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3 years ago

Calculate the distance between the points (-1, 3) and (4, -1).

Mathematics

2 answers:

BigorU [14]3 years ago

5 0

The distance between those two points is 41 and in decimal form to the nearest tenth, that's 6.4

Explanation:

Use the distance formula: √(x2 - x1)² + (y2 - y1)²

Then we plug in our x's and y's:

√(4 - (-1))² + ((-1) - 3)²

Then you simplify:

√(5)² + (-4)² = √25 + 16

√41 (And if you need to, you can put this into decimal form.)

Tamiku [17]3 years ago

3 0

Answer:

6.4

Step-by-step explanation:

Use the distance formula and then fill in points for the variables.

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Answer:

The average rate of change of g from x = a to x = a + h is -3.

Step-by-step explanation:

We are given the function:

$g(x) = -3x + 4$

And we want to determine its average rate of change of the function for x = a and x = a + h.

To determine the average rate of change, we find the slope of the function between the two points. In other words:

$\displaystyle \text{Avg} = \frac{g(a + h) - g(a) }{(a + h ) - a}$

Simplify:

$\displaystyle \begin{aligned} \text{Avg} &= \frac{g(a + h) - g(a) }{(a + h ) - a} \\ \\ &=\frac{(-3(a+h) + 4) - (-3a+4)}{h} \\ \\ &= \frac{(-3a -3h + 4) + (3a - 4) }{h} \\ \\ &= \frac{-3h}{h} \\ \\ &= -3\end{aligned}$

In conclusion, the average rate of change of g from x = a to x = a + h is -3.

This is the expected result, as function g is linear, so its rate of change would be constant.

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The graph is attached. :D

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