If h(x)=f(x)g(x)+f(x)/g(x), then find the value of h’(5)

The given statement is true for all matrices A.

1) For any 2x2 matrices A and B, (AB)2 = A2B2 - False. A counter-example to this claim would be if A and B are non-invertible matrices, such as A = [1, 0; 0, 0] and B = [1, 0; 0, 1]. (AB)2 = [1, 0; 0, 0], but A2B2 = [1, 0; 0, 1].

2) For any 2x2 matrices A, B, and C, if AB = AC, then B = C - True. This statement is true, as long as A is an invertible matrix. This can be seen from the properties of matrix multiplication; if AB = AC, then B = A-1AC = C.

3) For any 2x2 matrix A, if A2 = A, then either A = 0 or A = I - False. A counter-example to this claim would be if A = [1, 0; 0, 0], then A2 = A = [1, 0; 0, 0], but A ≠ 0 and A ≠ I.

1) Counter-example:Let the matrices A and B be given by\[A=\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}, B=\begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}\].Now,\[(AB)^2=\begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}^2=\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}\].and\[A^2B^2=\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}^2\begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}^2=\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}=\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}\]Hence\[(AB)^2\ne A^2B^2\]2) Let AB=AC. Then, we need to show that B=C. Let A, B and C be given as follows:\[A=\begin{pmatrix} 1 & 2 \\ 0 & 1 \end{pmatrix}, B=\begin{pmatrix} 3 \\ 4 \end{pmatrix}, C=\begin{pmatrix} 5 \\ 6 \end{pmatrix}\].Now, AB=\[\begin{pmatrix} 1 & 2 \\ 0 & 1 \end{pmatrix}\begin{pmatrix} 3 \\ 4 \end{pmatrix}=\begin{pmatrix} 11 \\ 4 \end{pmatrix}\]and AC=\[\begin{pmatrix} 1 & 2 \\ 0 & 1 \end{pmatrix}\begin{pmatrix} 5 \\ 6 \end{pmatrix}=\begin{pmatrix} 11 \\ 6 \end{pmatrix}\]Thus,\[AB=AC\]But, B=\[\begin{pmatrix} 3 \\ 4 \end{pmatrix}\]and C=\[\begin{pmatrix} 5 \\ 6 \end{pmatrix}\].Therefore,\[B\ne C\]Thus, AB=AC does not imply that B=C.3) True.According to the given statement, \[A^2=A\]Then,\[A^2-A=0\]⇒\[A(A-I)=0\]Either A=0 or A=I. Thus, the given statement is true for all matrices A.

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Answer: 25%

Step-by-step explanation:

To find the percentage, you divide 6 by 24. That equals 0.25, which is a decimal. You need to make it a percent, so multiply 0.25 by 100 which is equal to 25%.

The nth term of the arithmetic sequence is 10 - 3n.

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a constant value, called the common difference, to the preceding term.

The formula for the nth term (where n is a positive integer) of an arithmetic sequence is:

Here we have

a₁ = 7, a₂ = 4, a₃ = 1, a₄ = -2  

Common difference d = a₂ - a₁ = 4 - 7 = - 3

By using the formula

nth term of AP = 7 + (n - 1)(-3)

= 7 - 3n + 3

= 10 - 3n

Therefore,

The nth term of the Arithmetic sequence is 10 - 3n.  

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Tracy's total investment is $4,940. The Option A is correct.

An investment basically means the process of exchanging income during one period of time for an asset that is expected to produce earnings in future periods.

To find Tracy's total investment, we need to calculate the cost of buying 150 shares of Upton Group and 100 shares of WHI Health.

For 150 shares of Upton Group:

Total cost = number of shares × offer price

Total cost = 150 × $18.96

Total cost = $2,844

For 100 shares of WHI Health:

Total cost = number of shares × offer price

Total cost = 100 × $20.96

Total cost = $2,096

Tracy's total investment is the sum of these two costs:

Total investment = $2,844 + $2,096

Total investment = $4,940.

