Translate the verbal expression "Five less than the product of X and three" into an algebraic expression
1 answer:
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Answer:
Third turn point = 21 points
Step-by-step explanation:
Given:
First turn point = 12
Second turn point = 15
Find;
Third turn point
Computation:
First turn point = 12
Assume;
Point for outer circle = a
Point for inner circle = b
So,
3a = 12
Point for outer circle = 4 point
Second turn point = 15
So,
2a + b = 15
2(4) + b = 15
Point for inner circle = 7
Third turn point = 3 x 7
Third turn point = 21 points
Answer:
The three positions are not on the same line.
Step-by-step explanation:
We have three points: A:(3,2,0), B:(1,-1,2) and C:(5,5,2).
Let's build a vector that goes from one point to another; that vector will be the director of a line (if we draw a vector that goes from A to B, that vector will be the direction of the line that pass by A and B because it does not change). In order to build that vector, let's subtract B from A:
The equation of a line is:
Where p is every singular point of the line, is a particular point of the line (any that we are sure that it is on the line), r is the director vector and t is the independent variable.
Now we have the director vector: (2,3,-2), and we can verify that A and B are on the line:
Because there is a value for t that satisfies both A and B: If we do and t=0, we are going to obtain the point p=A; and if we do t=-1, we are going to obtain p=B. Let's see that:
If C is also in the same line, C must accomplish the equation: , so:
Let's simplify the equation writing the parametric equation, which is just to write the equation for each dimension:
You can verify that there is not a value of t that satisfies all three equations, so, the point C is not on the same line as A and B; which means that A, B and C are not on the same line.