All categories

2 years ago

Prove: An odd number squared is an odd number. = (2n + 1)2

Mathematics

1 answer:

Mnenie [13.5K]2 years ago

4 0

Answer:

${(2n + 1)}^{2} = 4 {n}^{2} + 4n + 1 = 2(2 {n}^{2} + 2n) + 1$

You might be interested in

Find the perimeter of the quadrilateral.

levacccp [35]

<em><u>Question:</u></em>

Find the perimeter of the quadrilateral. if x = 2 the perimeter is ___ inched.

The complete figure of this question is attached below

<em><u>Answer:</u></em>

<h3>The perimeter of the quadrilateral is 129 inches</h3>

<em><u>Solution:</u></em>

The complete figure of this question is attached below

Given that, a quadrilateral with,

Side lengths are:

$4x^2 + 8x\ inches \\\\3x^2-5x+20\ inches \\\\7x + 30\ inches \\\\31\ inches$

The values of the side lengths when x = 2 are

$(4x^2+8x)=(4\times 2^2+8\times 2)=(4\times 4+16)=16+16=32\ inch\\\\(3x^2-5x+20)=(3\times 2^2-5\times 2+20)=(3\times 4-10+20)=12+10=22\ inch\\\\(7x+30)=(7\times 2+30)=14+30=44\ inch$

Perimeter of a quadrilateral = Sum of its sides

Perimeter of given quadrilateral = 32 + 22 + 44 + 31 = 129 inches

Thus perimeter of the quadrilateral is 129 inches

5 0

2 years ago

Last year, a person wrote 126 checks. Let the random variable x represent the number of checks he wrote in one day, and assume

Arisa [49]

Answer: The mean number of checks written per day $=0.3452$

Standard deviation $=0.5875$

Variance $=0.3452$

Step-by-step explanation:

Given : The total number of checks wrote by person in a year = 126

Assume that the year is not a leap year.

Then 1 year = 365 days

Let the random variable x represent the number of checks he wrote in one day.

Then , the mean number of checks wrote by person each days id=s given by :-

$\lambda=\dfrac{126}{365}\approx0.3452$

Since , the distribution is Poisson distribution , then the variance must equal to the mean value i.e. $\sigma^2=\lambda=0.3452$

Standard deviation : $\sigma=\sqrt{0.3452}=0.5875372328\approx0.5875$

6 0

3 years ago

Can't figure out number 6. need help!!

joja [24]

Answer:

Step-by-step explanation:

Definition of supplementary

3 0

2 years ago

Read 2 more answers

An equation that passes through (0, -2/3) and (-3, -2/3)

9966 [12]

Answer:

y = 0x - 2/3

Step-by-step explanation:

We are asked to find the equation of the line

Step1: find the slope

( 0 , -2/3) ( 3 , -2/3)

m = (y_2 - y_1 )/ (x_2 - x_1)

x_1 = 0

y_1 = -2/3

x_2 = 3

y_2 = -2/3

Insert the values into the equation

m =( -2/3 - (-2/3) / (3 - 0)

= -2/3 + 2/3 / 3

= 0 / 3

m = 0

Step 2: sub m into the equation

y = mx + c

y = 0x + c

Step 3: sub any of the two points given into the eqn

y = 0x + c

Let's pick ( 3 , -2/3)

x = 3

y = -2/3

-2/3 = 0(3) + c

-2/3 = 0 + c

c = -2/3

Step4: sub c into the equation

y = mx + c

y = 0x + c

y = 0x - 2/3

Therefore, the equation of the line is

y = 0x - 2/3

8 0

2 years ago

At a fabric store, metallic ribbon costs $16 for 4 ft. White ribbon is priced at 3 ft per dollar. Use rates to show which kind o

Elis [28]

Metallic ribbon: 16$ for 4ft

Dividing both sides by four, we get:

1 feet -- 4 dollars

White ribbon 3$ for 1 feet

1 feet -- 3 dollars

<h2><u><em>Therefore, the Metallic ribbon costs more per feet.</em></u></h2>

4 0

1 year ago

Prove: An odd number squared is an odd number. = (2n + 1)2 ​

Prove: An odd number squared is an odd number. = (2n + 1)2