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serious [3.7K]
2 years ago
11

Find the sum using the formulas for the sums of powers of integers ( problem attached )

Mathematics
1 answer:
Natasha2012 [34]2 years ago
7 0

Correct Answer: - 550

We can use the distributive property to distribute the summation to the variables and then get the constant out to apply the summation formulas as shown below in the attached image.

The equation editor does not have a summation symbol, so I have attached the solution using the image.

The correct answer to this question is -550. First option is the correct one.

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Get the x terms by themselves on one side and a constant on the other side of the equal sign...

4x^2-8x=1  make the leading coefficient equal to one...

x^2-2x=1/4  now halve the linear coefficient, -2 in this case, square it, and add that value to both sides of the equation...-2/2=-1, -1^2=1 so

x^2-2x+1=1+1/4

x^2-2x+1=5/4  now the left side is a perfect square...

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So to label the axes the number of people would be on the left and number of forks on the bottom. choosing your scale means how you would choose to count. the independent variable is the forks and dependent is the people. For the scale I would count by 2s for the x-axis and 1s for the y-axis.
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3x^2-x=10<br><br> Find factors <br><br><br> Determine zeros
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Factors are (3x + 5) and (x - 2). Zeros are -5/3 and 2.

Step-by-step explanation:

  • Step 1: Given quadratic equation 3x² - x = 10 ⇒ 3x² - x - 10 = 0
  • Step 2: Use factoring method (product and sum rule) to find factors and zeros. So the equation can be written as below.

⇒ 3x² - 6x + 5x - 10 = 0

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⇒ 3x + 5 = 0 and x - 2 = 0

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