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vekshin1
3 years ago
6

Identify the situation that involves opposite quantities adding up to zero Climbing up 6 feet and climbing down 4 feet Hiking 10

feet due north, then hiking 10 feet due south Ascending 2 feet and descending 3 feet Earning $5 and spending $3​
Mathematics
1 answer:
ivolga24 [154]3 years ago
3 0

9514 1404 393

Answer:

  (b)  Hiking 10 feet due north, then hiking 10 feet due south

Step-by-step explanation:

Any pair of numbers that totals zero will be a pair of opposites. The offered choices are ...

  +6 -4 = 2 . . . not zero

  +10 -10 = 0

  +2 -3 = -1 . . . not zero

  +5 -3 = 2 . . . not zero

Hiking 10 feet due north, then hiking 10 feet due south is a situation involving opposite numbers adding up to zero.

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1)

n         1          2         3           4         5         6

f(n)    1033    932     831      730     629     528

First term (a₁):  <u>1033 </u>          Common difference (d): <u>-101 </u>

Explicit rule:  a_{n} = 1134 - 101n    Recursive rule: a_{n} = a_{n-1} - 101

a_{n} = a_{1} + d(n - 1)

a_{n} = 1033 - 101(n - 1)

a_{n} = 1033 - 101n + 101

a_{n} = 1134 - 101n

***********************************************************************************

2)

n         1          2         3           4         5         6

f(n)   -39      -29       -19        -9          9        19

First term (a₁):  <u> -39  </u>          Common difference (d): <u> +10  </u>

Explicit rule:  a_{n} = -49 + 10n    Recursive rule: a_{n} = a_{n-1} + 10

a_{n} = a_{1} + d(n - 1)

a_{n} = -39 + 10(n - 1)

a_{n} = -39 + 10n - 10

a_{n} = -49 + 10n

***********************************************************************************

3)

n         1          2         3           4         5         6

f(n)   3.75      2.5     1.25        0      -1.25     -2.5

First term (a₁):  <u> 3.75  </u>          Common difference (d): <u> -1.25  </u>

Explicit rule:  a_{n} = 5 - 1.25n    Recursive rule: a_{n} = a_{n-1} - 1.25

a_{n} = a_{1} + d(n - 1)

a_{n} = 3.75 - 1.25(n - 1)

a_{n} = 3.75 - 1.25n + 1.25

a_{n} = 5 - 1.25n


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