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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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Solve for x. The triangles in each pair are similar. <br>​
KatRina [158]

Answer:

Step-by-step explanation:

You need to pay very close attention to the triangle similarity statement.  This says that triangle NML is similar to triangle NVU.  But if you look at the way that triangle NVU is oriented in its appearance, it's laying on its side.  We need to set it upright so that angle N is the vertex angle, angle V is the base angle on the left, and angle U is the base angle on the right.  When we do that we see that sides NV and NM are corresponding and exist in a ratio to one another; likewise with sides VU and ML.  Setting up the proportion:

\frac{NV}{NM}=\frac{VU}{ML}

Filling in:

\frac{12}{36} =\frac{9}{9x}

Cross multiply to get

324 = 108x

and x = 3

3 0
3 years ago
Please help me with this
satela [25.4K]
Area of the trapezoid:
\frac{12.8 + 4.2}{2} (4.9) = 41.65 cm^2

Area of the rectangle:
4.2 x 3.1 = 13.02 cm^2

Area of each quarter circle:
\frac{ \pi  (3.1)^{2} }{4} = 7.54 cm^2

We have two quarter circles:
7.54 + 7.54 = 15.08

41.65 + 13.02 + 15.08 = 69.75 cm^2
5 0
2 years ago
Solve 2.02W = -3.636
ValentinkaMS [17]

Answer: W=-1.8

Step-by-step explanation:

Divide both sides by 2.02 and you are left with W=-1.8.

Hope this helps!

7 0
3 years ago
Read 2 more answers
Write the unit fraction depicted in the model as a percent.<br><br> One-fourth
yan [13]

Answer:

As

1/4×100 = 0.25×100

            = 25%

Thus,

1/4 = 25%

Step-by-step explanation:

Given the fraction

1/4

  • In order to write the fraction 1/4 as a percent, all we need is to multiply 1/4 by 100.

i.e.

1/4×100 = 0.25×100

            = 25%

Therefore, we conclude that:

1/4 = 25%

4 0
2 years ago
I NEED HELP ASAP!!!!!!!!!!
svetoff [14.1K]

Answer:

I know the answer

Step-by-step explanation:

x = random number then y = x + y then x = 68 So we can conclude

5 0
2 years ago
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