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goldfiish [28.3K]
3 years ago
15

Prove that (2n+1)^2 - (2n+1)^2 is a multiple of 8 for all positive integer values of n

Mathematics
1 answer:
kogti [31]3 years ago
4 0

Answer:

(2n + 1)[(2n + 1) � 1]

(2n + 1)(2n + 1 � 1)

(2n + 1)(2n), or 2n(2n + 1)

2n is an EVEN NUMBER, and adding 1 to an even number creates an ODD number

Therefore, 2n(2n+1)=EVEN NUMBER ODD NUMBER=EVEN NUMBER

Step-by-step explanation:

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True/False (4z + y) is the sum of two terms
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True. The answer is the product of 4 and a number plus another number. 
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Read 2 more answers
1.1(1.6x+0.4)-0.44= -17.6
sertanlavr [38]

Answer:

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

x

=

−

10.975

5 0
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An equation was used to predict the number of possible enrollments in an afterschool program for the first 6 months of the year.
AysviL [449]
55 + 80 + 95 + 100 +115 +90 =535 actual enrollments. 75 + 80 +85 +90 +95 + 100 = 525 predicted enrollments. 535 - 525 = 10 residuals.
6 0
3 years ago
What procedure will find the sum a+b of two numbers where a and b represent any integer?
ElenaW [278]

Answer:As rational number includes natural number, whole number ,integers  also.

⇒Natural number(1,2,3,4....) is a rational number also.

So, when A= Natural number , B=Any other natural number

Just add two natural number using simple law of addition.

⇒As Whole numbers(0,1,2,3,...) are Rational number also.

So If A=any whole number, B=Any other whole number

Add the whole number in any order using law of addition.

⇒Coming to integers (....-123,....-5,...-1,....12,....59,.....) By taking any two integers ,

1. Both of them are positive add using simple law of addition.

2. One of them is positive and other is negative , if larger one has positive sign before it just subtract smaller one from larger one and put positive sign before the result.and if larger one has negative sign before it ,subtract smaller one from larger one and put negative sign before the result.

⇒If both of them are negative , just add the two integers and apply negative sign before the result.

4. Rational number as fractions ,

A=m/n and B=p/q

A+B=m/n + p/q

find LCM of n and q.

If n and q are co-prime multiply n and q to get the LCM.For example if n=5, q=7, then LCM=5×7=35

If n and q are not co-prime find the factors of n and q .take out the common factors and then multiply the common factors with those factors which are not common.

For example, n=15, q=20

15=5×3

20=2×2×5

common factor=5

non common factor=2,2,3

LCM=5×2×2×3=60

Suppose LCM(n,q)= K

⇒p/q+m/n

=

So ,

which is the way to find LCM of rational number when theyare fractions.

Step-by-step explanation:

4 0
2 years ago
Find the GCF of the given list.<br>x^17 y^3, x^4 y^3, x^5 y^5 ​
trasher [3.6K]

Answer:

the greatest common factor is 1.

Step-by-step explanation:

The factors of 3 are: 1, 3

The factors of 3 are: 1, 3

The factors of 4 are: 1, 2, 4

The factors of 5 are: 1, 5

The factors of 5 are: 1, 5

The factors of 17 are: 1, 17

Then the greatest common factor is 1.

7 0
2 years ago
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