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3 years ago

What is the simplified form of the expression 3 + 8x − 2y − x + 1 + 4y?

Mathematics

2 answers:

QveST [7]3 years ago

8 0

4+7x+2y
that is your answer

loris [4]3 years ago

8 0

You want to combine like terms so that means each term has to have the same variable and exponent. There are no exponents so now we look at the variable. So, +8x and -x have the same variable so add them together. 8x+ -x which is the same as subtracting since -x is negative.

8x-x= 7x 7x is positive

You still have 3 and - 2y +4y and +1. Now combine -2y and +4y

-2y + 4y = 2y

you still have 2 like terms, 3 and 1.

3+ 1 is 4

so its 4+2y+7x

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3 years ago

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A) The first 4 terms of the sequences are: $a_{1} =16$ , $a_{2} =24$ , $a_{3} =32$ and $a_{4} =40$ .

B) An explicit formula for this sequence can be written as: $a_{n} =8*(n+1)$

C) A recursive formula for this sequence can be written as:

$\left \{ {{a_{1} =16} \atop {a_{n} =a_{n-1}+8}} \right.$

Step-by-step explanation:

A) You can find the firs terms of this sequence simply selecting an odd integer and summing the consecutive 3 ones:

$a_{n} = Odd_{n}+Odd_{n+1}+Odd_{n+2}+Odd_{n+3}$ (a.1)

$a_{1}=1+3+5+7=16$

$a_{2}=3+5+7+9=24$

$a_{3}=5+7+9+11=32$

$a_{4}=7+9+11+13=40$

B) Observe the sequence of odd numbers 1, 3, 5, 7, 9, 11, 13(...).

You can express this sequence as:

$Odd_{n}=(2*n-1)$ (b.1)

If you merge the expression b.1 in a.1, you obtain the explicit formula of the sequence:

$a_{n} = Odd_{n}+Odd_{n+1}+Odd_{n+2}+Odd_{n+3}$ (a.1)

$a_{n} = (2*n-1)+((2*(n+1)-1))+((2*(n+2)-1))+((2*(n+3)-1))$ (b.2)

$a_{n} = 8*n+8$ (b.3)

$a_{n} =8*(n+1)$ (b.s)

C) The recursive formula has to be written considering an initial term and an N term linked with the previous term. You can see an addition of 8 between a term and the next one. So you can express each term as an addition of 8 with the previous one. Therefore, if the first term is 16:

$\left \{ {{a_{1} =16} \atop {a_{n} =a_{n-1}+8}} \right.$ (c.s)

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