MATHEMATICS HIGH SCHOOL

Suppose you want to factor the expression x2 + 2xn+n?. Given that n>0, what are the factors? Explain.Select the correct answer below and, if necessary, fill in the answer box to complete your choice.

O A. The value of n can be any positive integer resulting in the same factor

O B. The value of n can be any positive integer resulting in the distinct factors

(Use a comma to separate answers as needed.)

O C. The value of n can be any prime integer resulting in the same factor

O

D. The value of n can be any prime integer resulting in the distinct factors

(Use a comma to separate answers as needed.)

O E. The expression cannot be factored for the given values of n.

Answers

Answer 1

Answer:

Answer:

A. The value of n can be any positive integer resulting in the same factor

Step-by-step explanation:

Given

$x^2 + 2xn + n^2$ --- the right expression

$n > 0$

Required

Possible values of n

$x^2 + 2xn + n^2$

Expand

$x^2 + 2xn + n^2 = x^2 + xn+xn + n^2$

Factorize

$x^2 + 2xn + n^2 = x(x + n)+n(x + n)$

Factor out $x + n$

$x^2 + 2xn + n^2 = (x + n)(x + n)$

From the expression above, we can see that the result has the same factor. This means that options (b), (d) and (e) are not possible

$x^2 + 2xn + n^2 = (x + n)^2$

The above also shows that n can take any positive value.

Hence: (a) is correct

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The length of a rectangle is 5 more than twice the width. if the perimeter of the rectangle is 76 meters, find the dimensions of the rectangle and choose the equation that represents the perimeter:1. 76=2w+5
2. 76=2w+2(2w+5)
3. 76=w+2w+5
4. 76=2w+(2w+5)

Answers

Answer:

Dimensions: 11 meters by 27 meters

2. $76=2w+2(2w+5)$

Step-by-step explanation:

Finding Dimensions:

The perimeter of a rectangle can be written as $2l+2w$ where $l$ is the length and $w$ is the width. It is given that the length is 5 more than twice the length of width and the perimeter of the rectangle is 76 meters.

With this information we can write:

Length = $2w+5$

$2(2w+5)+2w = 76$ (perimeter of the rectangle)

$4w+10+2w=76$

$6w=66$

$w=11$

Length = $2(11)+5$

Length = $27$

∴ The dimensions of the rectangle is 11 meters by 27 meters.

Perimeter

Since the length can be written as $2w+5$ , the equation that represents the perimeter of the rectangle is $76=2w+2(2w+5)$

What is the simplest form of the expression? sqrt 2 - sqrt 6 / sqrt 2 + sqrt 6

Answers

Answer:

$-2+√(3)$

Step-by-step explanation:

we have

$(√(2)-√(6))/(√(2)+√(6))$

Multiply the expression by the conjugate of denominator

$(√(2)-√(6))/(√(2)+√(6))*(√(2)-√(6))/(√(2)-√(6))\n \n=-(√(2)-√(6))^(2)/4$

$=-(1/4)*(2-4√(3)+6)\n \n=-(1/4)*(8-4√(3))\n \n=-2+√(3)$

$\displaystyle \n ( √(2) -√(6))/(√(2) +√(6)) = ( (√(2) -√(6))(√(2) -√(6)))/((√(2) +√(6))(√(2) -√(6))) = \n \n \n = ( (√(2) -√(6))^2)/((√(2))^2 -(√(6))^2) = ( 2-2√(2)√(6) + 6)/(2 -6) = \n \n \n = ( 8-2√(12) )/(-4) = ( 8-2√(4* 3) )/(-4) = ( 8-4√(3) )/(-4) = \boxed{-2+√(3)}$

2,7,26,101,400 what is the next number

Answers

The next number in the sequence is 1595.

Here, given that, the sequence of numbers is: 2,7,26,101,400....

The relationship between the successive numbers in the sequence:

$x_((n+1)) = 4x_n - n$

Now, applying it to the given sequence:

$x_1 = 2\nx_2 = 4 * 2 - 1 = 7\nx_3 = 4 * 7 - 2 = 26\nx_4 = 4 * 26 - 3 = 101\nx_5 = 4 * 101 - 4 = 400$

As we can see, the formula $x_((n+1)) = 4x_n - n$ holds true for each term in the sequence, and it gives us the correct values for the subsequent terms.

Now, to find the next number in the sequence,

we use the formula with n = 5:

$x_((5+1)) = 4 * x_5 - 5\nx_6 = 4 * 400 - 5\nx_6 = 1600 - 5\nx_6 = 1595$

So, the next number in the sequence is 1595.

learn more on sequence:

brainly.com/question/17430673

#SPJ3

$a_1=2\na_2=4*a_1-1=4*2-1=7\na_3=4*a_2-2=4*7-2=26\na_4=4*a_3-3=4*26-3=101\na_5=4*a_4-4=4*101-4=400\na_6=4*a_5-5=4*400-5=1595$

A 3x4x5 rectangular cuboid (e.g. a brick) is painted blue and cut into 1x1 cubes. what is the expected value for the painted sides of a randomly selected cube?

Answers

Answer:

8 cubes are painted on 3 sides

24 cubes are painted on 2 sides

22 cubes are painted on 1 sides

6 cubes are painted on 0 side

E = 3 * 8/60 + 2 * 24/60 + 1 * 22/60 + 0 * 6/60 = 47/30 = 1.567

What is the solution to the following expression if x=52x - 7

A. 105

B. 25

C. 18

D. 3

Answers

Actually it’s D. or 3

Staci is attending a music festival. The ticket to the festival costs $87.96. Staci plans to purchase $30.00 t-shirts from the event for close friends. She is taking $200.00 to the festival. What is the maximum number of t-shirts Staci can purchase?

Answers

since stacy is bringing $200, and the initial cost is $87.96 you would have to subtract $200-87.96 which equals $112.04 this is the money left that stacy could buy shirts with, to figure out how many she needs you would have to do $112.04÷$30.00 this equals a decimal of 3.734666666666667 which would have to round down to 3 because stacy cant make it 4 shirts because she doesn't have enough money. So stacy can purchase a maximum of 3 shirts.
hope this helped:))

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