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natulia [17]
3 years ago
14

Prove that the product of any two consecutive natural numbers is even.

Mathematics
1 answer:
Vitek1552 [10]3 years ago
6 0

Answer with Step-by-step explanation:

Let us assume the 2 consecutive natural numbers are 'n' and 'n+1'

Thus the product of the 2 numbers is given by

Product=n(n+1)\\\\

We know that the sum of 'n' consecutive natural numbers starting from 1 is

S_n=\frac{n(n+1)}{2}\\\\\therefore n(n+1)=2\times S_n............(i)

Thus from equation 'i' we can write

Product=2\times S_n

As we know that any number multiplied by 2 is even thus we conclude that the product of 2 consecutive numbers is even.

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garri49 [273]

The scale factor that Thea uses to go from Rectangle Q to Rectangle R is equal to 6.

<h3>What is the scale factor from rectangle Q to rectangle R?</h3>

In geometry, the scale factor is a ratio of the resulting length to the initial length. Since the area of the square is equal to the square of its side length, then the scale factor is equal to:

k² = A' / A

k = √(A' / A)

Where:

  • k - Scale factor
  • A' - Area of the rectangle R.
  • A - Area of the rectangle Q.

If we know that A = 2 and A' = 72, then the scale factor is:

k = √(72 / 2)

k = √36

k = 6

Then, the scale factor that Thea uses to go from Rectangle Q to Rectangle R is equal to 6.

To learn more on scale factors: brainly.com/question/22312172

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7 0
1 year ago
In the image, the distance from the swings to the slide is 35
Nikitich [7]
The Pythagorean theorem is a^2+b^2=c^2 where a and b are legs and c is the hypotenuse(longest side). you haven’t put a picture so I don’t know where 35 is a leg or the hypotenuse, but all you have to do is square the 2 shorter sides and add them and set it equal to the square of the longer side. You can do it!
5 0
3 years ago
The legs of a right triangle are 12 cm and 16 cm. What is the length of the hypotenuse? 15 cm 17 cm 20 cm 28 cm
GalinKa [24]
Answer: 20 cm

To solve this, use the Pythagorean Theorem, a² + b² = c², where a and b are the legs of the right triangle, and c is the hypotenuse of the right triangle.
**The Pythagorean Theorem only works for right triangles.**

Substitute in the values.
a² +  b² = c²
12² + 16² = c²

Solve for c, the hypotenuse.
12² + 16² = c²               
144 + 256 = c²
400 = c²
c = √400
c = 20

7 0
3 years ago
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Use the equation v = StartFraction 10 Over p EndFraction to determine the pressure when the volume is 10 liters. A. 10 c. 100 b.
Galina-37 [17]

The value of the pressure is 1 when the value of volume is 10 liters, the correct option is D.

<h3>What is the pressure?</h3>

Pressure is defined as the physical force exerted on an object.

The force applied is perpendicular to the surface of objects per unit area.

Given

The equation is

\rm V=\dfrac{10}{p}

Where the v is the volume and p is the pressure.

The value of p when the value of volume v is 10 liters is;

\rm V=\dfrac{10}{p}\\\\\rm 10=\dfrac{10}{p}\\\\P = \dfrac{10}{10}\\\\P=1

Hence, the value of the pressure is 1.

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2 years ago
The data set shows the number of stamps that each of 10 stamp collectors brought to a show.
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Only 71 is an outlier. 
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