find all natural numbers n such that 1+3+5+7+...+(2n-1) sum is divisible by 4
Answers
n ∈ natural even numbers
Step-by-step explanation:
1 + 3 + 5 + 7 + … + (2n-1)
a = 1b = 2Uₙ = 2n - 1sum of the first n terms :
Sₙ = n/2(a + Uₙ)
Sₙ = n/2(1 + 2n - 1)
Sₙ = n/2(2n)
Sₙ = n²
∴ so, the solution of n is all natural even numbers
Refer to the attachment
Related Questions
For Exercises 8 and 9, find the lengths of all three sides of the triangle.
Answers
9514 1404 393
Answer:
8. GH = 49; HJ = 35; JG = 35
9. KL = 26, LM = 26, MK = 20
Step-by-step explanation:
8. The sides opposite the marked angles are congruent.
JG = JH
3x +8 = 35
3x = 27 . . . . . . . subtract 8
x = 9 . . . . . . . divide by 3
We already know JG and JH, so we only need to find GH:
GH = 6x -5 = 6(9) -5 = 54 -5 = 49
Then the side lengths are ...
GH = 49, HJ = 35, JG = 35
__
9. This, too, is an isosceles triangle.
LK = LM
26 = 2y+8
18 = 2y . . . . . . . subtract 8
y = 9 . . . . . . . divide by 2
KM = 3(9) -7 = 27 -7 = 20
Then the side lengths are ...
KL = 26, LM = 26, MK = 20
A class contributed $19.00 in quarters and dimes to a local homeless shelter. In
all there were 100 coins. How many were there of each kind.
Answers
Answer: 60 quarters and 40 dimes
Step-by-step explanation:
Step 1: Setup Coin Value and Coin Total Equation:
Coin Value Equation → 0.1d + 0.25q = $19.00 where d = dimes and q = quarters
Coin Total Equation → d + q = 100
Step 2: Rearrange Coin Total Equation in terms of dimes (d)
d = 100 - q ← Revised Coin Total Equation
Step 3: Plug in our Revised Coin Total Equation for d into our Coin Value Equation:
0.1(100 - q) + 0.25q = $19.00
0.1(100) - 0.1(q) + 0.25q = $19.00
10 - 0.1q + 0.25q = $19.00
10 + (0.25 - 0.1)q = $19.00
10 + 0.15q = $19.00
Step 4: Subtract 10 from each side of the equation to isolate q
10 - 10 + 0.15q = $19.00 - 10
0.15q = 9
Step 5: Divide each side of the equation by 0.15 to isolate q
0.15q/0.15 = 9/0.15
q = 60
Step 6: Using our value for q, Solve for d using our Coin Total Equation:
d + 60 = 100
Subtracting 60 from both sides, we get d + 60 - 60 = 100 - 60
d = 40
Summarizing our word problem, we see that 60 quarters and 40 dimes add up to $19.00
what is 8x6huhvgjjjjhhjhojhkojkljfkgjkjkgjkdfjkfdjtjrjgjhghhjghtrht4khtrgvgjbhhjjhjhjj
Answers
Answer:
48
Step-by-step explanation:
The answer to 8x6 is 48.
the correct answer to 8x6 is 48
help!!
A bank building in the downtown area stands 42 feet tall. if the high rise office building is 102 times as tall as the bank building, how tall is the office building
Answers
Answer:
4284 feet tall
Step-by-step explanation:
42*102=4284 feet
fully simplify (2x^4-y)^2
Answers
Answer:
Here's ur answer:)
Step-by-step explanation:
what is the reciprocal of -9/8?
Answers
the reciprocal is 8/-9 just reverse the numbers
10r = –50 solve for r
Answers
Answer:
10r=-50
r = -50/10
r = -5
.........
Enrique wants a skateboard that cost $68.00. The sales-tax rate in his city is 612% . What is the total cost of the skateboard?
Answers
[tex]\large \boldsymbol {100\%=1} \\\\ \boldsymbol {612\%=6,12} \\\\ \rm Total \ \ cost :\\\\ \$68=6,12\cdot 68=\boxed { \$416,16}[/tex]
Kerri sold her purse for $351. She had originally purchased it for $316. Calculate her profit or loss percentage.
Answers
Answer:
she made a profit of $35
Step-by-step explanation:
351-316=35
Answer: profits by $35, gained 11%
Step-by-step explanation:
Which equations are in standard form? Check all that apply
y = 2x + 5
2x + 3y = -6
o 4x+3y = 12
Oy=x-9
=
Olx 3 = 6
0 *x+3 = 6
2 3
O x-y = 5
5x + 3y = 1
Answers
Answer:
2x + 3y = -6
4x + 3y = 12
x - y = 5
5x × 3y = 1
Step-by-step explanation:
Standard form formula ➡ Ax + By = C
Hope this helped :)
2. Find the value of x.
Answers
Answer:50
Step-by-step explanation:
The table shows the heights that four people parachute from an airplane. What is the range of the heights? Write your answer as a decimal or fraction in simplest form
Answers
The range is 7/20 of a mile.
Abbie is twice as old as susan susan is 5 year old than Marc how old is Marc?
9
7
5
2
Answers
Answer:
9
Step-by-step explanation:
Answer:
A.) 9
Step-by-step explanation:
This is so hard and I don’t know why
Answers
Answer:
Hey girl! I got you.
Step-by-step explanation:
So! The angle x and z are congruent, meaning that they are equal, so you got that part correct. They are indeed 103. Next you need to find y, and in this case you need to do 180 - 103 because the line that holds both angle z and angle y is equal to 180.
180 - 103 = 77, you got that correct also!
