Point P is on the number number line. The distance between O and P is four times the distance between P and 30. What is the sum of two possible values of P? What are two possibilities for the coordinates?
Let me make sure I understand what's asked.
"Point P is on the number number line. "
Does this mean it's on the x-axis?
The distance between O and P is four "times the distance between P and 30." Is that O (letter oh) or 0 (zero)?
Let the distances between P and O be denoted by D. Then d(O,P)=4*d(P,30)
If you mean two separate points P and O then there are an infinite number of solutions. If 0 is meant, then we have
(1/4)|P|=|P-30|
If P>30, then P/4=P-30 or 30=(3/4)P and P=40
If P<30, then P/4=30-P and (5/4)P=30 or P=24
Hopefully I read and understand the question correctly. I'll let you finish answering the questions and verify the solutions.
If something else is meant please post it.
Based on the information provided, it seems that the question is asking for the sum of two possible values of point P on the number line. Let's analyze the given information further.
1. The distance between O and P is four times the distance between P and 30.
Let's denote the distance between O and P as d(O,P) and the distance between P and 30 as d(P,30).
From the given information, we have the equation:
d(O,P) = 4 * d(P,30)
2. We need to find two possible values for P.
Now, let's solve the equation to find the two possible values of P.
When P > 30:
d(O,P) = P - 0
= P
d(P,30) = P - 30
Substituting these values into the equation, we have:
P = 4 * (P - 30)
Solving for P, we get:
P = 4P - 120
-3P = -120
P = 40
So, one possible value for P is 40.
When P < 30:
d(O,P) = 0 - P
= -P
d(P,30) = 30 - P
Substituting these values into the equation, we have:
-P = 4 * (30 - P)
Solving for P, we get:
-P = 120 - 4P
3P = 120
P = 40
So, another possible value for P is 24.
Therefore, the sum of the two possible values of P is 40 + 24 = 64.
Now, let's determine the two possible coordinates for the two values of P.
When P = 40, the coordinate of P is (40, 0).
When P = 24, the coordinate of P is (24, 0).
So, the two possible coordinates for P are (40, 0) and (24, 0).