Prove algebraically that the difference between the squares of any two consecutive
odd numbers is always a multiple of 8

Answers

Answer 1

Answer:

See below ↓

Step-by-step explanation:

Let the odd integers be :

2x + 12x + 3

Solving

(2x + 3)² - (2x + 1)²4x² + 12x + 9 - 4x² - 4x - 18x + 8 = 8(x + 1)On substituting any value for 'x', the value will be a multiple of x.

Examples

8(1) + 8 = 16 = 8 x 28(2) + 8 = 24 = 8 x 38(3) + 8 = 32 = 8 x 4
Answer 2

Answer:

Let one odd number be (2n + 1)

Therefore, its consecutive odd number is (2n + 3)

Difference between the two squares of these numbers:

[tex]\begin{aligned}\sf (2n+3)^2-(2n+1)^2 & = \sf (4n^2+12n+9)-(4n^2+4n+1)\\ & = \sf4n^2+12n+9-4n^2-4n-1\\ & = \sf 8n+8\\ & = \sf8(n+1)\end{aligned}[/tex]

Thus proving that the difference between the squares of any two consecutive odd numbers is always a multiple of 8.


Related Questions

Leslie asked a representative sample of 40 of her classmates about their favorite type of movie for an upcoming film festival.

Fill in the table to show reasonable predictions for the whole class.
Her class has a total of 160 students.

Answers

Answer:

Step-by-step explanation:

Solve for x (literal equations):
c=b-bx show work

Answers

Answer:

x = [tex]\frac{b-c}{b}[/tex]

Step-by-step explanation:

c = b - bx ( add bx to both sides )

bx + c = b ( subtract c from both sides )

bx = b - c ( divide both sides by b )

x = [tex]\frac{b-c}{b}[/tex]

Calculate the side lengths using the given scale.

Answers

Answer:

x= 5× 17

= 85milimetres

y= 65÷ 5

=13milimetres

How does your Web browser get a file from the Internet? Your computer sends a request
for the file to a Web server, and the Web server sends back a response. For one
particular Web server, the time X (in seconds) after the start of an hour at which a
randomly selected request is received has the uniform distribution shown in the figure. in

Answers

The probability that the request is received by this server within the first 5 minutes (300 seconds) after the hour is 0.0833 or 8.33%.

How does your Web browser get a file from the Internet?

Your computer sends a request for the file to a Web server, and the Web server sends back a response.

For one particular Web server, the time X (in seconds) after the start of an hour at which a randomly selected request is received has the uniform distribution shown in the figure.

The probability of finding value less than the X is,

[tex]P(X < x)=\dfrac{x-a}{b-a}[/tex]

Here, a and b are two bonds of uniform distribution.

The probability distribution of X can be modeled by a uniform density curve on the interval from 0 to 3600 seconds, as shown in the given figure.

The probability that the request is received by this server within the first 5 minutes (300 seconds) after the hour has to be found out. Thus,

[tex]P(X < x)=\dfrac{300-0}{3600-0}\\P(X < x)=0.0833\\P(X < x)=8.33\%[/tex]

Thus, the probability that the request is received by this server within the first 5 minutes (300 seconds) after the hour is 0.0833 or 8.33%.

Learn more about the probability distribution here;

https://brainly.com/question/9385303

#SPJ1

(2,132 x 10 -15 - (4,695 x 10 )​

Answers

Answer:

25,645

________________________________________________________

Solve

First, find 4,695 × 10

[tex]4,695 * 10 = 46,950[/tex]

Next, do 2,132 × 10

[tex]2,132 * 10 = 21,320[/tex]

Now, subtract by 15.

[tex]21,320 - 15 = 21,305[/tex]

Lastly, subtract by the product you found earlier.

[tex]46,950 - 21,305 = 25,645[/tex]

________________________________________________________

Questions?

Ask in comments box.

Every second, an elevator either has a 50% chance of going up and a 50% chance of going down. If the elevator starts at floor 15, what is the probability that, after 5 seconds, the elevator is at floor 18?

Answers

Using it's concept, it is found that there is a 0.1563 = 15.63% probability that, after 5 seconds, the elevator is at floor 18.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Starting at floor 15, these are the following outcomes that result in the elevator being at floor 18 in 5 seconds, each with [tex]0.5^5[/tex] probability:

4 up, 1 down.3 up, 1 down, 1 up.1 down, 4 up.1 up, 1 down, 3 up.2 up, 1 down, 2 up.

