Prove that for any natural value of n the value of the expression (n+2)^2-(n-2)^2 is a multiple of 8.
Answers
Answer:
We have the expression:
(n + 2)^2 - (n - 2)^2
Let´s break the parentheses:
(n + 2)^2 = n^2 + 4*n + 4
(n - 2)^2 = n^2 - 4n + 4
Then:
(n + 2)^2 - (n - 2)^2 = (n^2 + 4*n + 4) - (n^2 - 4n + 4) =
= (n^2 - n^2) + (4 - 4) + (4n - (-4n)) = 4n - (-4n) = 8*n
Then for any natural value of n, 8*n will be a multiple of 8.
Related Questions
in the coordinate plane, triangle ABC has vertices A(1,-2), B(1,0.5), and C(2,1) and triangle DEF has vertices D(4,-3), E(4,2), and F(6,3). The triangles are similar because DEF is the image of ABC under a dilation with center (_,_) and scale factor ___.
PLEASE HELPP
Answers
Answer:
(A) the center of dilation is at (-2,-1)
(E) the scale factor is 2
The triangle DEF is a dilation of triangle ABC with center of dilation at (0,0) and scale factor of 0.5.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The ratio of the lengths of corresponding sides of triangles ABC and DEF.
AB and DE are corresponding sides, so:
AB/DE = (distance between A and B) / (distance between D and E)
= 2.5 / 5
= 0.5
BC and EF are corresponding sides, so:
BC/EF = (distance between B and C) / (distance between E and F)
=1.118 / 2.236
= 0.5
AC and DF are corresponding sides, so:
AC/DF = (distance between A and C) / (distance between D and F)
AC/DF = 2.236 / 4.472
= 0.5
We see that all three ratios are equal to 0.5.
Hence, the triangle DEF is a dilation of triangle ABC with center of dilation at (0,0) and scale factor of 0.5.
To learn more on Triangles click:
https://brainly.com/question/2773823
#SPJ1
What is the answer and plz give me step by step explaining
Answers
Explanation:
You start with 6 + 8(x - 1) = 2(3x + 4)
Wow. That looks like a lot, so you need to take it one step at a time. Because of PEMDAS (Please Excuse My Dear Aunt Sally), which gives us the order of Parentheses (), Exponents(Baby Numbers), Multiply or Divide from left to right according to where it is in the problem, and Add or Subtract from left to right according to where it is in the problem, you need to look at your parentheses first. Let’s start with
8(x - 1). 8 is touching those parentheses all by itself, so it’s being multiplied with the stuff in the parentheses. 8 times x is 8x and 8 times 1 is 8. That gives you
6 + 8x - 8 = 2(3x + 4)
Do the same thing with 2(3x + 4). 2 is touching those parentheses all by itself so you multiply it by the stuff inside to get 6x + 8. You now have
6 + 8x - 8 = 6x + 8
But where do we go from here? Okay well what you’re trying to do is get a single x by itself on one side of the equals and the answer on the other side. So, we have
6 + 8x - 8 = 6x + 8
Let’s start on the left side with 6 + and - 8. If you have 6 and you take 8 away, you can’t because you’ll still need 2, so 6 - 8 = -2. That leaves you with
8x - 2 = 6x + 8
Then, you take the 6x from the right side and add it to the 8x on the left. You have 14x. This gives you
14x - 2 = 8
Look at -2. We want to get rid of that, so we would do the opposite of - which is + so we would add.
14x - 2 = 8
+ 2 + 2
——————
14x = 10
Now look at 14x, which is the same as 14 times x. The opposite of multiplying is dividing so divide.
14x = 10
/14 /14
X = 10/14 which simplifies into 5/7
Right 2 units and down 7 units
Answers
Answer:
-3.5
Step-by-step explanation:
Rise over run
ABCD is a square.
Solve for x
Answers
Hope you have a good day and good luck!
In a class of 12 boys and 8 girls, two students need to be chosen for classroom jobs.
What is the probability that Mary gets selected?
Answers
Answer:
55 percent chance or 11/20 or 0.55
Step-by-step explanation
9 1/12 = k/9 Solve for K
Answers
k/9-1=12
We move all terms to the left:
k/9-1-(12)=0
We add all the numbers together, and all the variables
k/9-13=0
We multiply all the terms by the denominator
k-13*9=0
We add all the numbers together, and all the variables
k-117=0
We move all terms containing k to the left, all other terms to the right
k=117
Hope this helps ya :) k= 81.75
Expand the following expression by using the distributive method. 6(3b-4c)
Answers
1
For every 2 teaspoons of white vinegar in a jar of homemade glue, there are 5 tablespoons of
cornstarch. How many teaspoons of white vinegar are there for every tablespoon of cornstarch?
