Find equation of set of points pieces that its distance from the point 3, 4, -5 and -2, 1, 4 are equal.

Step-by-step explanation:

Suppose we a point such that its distance from either the point or is the same.

Using this information we can formula:

distance AP = distance BP

first, let's find the distance from AP, using the distance formula.

similarly, we can find the distance BP

since both distances are exactly the same we can equate them

we can simplify it a bit squaring both sides, and getting rid of the subscripts.

what we have done here is formulated an equation which consists of any point P that will have the same distance from (3,4,-5) and (-2,1,4).

To put it more concretely,

This is the equation of the the plane from that consists of all points (P) from which the distance from both (3,4,-5) and (-2,1,4) are equal.

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40

if the probability is 1/12, 75 people will receive a $25 gift card

step-by-step explanation: