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2 years ago

Find the sum of 997 + 992 + 987 +...+ 257 +252

Mathematics

1 answer:

Vikentia [17]2 years ago

7 0

Answer:

93,675

Step-by-step explanation:

We see that the given sequence is an arithmetic sequence with first term 997, common difference -5, and last term 252.

The number of terms in the sequence (n) can be found from the formula for the n-th term:

an = a1 +d(n -1)

(an -an)/d +1 = n

(252 -997)/(-5) +1 = n = 150

The sum of these terms is the average of the first and last terms, multiplied by the number of terms:

S150 = (997 +252)/2·150 = 93,675

The sequence sum is 93,675.

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Which of these statements is correct?

tatuchka [14]

Answer:

The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution is correct.

Step-by-step explanation:

1) The system of linear equations 6x - 5y = 8 and 12x - 10y = 16 has no solution.

Solve these linear equations simultaneously

Step 1 : Find y in terms of x from any one equation

6x - 5y = 8

y = 8 - 6x

-5

Step 2 : Substitute y in terms of x from step 1 in the second equation.

16x - 6y = 22

16x - 6 (8 - 6x) = 22

-5

80x - 48 + 36x = 22 x -5

94x = 43

x = 0.457

This statement is incorrect as it does have a solution.

2) The system of linear equations 7x + 2y = 6 and 14x + 4y = 16 has an infinite number of solutions.

Solve these linear equations simultaneously

Step 1 : Find y in terms of x from any one equation

7x + 2y = 6

y = 6 - 7x

Step 2 : Substitute y in terms of x from step 1 in the second equation.

14x + 4y = 16

14x + 4(6 - 7x) = 16

14x + 12 - 14x = 16

0 ≠ 4

This statement is not true as there are no solutions.

3) The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution.

Solve these linear equations simultaneously

Step 1 : Find x in terms of y from any one equation

8x - 3y = 10

x = 10 + 3y

Step 2 : Substitute x in terms of y from step 1 in the second equation.

16x - 6y = 22

16(10 + 3y) - 6y = 22

20 + 6y - 6y = 2

0 ≠ -18

This statement is true because there are no solutions

4) The system of linear equations 9x + 6y = 14 and 18x + 12y = 26 has an infinite number of solutions.

Solve these linear equations simultaneously

Step 1 : Find x in terms of y from any one equation

9x + 6y = 14

x = 14 - 6y

Step 2 : Substitute x in terms of y from step 1 in the second equation.

18x + 12y = 26

18 (14 - 6y) + 12y = 26

8 - 12y + 12y = 26

0 ≠ 18

This statement is incorrect because there are no solutions. It does not have infinite number of solutions.

!!

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MATH SMARTIES I WILL GIVE BRAINLIEST AND CAN YOU EXPLAINE WHY YOU THINK ITS THAT ANSWER (SHOW WORK) SO I CAN UNDERSTAND THANK YO

Katen [24]

Answer:

gasoline

Step-by-step explanation:

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Write the equation of the line that passes thriugh the points (3,-2) and (5,-9)?

Tanya [424]

Answer:

y = -7/2x + 17/2

Step-by-step explanation:

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4 0

2 years ago

A spinner used in a board game is divided into 12 equally sized sectors. Seven of these sectors indicate that the player should

xeze [42]

Answer:

20.8 inches squared

Step-by-step explanation:

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45.1 is the area of sectors where the token doesn't move, which 5 sectors doesn't move the token (don't forget that the bonus points doesn't move token). Then

45.1/5=9.02

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108.24=1/2(r^2)sin150

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3 years ago

What is the most efficient first step to isolate the variable term on one side of this equation?

Nat2105 [25]

Answer:subtract by 4x on each side first

Step-by-step explanation:

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