Mathematics, 27.09.2019 15:00 krystalruby1219

Amelia is starting a new exercise routine. on the first day, she will do 8 sit-ups. on the second day, she will do 12 sit-ups. on the third day, she will do 16 sit-ups. on the fourth day, she will do 20 sit-ups. write an explicit formula for the sequence of the number of sit-ups amelia will do.

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Answer from: myla18jabbar

4 + 4d d =days so for every day she does 4 more

Answer from: Juicebox18

Day Number of Sit ups

1 8

2 12

3 16

4 20

Second Day- First Day =12 -8=4

Third day - Second day=16-12=4

Fourth Day - Third Day =20 -16=4

Since the Difference between two consecutive terms is same, So it is an Arithmetic Progression.

Through the help of Explicit formula,that is nth term of the sequence ,we can find any term of the sequence.Here

$a=8, d=4\\\\A_{n}=a+(n-1)d\\\\A_{n}=8+(n-1)4=8 +4 n-4\\\\A_{n}=4 n +4$

Explicit Formula for this sequence = 4 n +4, n=Number of days,that is natural number 1,2,3,4,5.......

Answer from: Quest

∠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.

Answer from: Quest

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

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Amelia is starting a new exercise routine. on the first day, she will do 8 sit-ups. on the second da...