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3 years ago

N is a positive intiger. Explain why 2n+1 must be an odd number.

Mathematics

1 answer:

pogonyaev3 years ago

6 0

Answer:

Because the number would be multiplied by an even number, which is 2. If the number (odd or even) is multiplied by two, then the result would be an <em>even number</em>.

Proof:

2(1) = 2

2(6) = 12

2(7) = 14

2(3) = 6

The number would then be added by an odd number, which is 1. If an even number is added with an odd number, then the result would be an odd number.

Proof:

2 + 1 = 3

12 + 1 = 13

14 + 1 = 15

6 + 1 = 7

You might be interested in

Which of the following is a rational number? I give 20 pts!

LenKa [72]

Answer:

It's b. 100

Step-by-step explanation:

10 x 10= 100 = rational number, other include a series of numbers that cannot be written down.

Sorry if this is wrong hope I did the math right. :)

4 0

3 years ago

Help it’s slope idk how to do it

Over [174]

a. $\boxed{y-602=\frac{2}{3}(x-3)}$

b. For every month the pine tree grows about 0.67 inches.

c. <em> </em>It represents the height of the tree at the moment Ariel started to record the heights.

<h2>Explanation:</h2>

In this exercise we have that in July Ariel recorded the height of a pine tree and how quickly it was expected to grow in next several months. From the Table, we can get the following points:

$P_{1}(3,602) \\ \\ P_{2}(6,604) \\ \\ P_{3}(q,606) \\ \\ P_{4}(12,608)$

It is obvious that this problem follows a linear equation, so our goal is to find the equation that matches the Table.

The point slope form of the equation of a line is:

$y-y_{1}=m(x-x_{1}) \\ \\ Where: \\ \\ m:Slope \\ \\ (x_{1}, y_{1}):A \ point \ on \ the \ line$

Finding (m):

$Using: \\ \\ P_{1}(x_{1},y_{1}) \rightarrow P_{1}(3,602) \\ \\ P_{2}(x_{2}, y_{2}) \rightarrow P_{2}(6,604) \\ \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{604-602}{6-3} \\ \\ m=\frac{2}{3}$

Finally, the equation of the line is:

$(x_{1}, y_{1}) \rightarrow (3,602) \\ \\ \boxed{y-602=\frac{2}{3}(x-3)}$

In this case, we have that:

The x-axis represents the <em>Number of Months </em>the pine tree was expected to grow.
The y-axis represents the <em>Height of the Tree </em>in inches.

Since the slope o a line is:

$Slope=\frac{Change \ in \ y}{Change \ in \ x}=\frac{2}{3}$

Then, this means that<em> every three months the pine tree grows two inches, </em><em>or </em><em>for every month the pine tree grows about 0.67 inches.</em>

The y-intercept can be found setting $x=0$ . So, from our equation: