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

A patrolman spends three times as many hours patrolling as she does completing paper work. If she works 36 hours per week, how m

fomenos

Answer:

27 hours

Step-by-step explanation:

Let her work "x" hours for paperwork

Since, patrolling amount of hours is THREE TIMES that,

Patrolling = 3x hours

Total Hours = 36

That is including paperhour work (x) and patrolling (3x). So we can setup an equation in x and solve for x first:

x + 3x = 36

4x = 36

x = 36/4

x = 9 hours

Amount of Hours for Patarolling = 3x hours = 3(9) = 27 hours

So, she spends 27 hours patrolling

4 0

3 years ago

Carl went to the store to buy items for his party.He bought two packs for plates for $3.24 and a pack of cups for $5.70. He also

Andre45 [30]

3.24 + 5.70 + 6.17 = 15.11

20.00 - 15.11 = 5.11

He got 5.11$ of change back.

7 0

3 years ago