5 outcomes, hence the probability is:

[tex]p = 5 \times (0.5)^5 = 0.1563[/tex]

0.1563 = 15.63% probability that, after 5 seconds, the elevator is at floor 18.

More can be learned about probabilities at https://brainly.com/question/14398287

Work out
21
% of
£
944.13
Give your answer rounded to 2 DP. I need right awnsers you can use calculators

Answers

Answer: £198.27

Step-by-step explanation:

944.13x0.21=198.2673Rounded to 2 decimal places that is 198.27

Which ordered pairs match the mapping diagram? O (1, 0), (7, 2), (3, 1), (-1, 1), (-7, -6) (0, 1), (2, 7), (3, 4), 4, 1), -6, 7) O(0, 1), (0, 4), (0, 7), (2, 7), (6, 7) (0 1), (2, 7), 3, 4), (4, 1), (6, 7)​

Answers

Answer:

I've done this b4

(0, 1), (2, 7), (3, 4), (-4, 1) , (-6, 7)

Given the following construction, which of the following can you now create?

Select ALL that apply.


options:

square


equilateral triangle


rhombus


the midpoint of segment AB


perpendicular bisector of segment AB

Answers

square is the correct answer

a rectangular shoebox has a volume of 160 cubic inches. the base of the shoebox measures 8 inches by 5 inches. how long is the shoebox?

Answers

Volume = w*h*d
8*5*d = 160
D= 160/40
D=4

9. The value of U.S. postage stamps increases -5% per year. The current price is 55€. Estimate what the price will be in 20 years​

Answers

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &\$0.55\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &20\\ \end{cases} \\\\\\ A=0.55(1 + 0.05)^{20}\implies A=0.55(1.05)^{20}\implies A\approx 1.46[/tex]

I need help trying to solve for MNO it’s for our right triangle trigonometry unit.

Answers

Answer:

Angle O is 64. m is 16.7 rounded to the nearest tenths place. n is 22.4 to the nearest tenths place.

Step-by-step explanation:

Angle O- 180-(26+90)

M- COS(26)=n/15

N- COS(26)=n/15^2+15^2=c^2

i need to find volume of this triangular pyramid

Answers

Answer:

135 Cubic Inches

Step-by-step explanation:

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a great day!

i do not know this answer

Answers

18.85 i don’t feel like explaining just trust me

2x + y - 3z , x = 2/5 , y = 2/3 , z = 1/6 what does it equal

Answers

29/30

2x + y - 3z

2 x 2/5 + 2/3 - 3x1/6

4/5 + 2/3 - 3/6

x 3 x 5

12/15 + 10/15 - 3/6

22/15 - 3/6

x2. x5

44/30 - 15/30

= 29/30

Hope this helps!

Solve for x. round to the nearest tenth.
37°
x
48

Answers

Answer:

1.3

Step-by-step explanation:

To find what x equals, you need to first divide by 48 and 37.

This is because that x is being multiplied by 37.

48 ÷ 37 = 1.297.......

The 97 in 1.297 is repeating and goes on forever.

Rounding the the nearest tenth would create the number 1.3 as the correct answer.

Are the triangles similar? If so, how do you know?

Answers

The triangles are similar because the one on the left is just twice as big as the one on the right.

1. Find the values of a and b. The diagram is not to scale. 121 354​

Answers

Answer:

3 or it could also be 1 ( also like demon slayer me tooo )

PLEASE ANSWER I WILL GIVE BRAINLIEST TO CORRECT ANSWER

Answers

Answer:

6x+4y=16

Step-by-step explanation:

2 ( 3x)  + 2 (2y) = 2 (8)

   6x + 4y = 16     <===== add this equation to the top equation to get

11x = 22

then x = 2    use this value of x in any of the equations to calculate y

5(2) - 4y = 6

10 - 4y = 6

    -4y = -4

        y = 1

it takes 3 eggs to make two dozen cookies. About what fraction of an egg are in two cookies

Answers

keeping in mind that two dozen cookies is just 24 cookies, then

[tex]\begin{array}{ccll} eggs&cookies\\ \cline{1-2} 3 & 24\\ x& 2 \end{array} \implies \cfrac{3}{x}=\cfrac{24}{2}\implies \cfrac{3}{x}=12\implies 3=12x \\\\\\ \cfrac{3}{12}=x\implies \cfrac{1}{4}=x[/tex]

The problem is the screenshot

Answers

Answer:

(x = 0,y = 0),(x = 1, y = 5),(x= 2, y =10)

Step-by-step explanation:

the rule is to multiply x by 5.

when x = 0, y =5(0) = 0

when x = 1, y =5(1) = 5

when x = 2, y =5(2) = 10

Hope this helps!

