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3 years ago

The sum S of the first n integers is given by the formula S=1/2n(n+1). How many integers must be taken to have a sum of

Mathematics

1 answer:

statuscvo [17]3 years ago

5 0

Answer:

Step-by-step explanation:

We require to solve for n, hence

$\frac{1}{2}$ n(n + 1) = 325

multiply both sides by 2 to eliminate the fraction

n(n + 1) = 650

n² + n = 650

subtract 650 from both sides to have equation in standard form

n² + n - 650 = 0 ← in standard form

(n + 26)(n - 25) = 0 ← in factored form

equate each factor to zero and solve for n

n + 26 = 0 ⇒ n = - 26

n - 25 = 0 ⇒ n = 25

however, n > 0 ⇒ n = 25

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x+2y+2z=3. 2x-2y-z=3. x-2z=-5

d1i1m1o1n [39]

Answer:

x = 1, y = -2, z = 3.

Step-by-step explanation:

x + 2y + 2z = 3 A

2x -2y - z = 3 B

x - 2z = -5 C

If we add equations A and B we eliminate y:

3x + z = 6 E

Multiply E by 2 :

6x + 2z = 12 F

Adding C and F we get:

7x = 7

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Plug this into equaton C:

1 - 2z = -5

-2z = -5 - 1 = -6

z = 3.

Now plugging x = 1 and z = 3 in equation A:

1 + 2y + 2(3) = 3

2y = 3 - 1 - 6 = -4

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2 years ago

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2 years ago

How to find the missing side of a triangle

Akimi4 [234]

Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

Serena has attached a 10 inch ribbon to the corners of a frame to hang it on the wall. The frame 9 inches wide. How far above th

kherson [118]

Answer: The hook would be 2.2 inches (approximately) above the top of the frame

Step-by-step explanation: Please refer to the picture attached for further details.

The top of the picture frame has been given as 9 inches and a 10 inch ribbon has been attached in order to hang it on a wall. The ribbon at the point of being hung up would be divided into 5 inches on either side (as shown in the picture). The line from the tip/hook down to the frame would divide the length of the frame into two equal lengths, that is 4.5 inches on either side of the hook. This would effectively give us two similar right angled triangles with sides 5 inches, 4.5 inches and a third side yet unknown. That third side is the distance from the hook to the top of the frame. The distance is calculated by using the Pythagoras theorem which states as follows;

AC^2 = AB^2 + BC^2

Where AC is the hypotenuse (longest side) and AB and BC are the other two sides

5^2 = 4.5^2 + BC^2

25 = 20.25 + BC^2

Subtract 20.25 from both sides of the equation

4.75 = BC^2

Add the square root sign to both sides of the equation

2.1794 = BC

Rounded up to the nearest tenth, the distance from the hook to the top of the frame will be 2.2 inches