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Elden [556K]
3 years ago
5

Find the sum of the first 2,000 positive integers (the numbers 1 through 2000).

Mathematics
1 answer:
MAVERICK [17]3 years ago
6 0

According to Gauss, the formula to find the sum of a series is:

S=n(n+1)/2 where n is the number of terms in the series

Since n=2000, then:

S=2000(2000+1)/2

S=4002000/2

S=2001000

The famous mathematician Gauss had used this same method to find the sum of the digits 1 to 100 while in elementary school. So the sum of the first 2000 positive integers is 2,001,000

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BabaBlast [244]

Answer:

The word "of" in the question means multiply, so you need to multiple these two fractions.

2/3 x 4/5 = 8/15

8 0
3 years ago
Read 2 more answers
Help!! Picture below
deff fn [24]

Answer:

Option A. (a/2,0)

Step-by-step explanation:

we know that

If triangle ABC is a right isosceles triangle

then

AB=AC

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the x-coordinate of the midpoint M is equal to

(0+a)/2=a/2

The coordinates of point M are (a/2,0)

7 0
3 years ago
Which of the following points lies on the circle whose center is at the origin and whose radius is 10?
Naddik [55]
Since the standard form of the circle is:

(x-h)^2+(y-k)^2=r^2, and (h,k)=(0,0) and r=10 so we have:

x^2+y^2=100   Looking at the points you have:

(√10, 0) does not work as (√10)^2+0^2=10+0=10

(0, 2√5) does not work as 0^2+(2√5)^2=0+20=20

(5√2, 5√2) works as (5√2)^2+(5√2)^2=50+50=100
6 0
4 years ago
Graphing linear equations questions 1-13
Brums [2.3K]
1. the graph of 2x + 1 = y for all real numbers will be a line. the graph with the restricted domain will be a line segment meaning it has endpoints (1, 3) and (4, 9).

2. is open ended, meaning you can make A, B, C anything you want as long as what they specify is met.
(a) A = 0
(0)x + By = C
let's make B = 1 and C = 5
y = 5

(b) B = 0
Ax + (0)y = C
let's make A = 1 and C = 5
x = 5

(c) C = 0
Ax + By = 0
let's make both A and B = 1
x + y = 0

3. plot both intercepts (x on x-axis, y on y-axis) then draw a line through the dots.

4-7. linear equations do not have exponents on any of the variables. 1/y is the same as y^(-1) so both 4 and 7 are non-linear.

8-13. you will have to graph these. put them in slope intercept form: y = mx+b if they're not already , plot the y-intercept first (0, b) then use the slope m draw the line by going rise over run.

example 13.
3x + 4y = 12
4y = -3x + 12
y = (-3/4) + 3
plot (0,3)
go down -3 , right 4 make a point.
reverse from (0,3) go up 3 left -4 and make a point. connect with line.
7 0
3 years ago
IM BEGGING YOU, IF YOU SEE THIS PLEASE TRY AND ANSWER IT!!! BRAINLIEST WOULD BE ALL YOURS!
Oksana_A [137]

Answer:

\displaystyle a_n=8+9(n-1)

<em>Correct option: C]</em>

Step-by-step explanation:

<u>Arithmetic Sequences</u>

Each term in an arithmetic sequence is obtained as the previous term plus a constant number called the common difference. The general term is

\displaystyle a_n=a_1+(n-1).r

We are given this information

\displaystyle a_1=8\ ,\ a_7=62

Replacing those values in the formula

\displaystyle 62=8+(7-1).r

Solving for r

\displaystyle r=\frac{62-8}{6}=\frac{54}{6}=9

\displaystyle r=9

The general term is, then

\displaystyle a_n=8+(n-1)9

Or equivalently

\displaystyle a_n=8+9(n-1)

Correct option: C]

5 0
3 years ago
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