prove the difference of the squares of two successive intergers is equal to the sum of the intergers
Answers
Answer:
[tex]\displaystyle \begin{aligned} \displaystyle (n+1)^2 - n^2 &= 2n +1 \\ &= n (n+1)\end{aligned}[/tex]
Where ? = 2.
Step-by-step explanation:
We want to prove that the difference of the squares of two successive integers is equal to the sum of the integers.
In other words, we want to show that for any given integer n:
[tex]\displaystyle (n+1)^2 - n^2 = n + (n+1)[/tex]
From the original equation, expand:
[tex]\displaystyle = (n^2 + 2n + 1) - n^2[/tex]
Combine like terms:
[tex]= 2n +1[/tex]
And rewrite. Hence:
[tex]\displaystyle = n + (n + 1)[/tex]
Therefore:
[tex]\displaystyle \begin{aligned} \displaystyle (n+1)^2 - n^2 &= 2n +1 \\ &= n (n+1)\end{aligned}[/tex]
In conclusion, ? = 2.
Related Questions
solve for x, need help asap!
Answers
Let's solve for x using trigonometric relation ( Cos )
we know,
[tex] \cos(30 \degree) = \dfrac{base}{hypotenuse} = \dfrac{ \sqrt{3} }{2} [/tex]
now
[tex] \dfrac{x}{8} = \dfrac{ \sqrt{3} }{2} [/tex]
[tex]x = 8 \times \dfrac{ \sqrt{3} }{2} [/tex]
[tex]x = 4 \sqrt{3} [/tex]
hence, the value of x is [tex] 4 \sqrt{3} [/tex]
7 divided by 345689
Answers
Answer:
Do you mean 345689/7 if so it equals this 49384.1428571. If you didn't and you mean 7/345689 it equals this. 0.00002024941
what number divided by four equals three?
Answers
Answer:
12 divided by 4 equals 3
Step-by-step explanation:
Kelly said that 97/1000 can be written as 0.97 is correct? Explain.
Answers
Answer:
No
Step-by-step explanation:
To write 97/1000 as a decimal you have to divide numerator by the denominator of the fraction.
We divide now 97 by 1000 what we write down as 97/1000 and we get 0.097
And finally we have:
97/1000 as a decimal equals 0.097
HELP PLS
Given the exponential function f(x) and the logarithmic function g(x), which of the following statements is true?
*Exponential function f of x equals 3 to the power of x minus 1 that increases to the right passing through the point 0 comma 0 and logarithmic function g of x equals log in base 3 of x minus 3 increasing from left to right passing through the point 1 comma negative 3
A. As x approaches infinity, f(x) approaches infinity, and g(x) approaches 0.
B. As x approaches infinity, f(x) approaches 2, and g(x) approaches 0.
C. As x approaches infinity, f(x) approaches 2, and g(x) approaches infinity.
D. As x approaches infinity, f(x) approaches infinity, and g(x) approaches infinity.
Answers
Answer:
As x→∞, f (x)→∞ and g(x)→∞.
Step-by-step explanation:
Looking at the graph there is no asymptote interrupting either f(x) or g(x) so when the graphs will continue on they will just approach infinity. Also just took this assessment and got a 100%.
For the following system of equations, determine how many solutions there are. y = 5(x − 4) and 4x + 12 = −y
Answers
Answer:
It has two solutions
Step-by-step explanation:
[tex]y = 5(x - 4)[/tex]
substitute for y in second equation:
[tex]4x + 12 = - y \\ 4x + 12 = - \{5(x - 4) \} \\ 4x + 12 = - 5x + 20 \\ 9x = 8 \\ x = \frac{8}{9} [/tex]
then for y:
[tex]y = 5(x - 4) \\ y = 5( \frac{8}{9} - 4) \\ \\ y = 5( - \frac{28}{9} ) \\ \\ y = - \frac{140}{9} [/tex]
HELP ME PLS!!!!!!!!
Answers
9514 1404 393
Answer:
$58
Step-by-step explanation:
James currently has $67 less than $125:
$125 -67 = $58
James currently has $58.
A line passes through the point (-6,-9) and has a slope of . Write an equation in slope-intercept form for this line.
Answers
Answer:
y = [tex]\frac{5}{2}[/tex]x + 6
Step-by-step explanation:
Solve for y: -5(2y+3) +5=40
Answers
Answer:
Step-by-step explanation:
-5(2y + 3) +5 = 40
-10y - 15 + 5 = 40
-10y = 40 +15 - 5
-10y = 50
y =[tex]\frac{50}{-10\\}[/tex]
y = -5
Find the value of x 8/x=6/30
Answers
Answer:
x = 40
BRAINLIEST, PLEASE!
