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3 years ago

How do you find an explicit formula?

1 answer:

6 0

If you can find an explicit formula for a sequence, you will be able to quickly and easily find any term in the sequence simply by replacing n with the number of the term you seek. An explicit formula designates the nth term of the sequence, as an expression of n (where n = the term's location).

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Find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points.

ddd [48]

Answer:

a) The slope of the line is parallel to the another line m=4

b) The slope of the line is perpendicular to the another line m= $\frac{-1}{4}$

Step-by-step explanation:

Step1:-

Slope of a line :-

If θ is the inclination of a line 'l' then tanθ is called the slope or gradient of the line 'l'.The slope of a line is denoted by m=tanθ

The slope of a line given two points m= $\frac{y_{2}-y_{1} }{x_{2} -x_{1} }$

Parallel lines:-

Two non-vertical lines are parallel if and only if their slopes are parallel

Perpendicular lines:-

Two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

$m_{2} = \frac{-1}{m_{1} } \\$

Step 2:-

a)The slope of a line when given two points (-1,-4) and (0,0)

$m = \frac{0-(-4)}{0-(-1)} =4$

Two non-vertical lines are parallel if and only if their slopes are parallel

$m_{1} = m_{2}$

Therefore the slope of the line that is parallel to the another line

$m_{1} =m_{2} =4$

Step 3:-

b) Two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

$m_{2} = \frac{-1}{m_{1} } \\$

$m_{2} =\frac{-1}{4}$

Therefore the slope of the line is perpendicular to the another line is

$m=\frac{-1}{4}$

3 0

3 years ago

Read 2 more answers

9) A heptagon has 6 exterior angles with measures of 47, 55, 62, 64, 54, and 49. What is the measure of the interior angle adjac

svetlana [45]

Answer:

seventh interior angle=∠x=29°

Step-by-step explanation:

sum of interior angle of polygon is equal to 360°

let seventh angle of heptagon is x

∠x+47°+55°+62°+64°+54°+49°=360°

∠x=360°-(47°+55°+62°+64°+54°+49°)

∠x=360°-331°=29°

∠x=29°

seventh interior angle=∠x=29° answer

6 0

3 years ago

show a model to show a fraction that is equivalent to 1/3 and a fraction that is not equivalent to 1/3

murzikaleks [220]

Equivalent: 2/6 Not Equivalen: 10/13

3 0

3 years ago

Read 2 more answers

The area of a square garden is 200 m^2. How long is the diaginal

JulijaS [17]

Answer:

400

Step-by-step explanation:

6 0

3 years ago

Let B1W2 denote the outcome that the first ball drawn is B1 and the second ball drawn is W2. Because the first ball is replaced

Sati [7]

Answer:

$\{B_1B_1, B_1B_2, B_1W_1, B_1W_2, B_1W_3, \\B_2B_1, B_2B_2, B_2W_1, B_2W_2, B_2W_3, \\$

$W_1B_1,W_1B_2, W_1W_1, W_1W_2, W_1W_3, \\W_2B_1, W_2B_2, W_2W_1,W_2W_2, W_2W_3, \\W_3B_1, W_3B_2, W_3W_1, W_3W_2, W_3W_3\}$

Step-by-step explanation:

$\text{If an urn contains two blue balls} (denoted \:B_1 \:and \:B_2) \text{and three white balls}$ , $(denoted \:W_1, W_2, \:and\: W_3)$

If One ball is drawn, its color is recorded, and it is replaced in the urn. Then another ball is drawn and its color is recorded.

The 25 Possible outcomes of this experiment are listed below:

$\{B_1B_1, B_1B_2, B_1W_1, B_1W_2, B_1W_3, \\B_2B_1, B_2B_2, B_2W_1, B_2W_2, B_2W_3, \\$

$W_1B_1,W_1B_2, W_1W_1, W_1W_2, W_1W_3, \\W_2B_1, W_2B_2, W_2W_1,W_2W_2, W_2W_3, \\W_3B_1, W_3B_2, W_3W_1, W_3W_2, W_3W_3\}$

The tree diagram of this event is also attached.

6 0

3 years ago