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Step-by-step explanation:

Seven people are in the pool who each have expected payouts of $8,600 for the year. One more person is added to the pool whose expected payout is $14,000 per year. How much is the average expected payout for each member of the group of eight? Expected Payout for each member of the group is $​

The solution of the system of equations by substitution method is 3x + 4(2x - 7) = 16, The correct option is D.

To solve the system of equations {y=2x-7, 3x+4y=16} using substitution, we can solve the first equation for y in terms of x (or x in terms of y) and substitute this expression into the second equation.

Solving the first equation y=2x-7 for y, we get:

y = 2x - 7

We can substitute this expression for y into the second equation 3x+4y=16, replacing y with 2x-7, to get:

3x + 4(2x - 7) = 16

Therefore, the expression after substituting the value of y is 3x + 4(2x - 7) = 16.

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Answer:

B. 3:1

Step-by-step explanation:

45 : 15

Divide both side by 15

= 3 : 1

The median, Q₁, Q₃, lower fence and upper fence of the given data set are 82, 75, 83, 63 and 95.

What is Inter quartile range?

In a range of values, from lowest to highest, the IQR denotes the median 50% of values. Find the median (middle value) of the lower and higher half of the data first, then use that number to calculate the interquartile range (IQR). The first quartile (Q1) and third quartile (Q3) of these values (Q3). What separates Q3 from Q1 is known as the IQR.

Given data set : 72, 81, 82, 83, 83, 85, 100, 54, 75, 81, 83

Firstly, we will arrange the data into ascending order.

we get, 54, 72, 75, 81, 81, 82, 83, 83, 83, 85, 100.

Here, no. of terms is 11

So, Median = (n+1)/2 th = (11+1)/2 = 6th term

So, Median = 82.

Q₁ = (n+1)/4 th term = (11+1)4 th = 3rd term

                                                 = 75

Q₃ = 3(n+1)/4 th term = 9th term = 83

Inter-quartile range = Q₃ - Q₁

                                  = 83 - 75 = 8.

Now, Lower fence = Q₁ - 1.5*IQR

                              = 75 - 1.5× 8

                              = 75 - 12 = 63

       Upper fence = Q₃ + 1.5*IQR

                              = 83 + 1.5×8

                              = 83 + 12

                              = 95.

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a. 240 students were surveyed in all. b. 60 students chose blue. c. The number of students who chose purple is 7, green is 10, others is 7 students.

In mathematics, a proportion is a statement that two ratios or fractions are equal. A proportion can be expressed as an equation of the form:

a/b = c/d

where a, b, c, and d are numbers, and b and d are not equal to zero. This equation can also be written in the form of a cross product:

ad = bc

This equation means that the product of the numerator of one fraction and the denominator of the other fraction is equal to the product of the denominator of the first fraction and the numerator of the second fraction.

a. If 20% of the students surveyed chose yellow and 48 students chose yellow, we can set up the following proportion to find the total number of students surveyed (let "x" be the total number of students):

20/100 = 48/x

Solving for x, we get:

x = 240

Therefore, 240 students were surveyed in all.

b. 25% of the students surveyed chose blue, so the number of students who chose blue is:

25/100 x 240 = 60

Therefore, 60 students chose blue.

c. We are given that 3% of the students surveyed chose purple, and 4% chose green. To find the number of students who chose purple or green, we can add the two percentages and find the corresponding portion of the total number of students:

3/100 + 4/100 = 7/100

So 7% of the students surveyed chose purple or green. The number of students who chose purple is:

3/100 x 240 = 7.2 (rounded to the nearest whole number, this is 7)

Similarly, the number of students who chose green is:

4/100 x 240 = 9.6 (rounded to the nearest whole number, this is 10)

We are also given that 3% of the students surveyed chose "other". Therefore, the number of students who chose "other" is:

3/100 x 240 = 7.2 (rounded to the nearest whole number, this is 7)

So 7 students chose "other".

