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andrew11 [14]
2 years ago
15

"Which of the following sequences of numbers are arithmetic sequences? Check all that apply.

Mathematics
2 answers:
defon2 years ago
5 0
B) 154, 171, 188, 205, 222
A constant value (17) is added to get the next number
klasskru [66]2 years ago
3 0

Answer:

Option B, C, D

Step-by-step explanation:

We have to find the arithmetic sequence from the sequences given in the question.

To solve this question we will use the property of an arithmetic sequence that every successive term of an arithmetic sequence has a common difference.

(A) 1, -2, 3, -4, 5 .....

d_{2}-d_{1} = -2 -1 = -3

d_{3}-d_{2} = 3 - (-2) = 3 + 2 = 5

Sequence is not an arithmetic sequence

(B)  154, 171, 188, 205, 222 .....

a_{2}-a_{1} = 171- 154 = 17

a_{3}-a_{2} = 188 - 171 = 17

The sequence is an arithmetic sequence having common difference = 17

(C) 12,345, 12,346, 12,347......

a_{2}-a_{1} = 12,346 - 12,345 = 1

a_{3}-a_{2} = 12,347 - 12,346 = 1

Therefore, the sequence is an arithmetic sequence

(D) -3, -10, -17, --24, -31

a_{2}-a_{1} = -10 + 3 = ( -7 )

a_{3}-a_{2} = -17 + 10 = ( -7 )

This sequence is an arithmetic sequence

(E) 1, 8, 16, 24, 32 ....

a_{2}-a_{1} = 8 - 1 = 7

a_{3}-a_{2} = 16 - 8 = 8

Difference in terms is not common. Therefore, sequence is not an arithmetic sequence.

Option B,C,D are arithmetic sequences.

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Help please!! i need this last one to finish!!!! 44 points!!
AleksandrR [38]

Answer:

The point is at about (4.5, 100).

Step-by-step explanation:

Minka's line is p = 22t, which has a y-intercept of 0.

Kenji's line is p = 50 + 11t, which has a y-intercept of 50.

Find the line with y-intercept at 0 and the line with y-intercept at 50. Follow the two lines until they intersect. The point of intersection is about (4.5, 100).

You can find this point by setting the two equations equal to each other:

22t = 50 + 11t

Subtract 11t from both sides.

11t = 50

t = 50/11 ≈ 4.545

Then you can find the p value for this point by plugging t = 4.545 into either equation.

p = 22(4.545) = 99.99

p = 50 + 11(4.545) = 99.995

On the graph the point is about (4.5, 100).

5 0
3 years ago
Combine like terms: 3p2q2-3p2q3+4p2q3-3p2q2+pq PLEASE HELP!!! ASAP!!!
ch4aika [34]

Answer:

p²q³ + pq and pq(pq² + 1)

Step-by-step explanation:

Given

3p²q² - 3p²q³ +4p²q³ -3p²q² + pq

Required

Collect like terms

We start by rewriting the expression

3p²q² - 3p²q³ +4p²q³ -3p²q² + pq

Collect like terms

3p²q² -3p²q² - 3p²q³ +4p²q³ + pq

Group like terms

(3p²q² -3p²q²) - (3p²q³ - 4p²q³ ) + pq

Perform arithmetic operations on like terms

(0) - (-p²q³) + pq

- (-p²q³) + pq

Open bracket

p²q³ + pq

The answer can be further simplified

Factorize p²q³ + pq

pq(pq² + 1)

Hence, 3p²q² - 3p²q³ +4p²q³ -3p²q² + pq is equivalent to p²q³ + pq and pq(pq² + 1)

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