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ivolga24 [154]
3 years ago
7

Prove the following statement.

Mathematics
1 answer:
jolli1 [7]3 years ago
3 0
<h2>Step-by-step explanation:</h2>

As per the question,

Let a be any positive integer and b = 4.

According to Euclid division lemma , a = 4q + r

where 0 ≤ r < b.

Thus,

r = 0, 1, 2, 3

Since, a is an odd integer, and

The only valid value of r = 1 and 3

So a = 4q + 1 or 4q + 3

<u>Case 1 :-</u> When a = 4q + 1

On squaring both sides, we get

a² = (4q + 1)²

   = 16q² + 8q + 1

   = 8(2q² + q) + 1

   = 8m + 1 , where m = 2q² + q

<u>Case 2 :-</u> when a = 4q + 3

On squaring both sides, we get

a² = (4q + 3)²

   = 16q² + 24q + 9

   = 8 (2q² + 3q + 1) + 1

   = 8m +1, where m = 2q² + 3q +1

Now,

<u>We can see that at every odd values of r, square of a is in the form of 8m +1.</u>

Also we know, a = 4q +1 and 4q +3 are not divisible by 2 means these all numbers are odd numbers.

Hence , it is clear that square of an odd positive is in form of 8m +1

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Complete the equation describing how x and y are related.<br> Please need help!!!
yKpoI14uk [10]

Answer:

3

Step-by-step explanation:

The equation being used to express the answer is called slope-intercept form.

y = m x + b

m is the slope, b is the y-intercept (where x = 0)

The formula to find slope (m) using two points is called point slope form.

m = (y1 - y2)/(x1 - x2)

Pick two coordinates and plug them in.

m = (1 - 4)/(0 - 1)

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5 0
3 years ago
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Determine if the two lines are parallel, perpendicular, or neither.<br><br> x=5 x=−5
gregori [183]

Answer:

Parallel

Step-by-step explanation:

6 0
3 years ago
Please help it's urgent.
arlik [135]

Answer:

It is the second triangle.

Step-by-step explanation:

This is because the area of the square is given as 25^2 as the perpendicular, 144^2 as the base, and the hypotenuse is 169^2.

Length of the perpendicular = 5^2 (Because 25^2 / 5^2)

Length of the base = 12^2

Length of the hypotenuse = 13^2

So, the Pythagoras theorem is,

=> H^{2} = P^{2} + B^{2}

=> 13^{2} =12^{2} +5^{2}

This is true, because, 13*13 = 12*12 + 5*5

=> 169 = 144 + 25

=> 169 = 169

If my answer helped, kindly mark me as the brainliest!!

Thanks!!

3 0
3 years ago
Simplify.
kenny6666 [7]
The answer you are looking for is -5x^5-5x^4+6x^3-x^2-7x+20
-I hope this is the answer you are looking for, please feel free to post your future questions on Brainly.com.
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At 3:00 AM, the temperature was 44 degrees. By 7:00 AM, the temperature had risen to 60 degrees. What was the average change in
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