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WARRIOR [948]
2 years ago
15

It’s all there in the picture will give brainlest to correct answer

Mathematics
1 answer:
SVEN [57.7K]2 years ago
3 0

Answer:

1. 10

2. 1 and 18

3. 17

4. 8

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Three consecutive odd integers are such that the sum of the first and second is 31 less than 3 times the third. Find the integer
Otrada [13]

1st:x

2nd x+2

3rd: x+4

(x)+(x+2) = 3(x+4)-31

distribute

2x+2 = 3x+12-31

2x+2 =3x-19

subtract 2x from each side

2 = x-19

add 19 to each side

21 =x

Answer: 21,23,25

3 0
3 years ago
Write the trinomial as a square of a binomial or as an expression opposite to a square
timurjin [86]
(3a-7)^2

1. 9a^2-21a-21a+49
2. 3a(3a-7)-7(3a-7)
3. (3a-7)(3a-7)
4. Combine like terms
3 0
2 years ago
The Miller family likes to paddle along the North River.
miss Akunina [59]

Answer:

4.7 miles per day.

If number two is meaning to add 4.7(.5)= 2.3(3) plus the original 14 miles over a three day travel from number one. Then the total distance for the six day trip would be 14+ 2.3(3)= 20.9

If it is meaning a total of 6 days traveling at half the speed

4.7÷2= 2.3 2.3 × 6= 13.8 miles

3 0
2 years ago
Write in expanded form 5,002,190
makvit [3.9K]
5,000,000+2,000+100+90
5 0
3 years ago
Read 2 more answers
What is a quick and easy way to remember explicit and recursive formulas?
Oliga [24]
I always found derivation to be helpful in remembering. Since this question is tagged as at the middle school level, I assume you've only learned about arithmetic and geometric sequences.

First, remember what these names mean. An arithmetic sequence is a sequence in which consecutive terms are increased by a fixed amount; in other words, it is an additive sequence. If a_n is the nth term in the sequence, then the next term a_{n+1} is a fixed constant (the common difference d) added to the previous term. As a recursive formula, that's

a_{n+1}=a_n+d

This is the part that's probably easier for you to remember. The explicit formula is easily derived from this definition. Since a_{n+1}=a_n+d, this means that a_n=a_{n-1}+d, so you plug this into the recursive formula and end up with 

a_{n+1}=(a_{n-1}+d)+d=a_{n-1}+2d

You can continue in this pattern, since every term in the sequence follows this rule:

a_{n+1}=a_{n-1}+2d
a_{n+1}=(a_{n-2}+d)+2d
a_{n+1}=a_{n-2}+3d
a_{n+1}=(a_{n-3}+d)+3d
a_{n+1}=a_{n-3}+4d

and so on. You start to notice a pattern: the subscript of the earlier term in the sequence (on the right side) and the coefficient of the common difference always add up to n+1. You have, for example, (n-2)+3=n+1 in the third equation above.

Continuing this pattern, you can write the formula in terms of a known number in the sequence, typically the first one a_1. In order for the pattern mentioned above to hold, you would end up with

a_{n+1}=a_1+nd

or, shifting the index by one so that the formula gives the nth term explicitly,

a_n=a_1+(n-1)d

Now, geometric sequences behave similarly, but instead of changing additively, the terms of the sequence are scaled or changed multiplicatively. In other words, there is some fixed common ratio r between terms that scales the next term in the sequence relative to the previous one. As a recursive formula,

a_{n+1}=ra_n

Well, since a_n is just the term after a_{n-1} scaled by r, you can write

a_{n+1}=r(ra_{n-1})=r^2a_{n-1}

Doing this again and again, you'll see a similar pattern emerge:

a_{n+1}=r^2a_{n-1}
a_{n+1}=r^2(ra_{n-2})
a_{n+1}=r^3a_{n-2}
a_{n+1}=r^3(ra_{n-3})
a_{n+1}=r^4a_{n-3}

and so on. Notice that the subscript and the exponent of the common ratio both add up to n+1. For instance, in the third equation, 3+(n-2)=n+1. Extrapolating from this, you can write the explicit rule in terms of the first number in the sequence:

a_{n+1}=r^na_1

or, to give the formula for a_n explicitly,

a_n=r^{n-1}a_1
6 0
3 years ago
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