A. 1
5
В.
C 1
D. 5
Answers
The number of teaspoons of white vinegar are there for every tablespoon of cornstarch is 0.4.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, for every 2 teaspoons of white vinegar in a jar of homemade glue, there are 5 tablespoons of cornstarch.
The number of teaspoons of white vinegar are there for every tablespoon of cornstarch = 2/5
= 0.4
Therefore, the number of teaspoons of white vinegar are there for every tablespoon of cornstarch is 0.4.
To learn more about the unitary method visit:
brainly.com/question/22056199.
#SPJ6
WILL GIVE BRAINLIEST PLS HELP!!!!! - Which expression represents a cube root of –8?
Answers
Answer:
A
Step-by-step explanation:
Answer:
C or 2(cos(pi/3)+i sin (pi/3))
PLEASE HELP if you help you like to play among us
Subtracting a number is the same as adding its opposite.
Use this understanding to complete each of the equations below.
CLEAR CHECK
Answers
Answer:
-5 - (-7) = -5 + -7
= 2
-5 - 7 = -5 + -7
= -12
the sale price of an item is $160 after a 20% discount what was the original price of the item
Answers
Answer:
200
Step-by-step explanation:
Because first you divide 160 by 4 (100-20=80, 80/100 simplified is 4/5) and you get 40. Then you multiply 40 by 5 and you get 200. Their are many ways to solve it. I personally think this is the easiest.
HOPE THIS HELPS
20% of 200 is 40 so 200-40 is 160 which is the price of the item while on sale
2x – 3y = -5
y = 2 + x
The value of y in the system of equations is:
y = -1.
y = -3.
y = 1.
y = 3
Answers
Answer:
y = 3
Step-by-step explanation:
2x-3y = -5 --------- (1)
y = 2+x ------- (2)
substitute (2) into (1)
2x-3y = -5
2x-3( 2+x ) = -5
2x-6-x = -5
2x-x = -5+6
x = 1
substitute x = 1 into (2)
y = 2+x
y = 2+1
y = 3
does anyone know the answer ?
Answers
Answer:
i think its inches per foot b/c it says what where the final units for this conversion i hope this is helpful.
Step-by-step explanation:
You have $125 in a savings account and you deposit an equal amount into your account each week. After 5 weeks the account holds $170. Write an equation that represents the amount y (in dollars) of money in the account after x weeks.
Answers
Answer: 10x=y
Step-by-step explanation:
So if you subtract 170-125 you get 50. If you divide 50 by the 5 weeks you geat 10. So there is ten dollars a week going into the bank account.
solve y (1/2)y+6=(3/4)y–4
Answers
Answer:
Y = 40
Step-by-step explanation:
Change 1/2 to 2/4
2/4 y + 6 = 3/4y - 4
subtract 2/4y
6 = 1/4y -4
add 4
10 = 1/4y
multiply by 4 to get fraction to 1y or y
y = 40
I GOT IT RIGHT ON MY QUIZ
Ron measured his garden to be 12‘ x 8 1/3‘. He plant vegetables in 3/4 of his garden. What is the area of his vegetable garden?
Answers
Answer:
4/4
Step-by-step explanation:
Hope this helped have an amazing day!
Nick earns 3.5%
commission on every
car he sells. How much
would he earn if he sold
a $14.000 car?
Answers
The amount he would earn is $490.
What does multiplication mean?
Multiplication is the process of determining the product of a number. It is determined by following some mathematical processes. The sign used to represent multiplication is ×.
How much will he earn?Commission = 3.5% x $14,000
0.035 x $14,000 = $490
To learn more about multiplication, please check: https://brainly.com/question/13814687
Solve kx - 3 = 5 for x.
