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vlabodo [156]
3 years ago
7

Prove that for any natural n the value of the expression (n+7)^2–n^2 is divisible by 7.

Mathematics
1 answer:
Afina-wow [57]3 years ago
3 0

Step-by-step explanation:

(n + 7)² – n²

n² + 14n + 49 – n²

14n + 49

7 (2n + 7)

7 is a factor, so for any natural n, (n + 7)² – n² is a multiple of 7.

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Find the coordinates of the midpoint of AS if A(-4, 7) and S(5,3).
lesya692 [45]

Answer:

The answer is

<h2>( \frac{1}{2}  \: ,  \: 5)</h2>

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

<h3>M = (  \frac{x1 + x2}{2} , \:  \frac{y1 + y2}{2} )</h3>

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

A(-4, 7) and S(5,3)

The midpoint is

<h3>M  = ( \frac{ - 4 + 5}{2} , \:  \frac{7 + 3}{2} ) \\  = ( \frac{1}{2} , \:  \frac{10}{2} )</h3>

We have the final answer as

<h3>( \frac{1}{2}  \: ,  \: 5)</h3>

Hope this helps you

8 0
3 years ago
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5300 at 12% for 12 months
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Step-by-step explanation:

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3 0
3 years ago
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The ratio of two complementary angles is 4:1. Find the measure of both angles.
zmey [24]

Answer:

72 : 18

Step-by-step explanation:

The ratio of the two complementary angles is 4 : 1

4x + 1x = 90

5x = 90

x =18

4x = 4(18) = 72

x = 18

Therefore the ratio is 72 : 18

Answer: 72 : 18

 

8 0
3 years ago
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9. An airplane is 325 miles from the airport. To get to the present positionthe plane flew 205 miles due south from the airport
Xelga [282]
*Answer* : 66,525


*explanation* : 325 x 205=
8 0
2 years ago
Make w the subject of the formula y-aw=2w-1
Gnoma [55]

w = \frac{1 + y}{a + 2}

collect the term in w together → ( subtract 2w from both sides)

y - aw - 2w = - 1 → ( subtract y from both sides)

- aw - 2w = - 1 - y → ( multiply through by (- 1) )

aw + 2w = 1 + y → ( take out w as a common factor )

w( a + 2)= 1 + y → ( divide both sides by (a + 2 ) )

w = \frac{1 + y}{a + 2}




8 0
3 years ago
Read 2 more answers
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