree or disagree with your friend? Explain your thinking.

(b) Your friend uses your rules to determine the outputs when the inputs are 18.5.

Explain why she cannot use 18.5, and describe types for numbers that CAN be used for inputs?

4. Use your formulas from #2 to calculate how much each option makes during week 20. (Show your work)

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.