Ken and Tami are making necklaces. Ken makes 25 necklaces. Tami makes m more necklaces then Ken. Which expression represents the

a(t) = 210 - 5t

(1) What does t represent?

Since t is given in minutes, it stands for time.

Interpreting t as the balloon’s altitude is incorrect since a(t) represents altitude.

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Time elapsed since the balloon starts descending

This is the correct interpretation.

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Time for the balloon to reach ground level is incorrect because that would be a fixed moment, not a variable t.

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(2) What does a(t) represent?

The balloon’s altitude

This is the correct answer.

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Time since descent began is incorrect because that is represented by t.

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Time to reach the ground is inaccurate since a(t) is altitude, not time.

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(3) What does a(5.5) signify?

It does not represent the time to reach 5.5 feet altitude.

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The altitude of the balloon after 5.5 minutes

This is the correct interpretation since a(5.5) is altitude when t = 5.5 minutes.

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It is not the time needed to reach the ground.

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5.5 minutes alone is not correct because a(t) denotes altitude, not time.

a(5.5) refers to altitude at t = 5.5 minutes.

Answer:

a) Which rental company charges a lower daily rate?

Payless rental company.

b) How many days must you rent a car for the total costs to equal?​

3 days.

Step-by-step breakdown:

We are comparing two rental services:

Discount Car Rentals and Payless Car Rentals.

x = rental duration in days

y = total cost.

a) Assuming the rental period starts at 2 days:

We need to formulate the equation for Discount Rentals.

For Discount Car Rentals:

2 days = $185

4 days = $265

6 days = $345

8 days = $425

The cost differential for 2 days = $265 - $185 = $80

Therefore, for 1 day the cost difference is = $80/2

= $40

For a one-day rental,

185 - 40 = $145

Thus, the equation for the payment of Discount Rentals is:

y = 40x + 105

b) For Payless Car Rentals:

The provided equation is: y = 55x + 60.

y = total cost, x = rental days

a) For 1 day:

y = 55(1) + 60

y = $115

b) For 2 days:

y = 55(2) + 60

y = 110 + 60

y = $170

c) For 3 days:

y = 55(3) + 60

= 165 + 60

= $225

d) For 4 days:

y = 55x + 60.

y = 55 × 4 + 60

y = 220 + 60

y = $280

e) For 5 days:

y = 55x + 60.

y = 55 × 5 + 60

y = 275 + 60

y = $335

f) For 6 days:

y = 55x + 60.

y = 55 × 6 + 60

y = 330 + 60

y = $380

g) For 7 days:

y = 55x + 60.

y = 55 × 7 + 60

y = 385 + 60

y = $445

h) For 8 days:

y = 55x + 60.

y = 55 × 8 + 60

y = 440 + 60

y = $500

a) Which rental company charges a lower daily rate?

The total expense of renting a vehicle as calculated above:

For 1 day from Discount Car Rentals = $145

For 1 day from Payless Car Rentals = $115

Based on these calculations, Payless rental company offers the lower rate.

b) For how many days is the rental required to have costs equal?

We set both equations equal to each other:

y = 40x + 105 = y = 55x + 60.

40x + 105 = 55x + 60

105 - 60 = 55x - 40x

45 = 15x

x = 45/15

x = 3 days.

Hence, after 3 days, the total cost of renting a vehicle from either Discount or Payless Car Rentals will be equal.

Answer: 1.2 < 1.7x

Step-by-step explanation: