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yaroslaw [1]
3 years ago
10

25 Points!! The graph represents the first three terms in an arithmetic sequence.

Mathematics
2 answers:
atroni [7]3 years ago
7 0

Answer:

I solved the sum and added it in the attachment!

Drupady [299]3 years ago
4 0

Answer:

Step-by-step explanation:

y-1=\frac{4-1}{2-1}(x-1)\\y-1=3(x-1)\\y=3x-3+1\\y=3x-2

b.

an=an-1+3

C.

when x=15

y=3×15-2=45-2=43

a15=43

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Consider the quadratic function f(x)=−x^2+x+30
yaroslaw [1]

Answer:

The smallest xx-intercept is x = -5

The largest xx-intercept is x = 6

The yy-intercept is y = 30.

Step-by-step explanation:

Given a quadratic function in the following format:

f(x) = ax^{2} + bx + c = 0, a \neq 0

The x-values of the x-intercepts are x_{1}, x_{2}, given by the following formulas.

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

We have that:

f(x) = -x^{2} + x + 30

This is not in the format above. I will multiply by (-1), so we have:

f(x) = x^{2} - x - 30

So, a = 1, b = -1, c = -30

\bigtriangleup = b^{2} - 4ac = (-1)^{2} - 4*(1)*(-30) = 1 + 120 = 121

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a} = \frac{-(-1) + \sqrt{121}}{2(1)} = \frac{12}{2} = 6

x_{2} = \frac{-b + \sqrt{\bigtriangleup}}{2*a} = \frac{-(-1) - \sqrt{121}}{2(1)} = \frac{-10}{2} = -5

This means that

The smallest xx-intercept is x = -5

The largest xx-intercept is x = 6

The y-intercept is the value of f(x) when x = 0. So

f(x)=−x^{2}+x+30

f(0) = 30

The yy-intercept is y = 30.

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3 years ago
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