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vagabundo [1.1K]
3 years ago
7

Help finding the sum

Mathematics
1 answer:
Mamont248 [21]3 years ago
5 0
It is asking you to find the sum of k^2 - 1 from k=1 to k=4. Since that is only 4 numbers, calculating the sum by hand wouldn’t be that bad.

(1^2 - 1) + (2^2 - 1) + (3^2 - 1) + (4^2 - 1) = 26

The easier way to find the sum is to use a few simple formulas.

When we have a term that is just a constant c, the formula is c*n.

When we have a variable k, the formula is k*n*(n+1)/2.

When we have a squared variable, the formula is k*n*(n+1)*(2n+1)/6.

In this case, we have a squared variable k^2 and a constant of -1.

So plug in n=4 to the formulas:

4*5*9/6 - 1*4 = 26

The answer is 26







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Circle theorems please help
suter [353]

Answer:

n = 28°

Step-by-step explanation:

The angle at the centre is twice the angle on the circle subtended on the same arc.

Also angles subtended on the same arc are congruent , thus

m = n

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70 + m = 98 ( subtract 70 from both sides )

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You have 10 liters of juice that is 40% juice and 60% water. You want the mixture to be 70% juice and 30% water. How many liters
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Answer:

14 liters

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10 liters : 4 liters of juice and 6 liters of water

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82 children visit a sports centre.
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Can someone help me with system of equations?
umka21 [38]

#1)

Answer:

x=1 and y=12

Explanation:

y=5x+7

y=2x+10

This system should use substitution because the value of y is given in terms if x.

Substitution:

5x+7=2x+10

Solve:

3x=3

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Substitute x to solve for y by plugging x into one if the original equations(doesn’t matter which one is used).

y=5x+7

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y=5+7

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#2)

Answer:

x=-8 and y=2

Explanation:

y=2x+18

9y=-2x+2

This system also uses substitution. The value of y us already given in terms if c in the first equations, so we will substitute in the second equation.

Substitute:

9(2x+18)=-2x+2

Solve:

18x+162=-2x+2

20x=-160

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Now that we have the value if x, plug it into one of the original equations(doesn’t matter which equation) and substitute to find y.

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7 0
4 years ago
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