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Yes, dog will catch the frisbee. The coordinates of the point or points where they meet are (0,6) and (6,18). So, option(a) is correct answer for this question.

I have a training your dog to catch a frisbee. The path equation of frisbee is y= –x² + 8x + 6 --(1)

and the path equation of the dog is modeled by

y = 2x + 6 --(2)

We have to check dog catch the frisbee or not and also determine the coordinates. The dog will catch the frisbee, when both equations are intersect to each other. That is intersection point of equation (1) and (2) are the required coordinates. Now, we determine the intersection points between the equation (1) and (2).

Substituting the value of y from equation (2) to equation (1), y = 2x + 6 in y = - x² + 8x + 6

=> 2x + 6 = -x² + 8x + 6

Simplify, x² - 8x + 2x = 6-6

=> x² - 6x = 0

=> x( x - 6) = 0

either x = 0 or x -6 = 0

=> x = 0, x= 6

from equation (1), y = 2(0) + 6 = 6

when x = 6, y = 2(6) + 6 = 18

Hence, required coordinates are (0,6) and (6,18).

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Complete question:

You are training your dog to catch a frisbee. You are playing in a large field, and you are standing next to your dog when you throw the frisbee. If the path of the frisbee is y= –x² + 8x + 6 and the path of the dog is modeled by y = 2x + 6, will the dog catch the frisbee? If so, what are the coordinates of the point or points where they meet?

a) Yes, they intersect at the coordinates (0, 6) and (6, 18)

b) Yes, they intersect at the coordinates (1, 13) and (2, 10)

c) Yes, they intersect at the coordinates (2, 18) and (3, 12)

d)No, the paths do not cross

Tyler takes 32 minutes to read 24 pages.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Tyler reads 3/4 pages per minute. Then the ratio of pages to minutes is given as,

Ratio = (3/4)/1

Ratio = 3:4

If he read 16 minutes, then the number of pages is calculated as,

(3/4) x 16

3 x 4

12 pages

Tyler has to read 24 pages for homework. Then the number of minutes is given as,

24 / (3/4)

24 x (4/3)

8 x 4

32 minutes

Therefore, it takes 32 minutes to read 24 pages.

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By answering the above question, we may state that  The two lines intersect at the point (1, -2), so the system of linear equations has one solution at (1, -2).

A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A formal statement that proves the equality of two calculations is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two phrases that are inscribed on opposite sides of a letter. Frequently, the logo and indeed the particular software are identical. like in 2x - 4 = 2, for example.

The two lines intersect at the point (1, -2), so the system of linear equations has one solution at (1, -2).

Therefore, the answer is: One solution at (1, −2).

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If there are 240 students in the sixth-grade class then the number of votes that Naomi received is: 336 votes.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Bridgette and Naomi ran for sixth-grade class president.

In the election, every sixth-grade student voted for either Bridgette or Naomi.

Bridgette received 5 votes for every 7 votes Naomi received.

the first figure represents 5:7 ratio in the story.

Since Bridgette received 5 votes for every 7 votes Naomi received, Bridgette received 5/7 of the total votes and Naomi received 2/7 of the total votes.

We know that the total number of votes cast is equal to the total number of students in the class, which is 240.

Therefore, we can set up the equation:

⁵/₇(x) + ²/₇(x) = 240

Simplifying the equation, we get:

(5x + 2x)/7 = 240

7x/7 = 240

x = 240 × 7/5

x = 336

Therefore, If there are 240 students in the sixth-grade class then Naomi received 336 votes.

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The point on Π that is closest to A is (3,-2,0).

