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3 years ago

What is the distance between the points (4, -2) and (-1, 10)?

Mathematics

1 answer:

velikii [3]3 years ago

8 0

Answer:

d = 13 (distance between two points)

Step-by-step explanation:

(4, -2) and (-1, 10)

(X1, Y1) and (X2, y2)

distance between two points = d = sqrt (X2 - X1)² + (Y2 - Y1)²

d = √ (-1 - 4)² + (10 - (-2))²

d = √25 + 144

d = √169

d = 13 (distance between two points)

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3 years ago

In Exercises 45–48, let f(x) = (x - 2)2 + 1. Match the function with its graph

MA_775_DIABLO [31]

Answer:

45) The function corresponds to graph A

46) The function corresponds to graph C

47) The function corresponds to graph B

48) The function corresponds to graph D

Step-by-step explanation:

We know that the function f(x) is:

$f(x)=(x-2)^{2}+1$

45)

The function g(x) is given by:

$g(x)=f(x-1)$

using f(x) we can find f(x-1)

$g(x)=((x-1)-2)^{2}+1=(x-3)^{2}+1$

If we take the derivative and equal to zero we will find the minimum value of the parabolla (x,y) and then find the correct graph.

$g(x)'=2(x-3)$

$2(x-3)=0$

$x=3$

Puting it on g(x) we will get y value.

$y=g(3)=(3-3)^{2}+1$

$y=g(3)=1$

Then, the minimum point of this function is (3,1) and it corresponds to (A)

46)

Let's use the same method here.

$g(x)=f(x+2)$

$g(x)=((x+2)-2)^{2}+1$

$g(x)=(x)^{2}+1$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2x$

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Evaluatinf g(x) at this value of x we have:

$g(0)=(x)^{2}+1$

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47)

Let's use the same method here.

$g(x)=f(x)+2$

$g(x)=(x-2)^{2}+1+2$

$g(x)=(x-2)^{2}+3$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2(x-2)$

$0=2(x-2)$

$x=2$

Evaluatinf g(x) at this value of x we have:

$g(2)=(2-2)^{2}+3$

$g(2)=3$

Then, the minimum point of this function is (2,3) and it corresponds to (B)

48)

Let's use the same method here.

$g(x)=f(x)-3$

$g(x)=(x-2)^{2}+1-3$

$g(x)=(x-2)^{2}-2$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2(x-2)$

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I hope it helps you!

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3 years ago

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Answer:

Step-by-step explanation:

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3 years ago

Read 2 more answers

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defon

Answer:

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Step-by-step explanation:

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3 years ago

What is the distance between the points (4, -2) and (-1, 10)?​

What is the distance between the points (4, -2) and (-1, 10)?