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2 years ago

(3,-5) (-1,5) you have to find the slope

Mathematics

1 answer:

nirvana33 [79]2 years ago

3 0

Answer:

Hope this helps!

Step-by-step explanation:

Slope = 5/-2

Slope (m) =

ΔY

ΔX

-2

= -2.5

θ =

arctan( ΔY ) + 180°

ΔX

= 111.80140948635°

ΔX = -1 – 3 = -4

ΔY = 5 – -5 = 10

Distance (d) = √ΔX2 + ΔY2 = √116 = 10.770329614269

Equation of the line:

y = -2.5x + 2.5

y =

- 5 x

+ 5

When x=0, y = 2.5

When y=0, x = 1

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2 years ago

Identify the sequence graphed below and the average rate of change from n = 1 to n = 3.

dsp73

Answer:

The required sequence is $a_n=20(\frac{1}{2})^{n-1}$ . The average rate of change from n = 1 to n = 3 is -7.5.

Step-by-step explanation:

From the given graph it is clear that the sequence is a GP because the all terms are half of their previous terms.

Here, $a_2=10,a_3=5,a_4=2.5,a_5=1.25$

$r=\frac{a_3}{a_2}=\frac{5}{10}=\frac{1}{2}$

The common ratio of GP is 1/2.

$r=\frac{a_2}{a_1}$

$\frac{1}{2}=\frac{10}{a_1}$

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The first term of the sequence is 20.

The formula for sequence is

$a_n=a(r)^{n-1}$

Where a is first term and r is common difference.

The required sequence is

$a_n=20(\frac{1}{2})^{n-1}$

The formula for rate of change is

$m=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

The average rate of change from n = 1 to n = 3 is

$m=\frac{f(3)-f(1)}{3-1}$

$m=\frac{5-20}{3-1}$

$m=\frac{-15}{2}=-7.5$

Therefore the required sequence is $a_n=20(\frac{1}{2})^{n-1}$ . The average rate of change from n = 1 to n = 3 is -7.5.

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