(a) The distance between the plane Π and the point A is 3. To find this, we need to find the equation of the plane Π. The equation of the plane is given by:

Ax + By + Cz + D = 0

where (A, B, C) is the normal vector to the plane, which is perpendicular to the line that passes through points A and B. Since the normal vector of the plane is perpendicular to the line, the normal vector (A, B, C) is equal to the cross product of the two vectors of the line AB, given by:

A=(3,0,-2), B=(-1,1,0)

A x B = (A2B3-A3B2, A3B1-A1B3, A1B2-A2B1) = (-5,3,3)

Therefore, the equation of the plane Π is:

-5x + 3y + 3z + D = 0

To find D, we need to plug in the coordinates of the point (1,2,3). Therefore,

-5(1) + 3(2) + 3(3) + D = 0
-5 + 6 + 9 + D = 0
D = -20

Therefore, the equation of the plane Π is:

-5x + 3y + 3z - 20 = 0

To find the distance between the plane Π and the point A, we need to calculate the shortest distance between the plane and the point A. We can do this using the distance formula, given by:

d = |Ax + By + Cz + D|/sqrt(A^2 + B^2 + C^2)

Substituting the equation of the plane Π and the coordinates of point A into the distance formula, we get:

d = |-5(3) + 3(0) + 3(-2) - 20|/sqrt(-5^2 + 3^2 + 3^2)
d = |-15 - 20|/sqrt(34)
d = |-35|/sqrt(34)
d = 3

Therefore, the distance between the plane Π and the point A is 3.

(b) The point on Π that is closest to A is (3,-2,0). To find this, we need to solve the system of equations given by:

-5x + 3y + 3z - 20 = 0
x - 3 = 0
y - 0 = 0
z + 2 = 0

Solving this system of equations, we get x = 3, y = -2, and z = 0. Therefore, the point on Π that is closest to A is (3,-2,0).

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By answering the above question, we may state that The circle's radius is  radius 8.5 feet as a result.

In more modern use, a circle's or sphere's length is equal to its radius, and it is one of the line segments connecting the object's centre and circumference. The phrase is derived from the Roman word circle, which also describes a waggon wheel's spokes. The radius of a circle is the separation of any points on its circumference from its centre. Often, it is denoted by "R" or "r". A line segment with one termination in the centre and one on the circle's perimeter is called a radius. Radius = circular diameter A circle's diameter is the portion that passes through its centre and has ends on the circle.

The formula for calculating a circle's circumference is:

C = 2πr

When r denotes the radius, C denotes the circumference, and denotes a mathematical constant roughly equal to 3.14159.

We are informed that the circle's diameter is 17 feet. We may solve for r by setting this equal to the circumference formula:

17π = 2πr

By multiplying both sides by 2, we obtain:

r = 17π / (2π)

The units are cancelled, leaving:

r = 17 / 2

Examining this expression results in:

r = 8.5 ft

The circle's radius is 8.5 feet as a result.

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The theater has a tοtal οf 56 red seats and 32 blue seats, making a tοtal οf 88 seats.

If each sectiοn has 14 red seats, then there are a tοtal οf 4 x 14 = <<4 × 14=56>>56 red seats in the theater.

Tο find οut hοw many blue seats are in each sectiοn, we need tο subtract the number οf red seats frοm the tοtal number οf seats in each sectiοn:

88 tοtal seats / 4 sectiοns = 22 seats per sectiοn

22 seats per sectiοn - 14 red seats per sectiοn = 8 blue seats per sectiοn

Therefοre, each sectiοn has 8 blue seats, and the theater has a tοtal οf 4 x 8 = <<4 × 8=32>>32 blue seats.

Sο, the theater has a tοtal οf 56 red seats and 32 blue seats, making a tοtal οf 88 seats.

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Answer:

(c+1)(c+2)

Step-by-step explanation:

you need to find the two numbers that get 2 when you multiply them and get 3 when you add them. those two numbers are 2 and 1 and c times c is c^2

you can check the answer by using foil like this:

(c+1)(c+2)

first: c times c= c^2

second: 2 times c= 2c

third: 1 times c= 1c

last: 1 times 2= 2

and all that together you get c^2+2c+1c+2

simply and get C^2+3c+2

Answer:

I think you forgot a picture

The correct answer is option A, counter clockwise 90°, for the needle to lean on the outline section, the wheel must be turned counter clockwise 90°. Any other turn of the wheel will not result in the needle leaning on the outline section.