Step-by-step explanation:
8/x = 6/30
8/x = 1/5
x = 8/(1/5)
x = 8(5)
x = 40
At the zoo the polar bears are fed 0.1 bucket of fish a day.
The penguins are fed 0.83 that amount. How much of a
bucket are the penguins fed?
Answers
Answer:
0.083
Step-by-step explanation:
0.1 x 0.83 = 0.083
There are 0.083 bucket are the penguins fed.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
At the zoo the polar bears are fed 0.1 bucket of fish a day.
And, The penguins are fed 0.83 that amount.
Now,
Since, At the zoo the polar bears are fed 0.1 bucket of fish a day.
And, The penguins are fed 0.83 that amount.
Hence, The bucket are the penguins fed is,
⇒ 0.83 × 0.1
⇒ 0.083
Learn more about the multiplication visit:
brainly.com/question/10873737
#SPJ2
what is the equivalent ratio of 24 to 6
Answers
Answer:
1/4
Step-by-step explanation:
24/6
4
4+4+4+4+4+4
brainiest to whoever right
Answers
Answer:
(x - 6)(x + 2)
Step-by-step explanation:
x^2 - 4x - 12
=x^2 - 6x + 2x - 12
=x( x - 6) + 2(x - 6)
=(x - 6)(x + 2)
Answer:
x^2 -4x-12
factorization of 12 =2×2×3 = 6×4
or in the place of 4x = we put (6-2)x
x^2-(6-2)x-12
x^2-6x+2x-12
x(x-6)+2(x-6)
(x-6) (x+2)
) A real estate agent sells a unit for $800 000. The commission rate is 2.75% of the selling price. Calculate the commission. (A) $25 000 (B) $27 750 (C) $220 000 (D) $22 000
Answers
Answer:
The answer is (D) $22 000
Step-by-step explanation:
800,000/100 = 8,000
I did this to show 1% of 800,000 is 8,000 (To find 1% of a number always divide it by 100)8,000*2.75=22,000
I did this because since I know 8,000 is 1% percent of the price I can times it by the percentage rate to find how much the commission is. Also note that there are other ways to solve this equation that may suit you better, this is the way I do it and I find it much more faster.If 2/5 of a pole is 3:6,what will be the length of 5/9 of it?
Answers
Answer:
Ans : the length of 5/9 is 5m
which fractions is equivalent is 6/10
1.3/5
2.9/12
3.20/50
4.40/50
Answers
Answer:
1 as
3/5 × 2/2 = 6/10
Step-by-step explanation:
Hope it helps
3. A sea gull was flying 4 feet above sea level when a fish below it jumped one foot out of the water. How far apart were the seagull and the (unlucky) fish?
Answers
Answer: 3ft difference
Step-by-step explanation:
Seagull = +4ft
Fish = +1ft (since it jumped 1ft above sea level)
4-1 = 3ft difference
Describe how many zeros this equation will have, and where they are.
(1 Point)
f (x) = -2x2 – 5x – 2
Answers
Answer:
Let y=x
2
−5x+6, when we substitute different values of x in the equation y=x
2
−5x+6 then value of y changes accordingly.
When x=0 then
y=(0)
2
−(5×0)+6=0−0+6=6
The point is (0,6)
When x=2 then
y=(2)
2
−(5×2)+6=4−10+6=10−10=0
The point is (2,0)
When x=3 then
y=(3)
2
−(5×3)+6=9−15+6=15−15=0
The point is (3,0)
Therefore, the coordinates are (0,6), (2,0) and (3,0) and the graph of the quadratic equation y=x
2
−5x+6 is as shown above.
Hence, from above graph, we get that x=2 or x=3.
_____ - (-5) = -15
pls help
Answers
Answer:
[tex]x - ( - 5) = - 15 \\ x + 5 = - 15 \\ x = - 15 - 5 \\ x = - 20 \\ thank \: you[/tex]
Answer:
y-(-5)=-15
y+5=-15
y=-15-5
y=-20
1.2.PS-9
Which numbers are rational?
8
11
7, 3.41, 0,
2
-9
3'
Select all that apply.
