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3 years ago

What are the explicit equation and domain for an arithmetic sequence with a first term of 8 and a second term of 5? 20 pts.

Mathematics

1 answer:

fgiga [73]3 years ago

6 0

ANSWER

$a_n = 11 - 3n$

EXPLANATION

The explicit rule for an arithmetic sequence is given by:

$a_n = a_1 + d(n - 1)$

It was given that:

$a_1 = 8$

and

$a_2 = 3$

The common difference is

$d = 5 - 8 = - 3$

We plug in the values into the explicit formula to get,

$a_n = 8+ - 3(n - 1)$

Expand to get,

$a_n = 8 - 3n + 3$

The explicit rule is

$a_n = 11 - 3n$

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3 years ago

What are the coordinates of point B on \overline{AC} such that AB = 1/2 BC

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Answer:

C. $B(x,y) = \left(3,-\frac{16}{3} \right)$

Step-by-step explanation:

Let $A(x,y) = (6,-7)$ , $B(x,y) = (x,y)$ and $C(x,y) = (-3,-2)$ . From statement we know that $AB = \frac{1}{2}\cdot BC$ , which is equivalent to the following linear algebraic formula:

$B(x,y) -A(x,y) = \frac{1}{2}\cdot [C(x,y)-B(x,y)]$ (1)

$B(x,y)-A(x,y) = \frac{1}{2}\cdot C(x,y)-\frac{1}{2}\cdot B(x,y)$

$\frac{3}{2}\cdot B(x,y) = \frac{1}{2}\cdot C(x,y)+A(x,y)$

$B(x,y) = \frac{1}{3}\cdot C(x,y) +\frac{2}{3}\cdot A(x,y)$ (2)

Then, the coordinates of point B on AC are:

$B(x,y) = \frac{1}{3}\cdot (-3,-2)+\frac{2}{3}\cdot (6,-7)$

$B(x,y) = \left(-1, -\frac{2}{3}\right)+\left(4, -\frac{14}{3} \right)$

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3 years ago

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Step-by-step explanation:

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2 years ago

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Answer:

b = 14-4

Step-by-step explanation:

Let the number of black bugs be b

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