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3 years ago

Prove that the difference between squares of consecutive even numbers is always a multiple of 4

Mathematics

2 answers:

jasenka [17]3 years ago

5 0

Answer:

Answer: Proved: the difference between squares of consecutive even numbers is always a multiple of 4. ... From the results above, we can see that 12, 20, and 28 are multiples of 4. Therefore, the difference between squares of consecutive even numbers is always a multiple of 4.

Step-by-step explanation:

svp [43]3 years ago

4 0

Answer:

Step-by-step explanation:

Let's call the numbers n and n + 2.

(n + 2)² - n²

= n² + 4n + 4 - n²

= 4n - 4

= 4(n - 1)

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What are the first nine multiples of 5, and 3?

andrezito [222]

First 9 multiples of 5:

$\begin{gathered} 5\cdot1=5 \\ 5\cdot2=10 \\ 5\cdot3=15 \\ 5\cdot4=20 \\ 5\cdot5=25 \\ 5\cdot6=30 \\ 5\cdot7=35 \\ 5\cdot8=40 \\ 5\cdot9=45 \end{gathered}$

First 9 multiples of 3:

$\begin{gathered} 3\cdot1=3 \\ 3\cdot2=6 \\ 3\cdot3=9 \\ 3\cdot4=12 \\ 3\cdot5=15 \\ 3\cdot6=18 \\ 3\cdot7=21 \\ 3\cdot8=24 \\ 3\cdot9=27 \end{gathered}$

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1 year ago

The perimeter of a rectangular construction site is 124 meters. The width is eight meters more than 5 times the length. Find the

tresset_1 [31]

Answer:

The perimeter of a rectangle is the sum of both lengths and both widths, which is equal to 54 meters. Let's call Length L and Width W.

The question is saying this: L = 3 meters + 3(W). We have 2 variables, which means we need at least 2 equations to solve. So far we have one, our second equation is from the perimeter.

2 lengths + 2 Widths = 54. Now, it's just a plug and chug.

2(3 + 3W) + 2W = 54.

6 + 6W + 2W = 54

8W = 48

W=6

L = 3 + 3(6) = 21

To double check: 2(21) + 2(6) = 42 + 12 = 54

The Width is 6 meters, and the Length is 21 meters.

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3 years ago

Which new angle is created by extending one side of a triangle

8090 [49]

Answer: The correct option is (C). an exterior angle.

Step-by-step explanation: We are to select the name of the new angle that is created by extending one side of a triangle.

Let ABC be a triangle as shown in the attached figure.

∠ABC, ∠ACB and ∠BAC are three interior angles of the triangle ABC.

Let us extend the side BC towards C to point D. The newly created angle is ∠ACD.

∠ACD is called the exterior angle of ΔABC.

Therefore, the newly created angle is an exterior angle.

Thus, option (C) is correct.

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3 years ago

Read 2 more answers

The Arno family is planning a 14 day April vacation. The location they've chosen has an average of 10 rainy days every April. Th

True [87]

Yes because only 1/3 of the days are rainy days, which is about 4.67 days of rain.

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3 years ago

A woman is standing at the edge of a slow-moving river which is one mile wide, and she wishes to return to her campground on the

vesna_86 [32]

Answer:

the best option would be to swim

Step-by-step explanation:

Hello! To solve this problem we must follow the following steps.

1. remember the concept of uniform motion with constant speed, which establishes the following equation

$t=\frac{X}{V}$

where

t=time

x=distance

V=speed

2. Calculate the time it takes to swim and calculate the time it takes to walk

walking:

x=10mile

v=5milles/h

$t=\frac{10}{5} =2h$

swimming

x=1mile

v=3milles/h

$t=\frac{1}{3} =0.3h$

3. Compare both results and choose the one with the least time.

as you can see it takes less time swimming, so this would be the best way

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3 years ago