Yall pls answer my question :( (brainlies) im having a mental breakdown rn :( Lizzy is training for an upcoming triathlon. To prepare, she runs and cycles each week. During the first week of the month, she ran 3 days and cycled 5 days for a total of 129miles. Last week, she ran 4 days and cycled 3 days for a total of 95 miles. Write and solve a system of equations to determine the number of miles she runs each day and the number of miles she cycles each day. Assume that she runs the same number of miles each day and cycles the same number of miles each day. Show all your work.

1. Juan's marathon training schedule is an example of a geometric sequence

2. Lizzy's marathon training schedule is an example of an arithmetic sequence

3. Lizzy will be better prepared for the marathon

Step-by-step explanation:

In the arithmetic sequence there is a common difference between each two consecutive terms

In the geometric sequence there is a common ratio between each two consecutive terms

Juan's Schedule

∵ Juan's will run one mile on the first day of the week

∴  = 1

∵ He will double the amount he runs each day for the next

  6 days

- That means he multiplies each day by 2 to find how many miles

  he will run next day

∴   = 1 × 2 = 2 miles

∴   = 2 × 2 = 4 miles

∴   = 4 × 2 = 8 miles

∴   = 8 × 2 = 16 miles

∴   = 16 × 2 = 32 miles

∴   = 32 × 2 = 64 miles

That means there is a common ratio 2 between each two consecutive days

1. Juan's marathon training schedule is an example of a geometric sequence

Lizzy's Schedule

∵ Lizzy's will run 10 miles on the first day of the week

∴  = 10

∵ She will increase the amount she runs by 3 miles each day for

  the next six days

- That means she adds each day by 3 to find how many miles

   she will run next day

∴   = 10 + 3 = 13 miles

∴   = 13 + 3 = 16 miles

∴   = 16 + 3 = 19 miles

∴   = 19 + 3 = 22 miles

∴   = 22 + 3 = 25 miles

∴   = 25 × 3 = 28 miles

That means there is a common difference 3 between each two consecutive days

2. Lizzy's marathon training schedule is an example of an arithmetic sequence

The rule of the sum of nth term in the geometric sequence is

∵  = 1 , r = 2 and n = 7

∴  

∴   = 127

∴ Juan will run 127 miles in the final week

The rule of the sum of nth term in the arithmetic sequence is

∵ n = 7,   = 10  and   = 28

∴

∴  = 133

∴ Lizzy will run 133 miles in the final week

∵ 133 miles > 127 miles

∴ Lizzy will run more miles than Juan

3. Lizzy will be better prepared for the marathon

Step-by-step explanation:

dont have ah breakdown friend i luv u and crown??

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