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3 years ago

What is the 5th term in the following sequence: 2, 5, 11, 23... Helpppp

1 answer:

4 0

Answer:The first few Thabit numbers are: 2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 6143, 12287, 24575, 49151, 98303, 196607, 393215, 786431, 1572863, ...

...

Thabit number.

Named after Thābit ibn Qurra

First terms 2, 5, 11, 23, 47, 191, 383, 6143, 786431

Largest known term 3×211,895,718 − 1

OEIS index A007505

Step-by-step explanation:

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2 years ago

Suppose a and b are the solutions to the quadratic equation 2x^2-3x-6=0. Find the value of (a+2)(b+2).

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(a+2)(b+2) = 4

Step-by-step explanation:

We are given the following quadratic equation:

$2x^2-3x-6=0$

Let a a and b be the solution of the given quadratic equation.

Solving the equation:

$2x^2-3x-6=0\\\text{Using the quadratic formula}\\\\x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{Comparing the equation to }ax^2 + bx + c = 0\\\text{We have}\\a = 2\\b = -3\\c = -6\\x = \dfrac{3\pm \sqrt{9-4(2)(-6)}}{4} = \dfrac{3\pm \sqrt{57}}{4}\\\\a = \dfrac{3+\sqrt{57}}{4}, b = \dfrac{3-\sqrt{57}}{4}$

We have to find the value of (a+2)(b+2).

Putting the values:

$(a+2)(b+2)\\\\=\bigg(\dfrac{3+\sqrt{57}}{4}+2\bigg)\bigg(\dfrac{3-\sqrt{57}}{4}+2\bigg)\\\\=\bigg(\dfrac{11+\sqrt{57}}{4}\bigg)\bigg(\dfrac{11-\sqrt{57}}{4}\bigg)\\\\=\dfrac{121-57}{156} = \dfrac{64}{16} = 4$

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3 years ago

What is the average rate of change of f(x), represented by the graph, over the interval [-2, 2]?

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To get the average rate of change (ARC) of f(x) over [x1, x2], we use the formula:
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Plugging in the values into the formula:
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The points connecting (-2,4) amd (2,4) is a horizontal line that is the rate of change is 0.

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