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2 years ago

Use the approach in Gauss's Problem to find the following sums of arithmetic sequences.

Mathematics

1 answer:

Svet_ta [14]2 years ago

6 0

The total value of the sequence is mathematically given as

498501

<h3>The sum of the sequence is..?</h3>

Generally, the equation for Gauss's Problem is mathematically given as

The sum of an arithmetic series;

1+2+3+...+n= n(n+1)/2

Given an arithmetic sequence,

1+2+3+...+998,

Here,

n = 998

1+2+3+...+n=n(n+1)/2

1+2+3+...+998=98(998 + 1)/2

998 x 999 1+2+3+...+998 =2

1+2+3+...+998 = 498501

In conclusion, 498501 is the total value of the sequence.

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For an equation to have infinitely many solutions, the solution will appear as a ______ statement.

DENIUS [597]

Answer:

true

Step-by-step explanation:

for example, when you solve an equation and you get something like 16=16, which is infinitely many solutions and is also a true statement

3 0

3 years ago

Two angles of a quadrilateral are 40 degree and 60 degree and the ratio of remaining two angles is 7:6. The degree measure of re

Semenov [28]

Answer:

140,120

Step-by-step explanation:

sum of angles in a quadrilateral =360

sum of the 1st two angles=60+40=100

360-100=260

the ratio of the remaining angles 7:6

therefore:

$\frac{7}{13} \times 260$

=140

for the second angle

260-140=120

5 0

3 years ago

Stella graphs the equation y=1/3x – 2

faltersainse [42]

we have

$y=\frac{1}{3}x-2$

Statements

case A) The graph is a straight line.

The statement is True

Because, this is a linear equation (see the attached figure)

case B) The line passes through the origin.

The statement is False

Because the point $(0,0)$ is not a solution of the equation

Verify

Substitute the value of x and y in the equation

$0=\frac{1}{3}*0-2$

$0=-2$ ------> is not true

the point $(0,0)$ is not a solution

therefore

The line does not pass through the origin

case C) The line passes through the point $(0,-2)$

The statement is True

Because the point $(0,-2)$ is a solution of the equation

Verify

Substitute the value of x and y in the equation

$-2=\frac{1}{3}*0-2$

$-2=-2$ ------> is true

the point $(0,-2)$ is a solution

therefore

The line passes through the point $(0,-2)$

case D) The slope of the line is $3$

The statement is False

Because, the slope of the line is $m=\frac{1}{3}$

case E) The y-intercept of the line is $2$

The statement is False

we know that

The y-intercept is the value of y when the value of x is equal to zero

For $x=0$

find the value of y

$y=\frac{1}{3}*0-2=-2$

the y-intercept is equal to $-2$

5 0

4 years ago

Read 2 more answers

Please help me with this question and please tell me how I would put this into a calculator please...

AnnyKZ [126]

Answer:

Step-by-step explanation:

$\frac{2}{3}x+4=\frac{2}{3} *\frac{3}{1}+4 = 2+4=6$

3 0

3 years ago

To eliminate 6X you would Transform 2x by multiplying what number ?

NARA [144]

Answer:

-3

Step-by-step explanation:

to eliminate 6x we need the same no. 6x but that should be negative. so

2X × -3 = -6X

and

6X+(-6X)=0

5 0

4 years ago