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Phantasy [73]
2 years ago
13

Prime number 157, 1057, 263, 3163

Mathematics
1 answer:
Sergio [31]2 years ago
5 0
157, 263, and 3163 are all prime numbers
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The function y = x 2 - 10x + 31 has a ____
katrin [286]

Answer:

Option B. minimum is correct for the first blank

Option C. 6 is correct for second blank.

Step-by-step explanation:

In order to find the maxima or minima of a function, we have to take the first derivative and then put it equal to zero to find the critical values.

Given function is:

f(x) = x^2-10x+31

Taking first derivative

f'(x) = 2x-10

Now the first derivative has to be put equal to zero to find the critical value

2x-10 = 0\\2x = 10\\x = \frac{10}{2} = 5

The function has only one critical value which is 5.

Taking 2nd derivative

f''(x) =2

f''(5) = 2

As the value of 2nd derivative is positive for the critical value 5, this means that the function has a minimum value at x = 5

The value can be found out by putting x=5 in the function

f(5) = (5)^2-10(5)+31\\=25-50+31\\=6

Hence,

<u>The function y = x 2 - 10x + 31 has a minimum  value of 6</u>

Hence,

Option B. minimum is correct for the first blank

Option C. 6 is correct for second blank.

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3 years ago
The government department responsible for laws concerning work is the _____.
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2 years ago
The function f(x) is a quadratic function and a limited table of values is provided below. Write the equation of the quadratic p
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Answer:

  f(x) = 3x^2 -21x +36

Step-by-step explanation:

The table gives the x- and y-intercepts, which are sufficient to write the equation in factored form. The x-intercepts of 3 and 4 tell you that factors are (x -3)(x -4). When x=0, this product is (-3)(-4) = 12, but the y-intercept value is 3 times that: 36. So, the factored equation is ...

  f(x) = 3(x -3)(x -4)

Multiplying this out, we get ...

  f(x) = 3(x^2 -7x +12)

  f(x) = 3x^2 -21x +36

4 0
3 years ago
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