Answers
9514 1404 393
Answer:
all except π are rational numbers
Step-by-step explanation:
Any ratio of integers, terminating decimal, or repeating decimal is a rational number. Pi (π) is represented symbolically because it cannot be written exactly. It is an irrational number.
All of the numbers listed except π are rational.
Express the following as the sum of twin primes
a) 84
b)36
c)24
d)425
Answers
Answer:
answer it's c)24...
Step-by-step explanation:
i think helping you..... please tell correct or no...
what is the annual salary equivalent to a semimonthly salary of $834.08?
Answers
Answer:
$20,017.92
Step-by-step explanation:
Semimonthly means twice a month.
There are 12 months in a year.
12 x 2 = 24 (because they are payed twice a month)
24 x 834.08 = 20017.92
Plz help me with these with steps
Answers
Answer:
10. 9/40
11. $72
Step-by-step explanation:
10.
Step 1: Have the whole cake as 1,
[tex]1-\frac{1}{8} -\frac{2}{5} -\frac{1}{4}\\= 1 -\frac{5}{40}-\frac{16}{40}-\frac{10}{40} \\= \frac{9}{40}[/tex]
11.
Step 1: Find the remaning income left
[tex]1-\frac{5}{16}-\frac{1}{4}-\frac{1}{24} -\frac{1}{48} \\= \frac{3}{8} \\[/tex]
Step 2: Calculate the weekly income
3 units = $27
1 unit = $9
Weekly income = $9 * 8 = $72
PLZZZ HELP ME
Solve the equation and check your solution.
1. 3(x+6)=18+3x
2. -2(x-1)=2-2x
3. x+4=-2+x
4. -2(x+2)=5-2x
Answers
Answer:
1. 0
2.0
3.2
4.1
Step-by-step explanation:
1.3x+18
2.-2x+2
3.x-x+4-2
5-2x-2+5-2x
Answer:
3x + 18 = 18 + 3x-2x + 2 = 2 - 2x4 = -2 (the statement is false)-4 = 5 (the statement is false)Please help
Solve the inequality.
1
x+ z
x+-3-3 or x - 3>-2
'
7.
x <
or x >[ ]
[?]
Answers
9514 1404 393
Answer:
x ≤ -7/2 or x > 1
Step-by-step explanation:
To solve the left inequality for x, subtract 1/2 from both sides:
x ≤ -3 -1/2
x ≤ -7/2
__
To solve the right inequality for x, add 3 to both sides.
x > -2 +3
x > 1
What length of cable, rounded to the nearest foot is needed to connect the top of a 60-foot tower to an anchor point 35 feet
from the base of the tower?
A) 73
B) 67
C)69
D)64
Answers
9514 1404 393
Answer:
C) 69 ft
Step-by-step explanation:
The desired length is the hypotenuse of a right triangle with legs 35 and 60. It can be found using the Pythagorean theorem.
length = √(60² +35²) = √4825 ≈ 69.46
The length needed is about 69 feet.
An apartment building contains 250 apartments. There are 50 more 2-bedroom apartments than 1-bedroom apartments. How many apartments of each type are there
Answers
Answer:
100
Step-by-step explanation:
Answer:
100 1- bedroom and 150 2- bedroom
Step-by-step explanation:
let x be the number of 1- bedroom apartments , then
x + 50 is the number of 2- bedroom apartments , so
x + x + 50 = 250 ( subtract 50 from both sides )
2x = 200 ( divide both sides by 2 )
x = 100
There are 100 1- bedroom apartments and 100 + 50 = 150 2- bedroom
Consider the sequence of numbers 50,48,46,44….
(A) What are the next three numbers in this sequence?
(B) Using n to represent the position of a number in this sequence, write an expression that allows you to calculate the nth number.
(C) use your expression to find the 100th number in this sequence
Answers
Step-by-step explanation:
(A) 42,40
(B) T(n) = 50 + (n-1)(-2)
= 50+2-2n
= 52-2n
(C) T(100) = 52 - 2(100)
= 52- 200
= - 148
how to find the sum of 12 and 36 using the gcf and distributive property
Answers
10) Pete is fast, Repeat is 3 times faster. If
Pete and Repeat can complete the job in
56 minutes, how fast is Pete? (I want
Pete's time only)
Answers
Answer:
14 minutes
Step-by-step explanation:
if Pete is x times fast then Repeat is 3x faster
so if both combine to complete a job in 56 minutes then we have
[tex]x + 3x = 56 \\ 4x = 56 \\ x = 14[/tex]
remember Pete is x hence Pete was 14 minutes fast