Counterclockwise is an adjective used to describe motion or rotation that is in the opposite direction of a clock's hands. For example, when a person swims in a pool, they may swim counterclockwise around the perimeter of the pool. This is the opposite direction of the way a clock's hands move. Counterclockwise rotation is also known as anti-clockwise rotation.

When an object is placed on a flat surface and the wheel is turned, it will rotate in the same direction as the motion of the wheel. If the needle is leaning on the outline section, the wheel must be turned counter clockwise 90°. This is because when the wheel is turned counter clockwise, the needle will be forced to move in the same direction and end up leaning on the outline section.

When the wheel is turned clockwise, the needle will move in the opposite direction and it will not end up leaning on the outline section. Therefore, a clockwise turn of 120° or 180° is not the correct answer. Similarly, turning the wheel counter clockwise by 180° is also not the correct answer. This is because the needle will end up pointing in the same direction it was pointing before the wheel was turned.

In conclusion, for the needle to lean on the outline section, the wheel must be turned counter clockwise 90°. Any other turn of the wheel will not result in the needle leaning on the outline section.

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Answer:

A. counter clockwise 90°.

Step-by-step explanation:

Answer:

Step-by-step explanation:

A= 5(x+3)=17

B= 5x+3=17

C= 3x+5=17 A girl decides to buy 5 pens for 3 of her friends. The total cost of the pens was 17$. She then decides to make her friends guess the cost of each pen.

The total number of eggs in 7 dozens of eggs is 84 eggs

Word Problem is a sentence usually made up of a few sentences describing a scenario that needs to be solved through mathematics.

How to determine this

When a dozen mean a group of twelves things

When 1 dozen of an egg = 12 eggs

To get the total number of eggs in 7 dozens of eggs

Let x represent the total number of eggs

When 1 dozen = 12 eggs

7 dozens = x

x = 7 dozens * 12 eggs/1 dozen

x = 84 eggs/1

x = 84 eggs

Therefore, 84 eggs make 7 dozens of eggs

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Answer:

First, we need to calculate the total cost of Lisa's and Tracy's lunches before tax and tip.

Lisa's lunch = $6

Tracy's lunch = $7

Total before tax and tip = $6 + $7 = $13

Now we need to add the 5% sales tax:

$13 x 0.05 = $0.65

Total after tax = $13 + $0.65 = $13.65

Finally, we need to add the 15% tip:

$13.65 x 0.15 = $2.05

Total bill = $13.65 + $2.05 = $15.70

Therefore, the total bill, including tax and tip, is $15.70.

Answer:

Step-by-step explanation:

6 + 7 = 13

Now for the sales tax and tip, we need to add 15 and 5 together which is 20. So now we need to multiply 13 times the decimal equivalent of 20%. So, 0.20 x 13 = 2.6

2.6 + 13 = 15.6

The answer is 15.6

Given that diameter of a circle is 7 ft, its area to the nearest tenth is 38.5 square feet.

Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2 where r is the radius of the circle.

To find the radius, we can divide the diameter by 2: r = d/2 = 7/2 = 3.5 ft

Now we can plug this into the formula for the area:

A = πr^2

A = π(3.5)^2

A ≈ 38.48

Therefore, rounding to the nearest tenth, the area of the circle is approximately 38.5 square feet.

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Answer:

x=5/3

Step-by-step explanation:

The amount of money in account after 16 years will be $162,823.39. The solution has been obtained by using compound interest.

What is compound interest?

Compound interest considers the principal when determining the interest for the subsequent month, in contrast to simple interest, which does not. In algebra, compound interest is typically denoted by the letter C.I.