You're on the right track, just explain in words how you know what each angle is equal to! Good luck! :)
The accompanying graph is a sketch of the function
y = f(x) over the interval 0 SXS 7.
What is the value of (f. f)(6)?
1) 1 2) 2 3) (4) -2
Answers
A composite function combines two or more functions to generate a new function.
The value of [tex]\mathbf{f(f(6))}[/tex] is -2
The require parameter is:
[tex]\mathbf{f(f(6))}[/tex]
First, we calculate f(6)
From the graph (see attachment)
[tex]\mathbf{f(6) = 2}[/tex]
So, the function [tex]\mathbf{f(f(6))}[/tex] becomes:
[tex]\mathbf{f(2)}[/tex]
In other words,
[tex]\mathbf{f(f(6)) = f(2)}[/tex]
Next, we calculate f(2)
From the graph
[tex]\mathbf{f(2) = -2}[/tex]
So:
[tex]\mathbf{f(f(6)) = -2}[/tex]
Hence, the value of [tex]\mathbf{f(f(6))}[/tex] is -2
Read more about composite functions at:
https://brainly.com/question/20379727
What is the measure of angle A′OB′?
Answers
Answer:79°
Step-by-step explanation:
In which situation will Kiyo end up in the same location as where she started?
Kiyo walks 3 steps forward, 9 steps backward, and 3 steps forward.
Kiyo walks 17 steps backward, 20 steps forward, and 2 steps backward.
Kiyo walks 7 steps forward, 10 steps backward, and 3 steps forward.
Kiyo walks 12 steps backward, 16 steps forward, and 8 steps backward.
GIVING BRAINLY
Answers
Answer:
In third condition
Step-by-step explanation:
In,
Kiyo walks 7 steps forward, 10 steps backward, and 3 steps forward.
which of the following best describes a sequence?
A.a linear equation
B.a list of numbers
C.a procedure for getting the answer
D.events that happen in definite order
Answers
Answer:
b.a list of numbers
Step-by-step explanation:
bbbbbbbbbbbbbbbbbb
plz help me i don’t understand
Answers
Answer:
A it wold be pushing 40 newton to the left
B opposite
C subtract
D i don know that one
E unbalanced
Step-by-step explanation:
Which equation best represents the line graphed above?
Answers
Answer:
the first one is correct
y=1/2x-1
HELP ME PLEASE PLEASE PLEASE
Answers
Answer:
See belowStep-by-step explanation:
A → Rational function = function with rational variablesB → Rational equation = equation with rational variablesC → Rational inequality = inequality with rational variablesD → None of these = variables with rootsGrouped as following:
A ⇒ 4, 5, 13B ⇒ 1, 2, 8, 11, 15C ⇒ 3, 6, 12D ⇒ 7, 9, 10, 14Given: 5n - 42 = 12n; Prove: n = -6
Statements and reasons
Answers
Answer:
yes n is -6
Step-by-step explanation:
b/c 5(-6)-42=12(-6)
-30-42=-72
-72=-72
Please help me due soon
Answers
Answer:
Ima say c but I'm not totally sure soo :)
Step-by-step explanation:
Step-by-step explanation:
answer is D
-5/3
because more the negative,lesser the value
ELPPP I SUCK AT THIS
I didnt mean to press 79 but it wouldn't let me unclick it I can still change my answer tho
Answers
Answer:
79
Step-by-step explanation:
80 divided by 8+72-3
10+72-3
82-3
79
Hope this helps!
Enter the ordered pair for the vertices for r (90°, 0)(QRST).
Answers
Answer:
below
Step-by-step explanation:
I didn't see the picture you try to post... but, the formula for rotation counterclockwise 90° is (x,y) original -> (-y,x) rotated
For rotation clockwise 90°: (x,y) -> (y,-x)
ry+r= x - t solve for x
Answers
Answer:
Step-by-step explanation:
ry+r=x-t
ry+r+t=x
x=r(y+1)+t
Solve for x ... please help me
Answers
Answer:
It is letter A
please i don’t wanna fail just give me the right answer thanks<3
Answers
Answer:
number of photos: 8, 12, 20, 28, 40
time (minutes): 2, 3, 5, 7, 10
Step-by-step explanation:
4W
3. Jenny is having a party. She has one
large container of soda with 179 ounces
in it. A second container holds 128
ounces, but half of it has already been
used. If there are 12 people at the party,
how much soda can each person have?
1
Answers
Answer: 25.5833333 or rounded is 26
Step-by-step explanation:
179+128=307
307 divided by 12 is 25.5833333
A kindergarten teacher bought $21 worth of stickers and cardstock for his class. The stickers cost $1.50 a sheet and the cardstock cost $3.50 per pack. The equation LaTeX: 1.5s+3.5c=21 represents the relationship between sheets of stickers, LaTeX: s, packs of cardstocks, LaTeX: c, and the dollar amount a kindergarten teacher spent on these supplies.
Answers
Answer:
Done
Step-by-step explanation:
Teacher bought $21 worth of stickers and cardstock for his class.
Cost of stickers = $1.50 per sheet
Cost of 's' sheets = $1.5s
Cost of cardstock = $3.50 per pack
Cost of 'c' packs = $3.5c
Equation representing the relationship between sheet of stickers and packs of cardstocks will be,
1.5s + 3.5c = 21
3.5c = -1.5s + 21
1).
y-intercept of the line → (0, 6)
x-intercept of the line → (14, 0)
Therefore, equation of the line represents the line on the graph.
2). Vertical intercept (0, 6) represents that he can purchase maximum 6 packs of cardstock with $21.
Similarly, horizontal intercept (14, 0) represents that he can purchase maximum 14 sheets of stickers with $21.
