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2 years ago

Use inductive reasoning to find the 10th term in the sequence 5, 8, 11, 14, ...

Mathematics

1 answer:

velikii [3]2 years ago

3 0

Answer: 32

Step-by-step explanation: this is arithmetic sequence

general formula = a+(n-1)d

nth term = 5+(n-1)3

=5+3n-3

=2+3n

10th term = 2+3(10)

=32

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Use the graph or table to write a linear function that relates y to x.

fredd [130]

Answer:

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Step-by-step explanation:

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3 years ago

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Which of the following are the coordinates of the vertex of y = −x2 + 2x + 1? (2, 1) (1, –2) (1, 2) (–2, 1)

IceJOKER [234]

Answer:

Step-by-step explanation:

We want to determine the vertex of the quadratic equation:

$\displaystyle y = -x^2 + 2x + 1$

Recall that the vertex is given by the formulas:

$\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$

In this case, a = -1, b = 2, and c = 1.

Determine the x-coordinate of the vertex:

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To determine the y-coordinate, evaluate the function at x = 1:

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In conclusion, the vertex of the quadratic equation is (1, 2).

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3 years ago

Determine whether each of these functions is O(x^2 ).

otez555 [7]

Answer:

(a) no
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(d) no

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"Of the order x^2" means the dominant behavior matches that of x^2 as x gets large. For polynomial functions, the dominant behavior is that of the highest-degree term.

For other functions, the dominant behavior will typically be governed in some other way. Here, the rate of growth of the x·log(x) function is determined by log(x), which has decreasing slope as x increases.

Only answer selection B has a highest-degree term of x^2, so only that one exhibits O(x^2) behavior.

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