Please mark as brainliest!

Answer:

0

5

10

Step-by-step explanation:

A table can be completed by plugging x-values into an equation or by graphing.

Plug in x-values

First, plug 0 into the equation to find the first y-value.

y=5(0)y=0

Next, plug in 1 for x

y=5(1)y=5

Finally, plug in 2

y=5(2)y=10

Additionally, each of these y-values increases by 5. So, once we found the first y-value, 0, we can just add 5 to find the next y-values.

Graphing

Also, you can use a graph to find the missing values. The y-intercept is 0 and the slope is 5. Using this information you can graph the equation. Then, find the x-values on the graph and match these values to y-values.

Can someone please solve this? When I put it in the calculator the slope is wrong.

Answers

Answer:

y=6

Step-by-step explanation:

When you put the points on a plane, you can see it is a horizontal line, therefore the slope is 0

Remember that 0 times any other number is 0

So, instead of having y=0x+6 you can simplify the 0x and you have y=6

2x - 5 = 3 what does X equal to?

Answers

x = 4 because 2 times 4 equals 8 and 8 minus 5 is 3

Help this is soooooo hard for me

Answers

Answer: Choice C  

Mean = 37.1

==================================================

Explanation:

Refer to the table below. The colum labeled "M" is the midpoint for each age interval. To find the midpoint, add up the endpoints and divide by 2. For example, the midpoint of 18 and 24 is (18+24)/2 = 42/2 = 21. Notice how the values of M are increasing by 7 each time.

The column labeled fM refers to multiplying the frequency f with the midpoint M. Example: fM = 6*21 = 126 in the first row.

Add up everything in the column labeled fM and you should get 1484. Divide this over the sum of the frequencies (40) and the mean is 1484/40 = 37.1

Answer:

c is the right answer

Step-by-step explanation:

hope i helped

I need sum help y’all boys

Answers

You have to multiply the Diameter, times Pi.(3.14)


7. 21.98

8. 62.8

9.75.36

10. 59.66
11. 84.78
12. 3082.2

 I dunno the last one. I probably do but
Hope This Helped!

The centre of the circle is (3,a) and a point on the circumference is (6,-1). if the radius of the circle is 3 units , find the value of a​

Answers

Answer: -1

Step-by-step explanation:

which of the best following point best represent 106

Answers

Answer:

b

Step-by-step explanation:

i hope this helped

Suppose the correlation coefficient between a student's homework score & their test score is found to be
0.92.
0.92.

What conclusion can you make about the relationship between a student's homework & test scores based on the correlation coefficient?
A
Students score an average of 92%92% on their homework & tests
B
A student's homework & test score have a strong association
C
There is a difference of 0.920.92 points from a student's homework & test grades
D
Only 92%92% of students pass on their homework & test scores

Answers

Answer:

A

Step-by-step explanation:

Tammy cuts four identical circles from a square piece of black poster board as shown. What is the area of the leftover poster board?
a) 6.240 square feet
b) 5.375 square feet
c) 18.760 square feet
d) 19.625 square feet

Answers

Answer:

B) 5.375

Step-by-step explanation:

The circles are half the square so their diameter will be half the length of the square

d=5/2=2.5

the formula is

area of shaded portion-area out unshaded portion

area of a square= l×l

5×5=25

area of a circle=πr^2

but since there are 4 circles it becomes 4πr^2

r=d/2=2.5/2=1.25

area of unshaded portion= 4×3.14×1.25×1.25

=19.625

area of leftover=25-19.625

= 5.375

what is the greatest common factor of 15, 5, and 50

Answers

Answer:

Therefore, the GCF of 15 and 50 is 5.

Step-by-step explanation:

Solution:

The greatest number that divides 15 and 50 exactly is their greatest common factor, i.e. GCF of 15 and 50.

⇒ Factors of 15 and 50:

Factors of 15 = 1, 3, 5, 15

Factors of 50 = 1, 2, 5, 10, 25, 50

Therefore, the GCF of 15 and 50 is 5.

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