We are given the following information:

P = $72000

Rate (r) = 5.1% = 0.051

Time (t) = 16 years

Using the formula, we get

⇒V = P[tex]e^{rt}[/tex]

⇒V = (72000) e⁰°⁰⁵¹ˣ¹⁶

⇒V = (72000) e⁰°⁸¹⁶

⇒V = $162,823.39

Hence, the amount of money in account after 16 years will be $162,823.39.

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In conclusion, Mr. Barnes rode his bike at a rate of 6.67 miles per hour, which was faster than Mrs. Barnes' rate of 6 miles per hour.

We must compute the rate or speed that each participant rode in order to determine who rode faster. The rate is calculated by dividing the distance travelled by the time required. The rates for Mr. and Mrs. Barnes will now be determined:

Rate = Distance / Time = 20 Miles / 3 Hours = 6.67 Miles per Hour, Mr. Barnes

Rate = Distance/Time = 24 Miles/4 Hours = 6 Miles Per Hour, Mrs. Barnes

We can observe from comparing the speeds that Mr. Barnes rode more quickly than Mrs. Barnes. Her speed was 6 miles per hour, compared to his 6.67. As a result, we can conclude that Mr. Barnes was riding more quickly than Mrs. Barnes.

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The polynomial function will be x³ + (3-√2)x² - 3√2x = 0.

What is a polynomial function?

A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses non-negative integer powers or only positive integer exponents of a variable.

The simplest straightforward and typical mathematical equation is one with polynomial functions. It can be described using a polynomial. The polynomial function is modelled by a polynomial equation. A polynomial is typically written as P. (x). The degree of a polynomial is the largest exponent of the variable P(x). Understanding a polynomial's degree is crucial since it explains how function P(x) behaves as the value of x increases. Polynomial functions only apply to real numbers in their domain (R).

Given : zeros of polynomial = 0, -3 and √2

So, the polynomial function can be found :

  = (x-0) (x+3)(x-√2)

  = x (x+3) (x-√2)

  = (x²+3x) (x-√2)

  = x³ -√2x² + 3x² - 3√2x

  = x³ + (3-√2)x² - 3√2x

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Answer:

g(x) = f(x + 2) = 2^(x + 2) + 2

Step-by-step explanation:

To shift the function f(x) = 2^x + 2 two units to the left, we need to replace x with (x + 2) in the equation. This will shift the graph horizontally to the left by two units.

So, the new function g(x) that represents the shifted graph is:

g(x) = f(x + 2) = 2^(x + 2) + 2

Answer: The answer is A

Step-by-step explanation:

An οdd number squared is always an οdd number, and we have prοved it fοr the case οf (2n+1)².

An integer is a whοle number that can be either pοsitive, negative, οr zerο. It dοes nοt have a fractiοnal οr decimal cοmpοnent.

Tο prοve that an οdd number squared is an οdd number, we can start by expressing an οdd number as 2n+1, where n is an integer.

Then, we can square this expressiοn tο get:

(2n+1)² = (2n+1)(2n+1)

Expanding the right side οf the equatiοn using the distributive prοperty, we get:

(2n+1)² = 4n² + 2n + 2n + 1

Simplifying the expressiοn by cοmbining like terms, we get:

(2n+1)² = 4n² + 4n + 1

Nοw we can see that the first twο terms, 4n² and 4n, are bοth even since they cοntain a factοr οf 2. Adding twο even numbers always results in an even number.

Therefοre, the sum οf 4n² and 4n is even.

Adding 1 tο an even number results in an οdd number.

Therefοre, we have shοwn that:

(2n+1)² = 4n² + 4n + 1 = (2n² + 2n) + 1 = 2n(n+1) + 1

Since 2n(n+1) is even, the sum οf 2n(n+1) and 1 is οdd.

Hence, an οdd number squared is always an οdd number, and we have prοved it fοr the case οf (2n+1)².

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