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Mariana [72]
3 years ago
5

What is the greatest integer that always divides the difference of the squares of any two different positive odd integers?

Mathematics
1 answer:
Anastasy [175]3 years ago
4 0

Answer:

The greatest integer is 8.

Step-by-step explanation:

Odd positive integers are positively directed numbers that can not be divided into to equal values without a remainder. Examples are: 1, 3, 5, 7, 9 etc.

Given the following positive odd integers:

i. 9 and 3

9^{2} - 3^{2} = 81 - 9

         = 72

ii. 3 and 1,

3^{2} - 1^{2} = 9 - 1

         = 8

iii. 7 and 5

7^{2} - 5^{2} = 49 - 25

         = 24

iv. 21 and 13

21^{2} - 13^{2} = 441 - 169

             = 272

Therefore, it can be observed that the greatest integer that always divides the difference is 8.

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The dimensions of a square are altered so that 8 inches is added to one side while 3 inches is subtracted from the other. The ar
Alex_Xolod [135]

Answer

Find out the original side length of the square .

To prove

Let us assume that the original length of the square be x.

Formula

Area\ of\ rectangle = Length\times Breadth

As given

The dimensions of a square are altered so that 8 inches is added to one side while 3 inches is subtracted from the other.

Length becomes  = x + 8

Breadth becomes = x -3

The area of the resulting rectangle is 126 in²

Put in the formula

(x + 8) × (x - 3) = 126

x² -3x + 8x -24 = 126

x ²+ 5x = 126 +24

x² + 5x - 150 = 0

x² + 15x - 10x - 150 = 0

x (x + 15) -10 (x +15) =0

(x + 15)(x -10) =0

Thus

x = -15 , 10

As x = -15 (Neglected this value because the side of the square cannot be negative.)

Therefore x = 10 inches be the original side of the square.






3 0
3 years ago
Combine as indicated by the signs. 4/ y^2-9 + 5/y+3
natka813 [3]
\frac{4}{y^{2}-9 } + \frac{5}{y+3} = \frac{4}{(y-3)(y+3) } + \frac{5}{y+3}= \frac{4}{(y-3)(y+3) } + \frac{5(y-3)}{(y-3)(y+3)}=
\\ \\=\frac{4}{(y-3)(y+3) } + \frac{5y-15}{(y-3)(y+3)}= \frac{5y-11}{(y-3)(y+3)}=\frac{5y-11}{y^{2}-9}

8 0
3 years ago
Please help me with this
nydimaria [60]

Answer:

it 8

Step-by-step explanation:

4^3 is 64

2^3 is 8

64/8 is 8

7 0
3 years ago
The municipal swimming pool in Nicetown has three different ways of paying for individual open swimming. Todd is trying to decid
balandron [24]
Sllope intercept form is y=mx+b
m is the slope , b is the y itnercept

so early pay
cost=70 flat rate
x=infinity
the equation would be y=70

deposit pluss
you have to pay an initial one time payment of 15 so
y=mx+15
then 4 dollars per day
4 times number of days
y=4x+15

daily pay is 6 dollars per day so 6 times number of days
y=6x



1.
a. y=70
b. y=4x+15
c. y=4x
6 0
3 years ago
Which number rounds to 341 when rounded to the nearest whole number ​
nata0808 [166]

Answer:

341.5 because it makes the most sense

7 0
3 years ago
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