A. x = 8 - k
B. x = 8k
C. x=2/k
D. x= 8/k
Answers
Answer: D
Step-by-step explanation:
I just got it wrong and D was the answer
nodadnotoday is my Spotify tho
How to I write 1 2/3 as an improper fraction help ASAP
Answers
[ 5/3 ]
Are the following equations parallel, perpendicular, or neither? y= 3x - 1 and y =
-1/3x + 10 *
Parallel
Perpendicular
Neither
Answers
Answer:
Perpendicular
Step-by-step explanation:
Hugo earns $2.00 for setting the table and $2.00 for washing the dishes. Let t be the number of times Hugo sets the table and let d be the number of times Hugo washes the dishes. Select all the expressions that could represent the total earned, E, in dollars, by Hugo *
2 points
A) E = 2(t + d)
B) E = 2t + 2d
C) E = 2t + d
D) E = 2 + td
Answers
B) E = 2t + 2d
Explanation:
t and d are being multiplied by 2 for the amount of work done by each.
HELP ME PLEASE WITH GIVE YOU BRANLEST 20 POINTS
Answers
Answer:
A: 1min 12sec B: 1 lap C: 25min and 12 sec
Step-by-step explanation:
A: 5/6 = 1/x (ratio of the laps and time)=1 min 12sec
B: 1 lap
C: 25 minutes and 12sec
4t + 2u
w;t= 2 and u= 1
Answers
15
Step-by-step explanation:
4t + 2u²- u³
4×2=8
2×1=2²=8
1³=1
8+8-1
16-1=15
Please help i’m giving out brainliest || Q1
Answers
the answer would be a I'm my mind
there is 8 box shaded and half of one box shaded
[ 0.5 = 1/2 ]
what are 2 ratios equivalent to 2:12
Answers
Answer:
possible answers include 1:6 and 4:24
Step-by-step explanation:
think of ratios like fractions. you can simplify a fraction by dividing each number by the same factor. 2/12 = 1/6 because you divide the top and bottom by 2. now, you need ANOTHER response. if you can divide the top and bottom you can also multiply. 2/12 now multiply 2 and 12 by 2 and you get 4/24.
What is the greatest common factor of 49, 62 and 80? OA) 1 OE) 2 OC) 3 OD) 5
Answers
Answer: A (1)
Step-by-step explanation:
The way to find a common factor is by dividing the given numbers by the largest possible multiple that still gives you a whole number
A
49/1=49
62/1=62
80/1=80
This is an option
B
49/2=24.5
62/2=31
80/2=40
This is not an option, 24.5 is not a whole number
C
40/3=16.333(repeating)
This is not an option, you are not given a whole number
D
49/4=12.25
This is also not an option, 12.25 is not a whole number
Answer
Our only possible answer is A-1
Graph the direct variation that includes the point (5,4). write the equation of the line.
How do I solve this?
Answers
Answer:u have to be missing something
Step-by-step explanation:
Answer:
does the question have a graph or is it just the word problem?
here is the answer if its just the word problem
Step-by-step explanation:
y= -5x+4
hope I helped :)
Question 2 (5 points)
(01.01 LC)
Which rational number equals 0 point 1 with bar over 1? (5 points)
Question 2 options:
1)
1 over 11
2)
1 over 10
3)
1 over 9
4)
1 over 8
Answers
Answer:
3. 1 over 9 is the correct answer
Answer:
option 3 is correct.
hope it helps
11. The table below shows the cost of comic books. Number of Comic Books Total Cost (dollars) 3 3.75 5 7 8.75 10 12.50 Based on the information in the table, which is the best prediction of the cost of 12 comic books?
Answers
Answer:
$15
Step-by-step explanation:
The unit rate or how much a comic book costs = total cost ÷ number of comic books
Using any given pair, let's use the first row (3, 3.75):
Unit rate = [tex] \frac{3.75}{3} = 1.25 [/tex]
This means a comic book cost $1.25.
Therefore, 12 comic books would cost:
12 × 1.25 = $15
Can two fraction with the same numerator and different denominators be equal? Use words and numbers to explain.
Answers
Step-by-step explanation:
Since equivalent fractions do not always have the same numerator and denominator, one way to determine if two fractions are equivalent is to find a common denominator and rewrite each fraction with that denominator. Once the two fractions have the same denominator, you can check to see if the numerators are equal.
The two fractions with the same numerator and different denominators can not be equal.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A division number is a number that addresses the piece of the entire, where the entire can be any number. It is a numerator and a denominator.
The fraction is in the form of a numerator and denominator. The two fractions can be equal if and only if their numerator and denominator are equal.
The two divisions with similar numerators and various denominators can not be equivalent.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ5