Supposse that the distance from the point $(x,y)$ to the point $(3,0)$ is equal to the distance from $(x,y)$ to the point $(7,0)$ . Then, by the formula of the distnace we must have

$\sqrt{(x-3)^2 + (y-0)^2}=\sqrt{(x-7)^2 + (y-0)^2}$

cancel the square root and the $(y-0)^2$ 's, and then expand the parenthesis to obtain

$x^2 - 6x + 9 = x^2 - 14x + 49$

then, simplifying we obtain

$8x = 40$

therfore we must have

$x=5$

this means that the points satisfying the propertie must have first component equal to 5. So we can give a lot of examples of such points: $(5,0), (5,7),(5,1/2), (5,-10),...$ . The set of this points give us a straight line and the points (3,0) and (7,0) are symmetric with respect to this line.

3 0

3 years ago

Answer number 20. Please answer all parts to the question.

emmasim [6.3K]

1: 7
2: Yes, 20 because it’s isolated from the rest of the points
(I don’t know the other ones, sorryyyyy)

5 0

2 years ago

Suppose you pick a tile out of a bag containing 26 tiles marked with the letters A through Z. What is the probability of picking

Liula [17]

Given that a bag contains 26 tiles marked with the letters A through Z.

The probability of picking a letter from the name JACK is 4 / 26

The probability of picking a letter from the name BEN is 3 / 26.

Therefore, the probability of picking a letter from the name JACK or from the name BEN iis given by 4 / 26 + 3 / 26 = 7 / 26

6 0

3 years ago