1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tatiyna
3 years ago
8

2. Determine the sum of the first 400 ODD numbers.​

Mathematics
1 answer:
il63 [147K]3 years ago
3 0

Odd numbers take the form 2n-1, where n\ge1 is an integer. When n=400, the last odd number would be 799. So we're adding

S=1+3+5+\cdots+795+797+799

By reversing the order of terms, we have

S=799+797+795+\cdots+5+3+1

and we can pair up terms in both sums at the same position to write

2S=(1+799)+(3+797)+(5+795)+\cdots(795+5)+(797+3)+(799+1)

so that we are basically adding 400 copies of 800, and from there we can find the value of the sum right away:

2S=400\cdot800\implies S=160,000

###

We could also make use of the formulas,

\displaystyle\sum_{i=1}^n1=n

\displaystyle\sum_{i=1}^ni=\dfrac{n(n+1)}2

We have

S=\displaystyle\sum_{i=1}^{400}(2i-1)=2\sum_{i=1}^{400}i-\sum_{i=1}^{400}1=400(400+1)-400=400^2=160,000

You might be interested in
A raffle prize of 14x^2/15dollars is to be divided among 7x people. Write an expression for the amount of money that each person
vladimir2022 [97]

For this case we must divide the following expression:

\frac {\frac {14x ^ 2} {15}} {7x}

And in this way we get the amount of money that each person will receive.

Then applying double C we have:

\frac {14x ^ 2} {15 * 7x} =\\\frac {14x ^ 2} {105x} =\\0.133x

Thus, each person has 0.133x of money!

Answer:

0.133x

7 0
3 years ago
Find the zeros, vertical asymptote, horizontal asymptote, slant asymptote, and graphing points.
kramer
Zeroes
set numerator to zero
x^2=0
x=0
zeroes are at (0,0)

HA

for p(x)/q(x)

when degree of p(x)<q(x), HA=0

when degree of p(x)=q(x), HA= leading coef of p(x) divided by leading coef of q(x)

when degree of p(x)>q(x) you probably have a slant assymtote

degrees are same (no slant assymtote)

leading coefs

1/1=1

HA is y=1

does it cross?

1=(x^2)/(x^2-4)

x^2-4=x^2

minus x^2 both sides

-4=0

false, it does not cross the HA



VA

simplify the fraction (it can't)

set the denomenator to zero

(x-2)(x+2)=0

VA's at x=2 and x=-2




so to graph

graph the point (0,0)

draw the lines

y=1

x=-2

x=2

reemmber, plus, minus, plus

so from left, it goes from above the HA right up to the VA of x=-2

then goes upside down U shape in between VA's going through (0,0)

then from top of VA x=2 down to y=1 then gets closer to y=1 but never touches


5 0
3 years ago
The sum of two numbers is $30$. the difference of twice the larger number and three times the smaller number is $5$. what is the
Shtirlitz [24]
X+y=30
2x-3y=5

y=30-x

2x-3(30-x)=30
2x-90+3x=30
5x=120
x=24

y=30-x
y=30-24
y=6

The positive difference between the two numbers is 18.
8 0
3 years ago
If 6×2 + 6y2 = 13xy, what is the ratio of x to y?
barxatty [35]

Answer:

Since 6X2 + 6Y2 = 13 xy

-- 6X2 / XY + 6Y2/XY =13

---> 6 X/Y + 6 Y/X =13

    6a + 6/a =13

--->  6a2  + 6 =13a

---> 6a2 -13a +6 =0

--->  6a2 -9a - 4a +6 =0

---> (2a-3) (3a-2) =0

2a-3 = 0

a= 3/2  

So the Ratio will be = 3:2

4 0
3 years ago
What is the answer to this question?
Inessa05 [86]

Answer: D. is the correct answer

7 0
3 years ago
Read 2 more answers
Other questions:
  • Are all whole numbers rational numbers
    14·1 answer
  • How many es does 45 go in two 855
    13·2 answers
  • An investor bought an antique table for $6000. He paid 5% as a deposit and borrowed the remainder from a bank for two years at 1
    14·1 answer
  • What is (-47/10)-(53/10) is it -3/5 or -10 the calculator says -10 I say -3/5
    12·2 answers
  • the radio of girls to boys in the junior high band is 5 to 7. At the beginning of the year, there were 72 students in the band.
    15·1 answer
  • Carrie is making a map of her favorite park, using a coordinate system with units of yards. The merry-go-round is at position (4
    12·1 answer
  • Help please with this math ;-; I beg of you
    9·2 answers
  • Please help will give brainliest please
    14·1 answer
  • Select the true statements about the number line
    6·2 answers
  • 7n-(4n-3) combining like terms with negative coefficient and distribution
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!