Answer:
Let the matrix associated to the system and
the vector of constant values of the system.
The equation of the line joining p and q is
. Since p and q are solutions of the linear system then, and
Let . Observe that . Then w is a solution of the homogeneous system Ax=0.
Now, let s=p+r(q-p) for some be a point in the line joining p and q. Observe that
Then As=b. This means that s is a solution of the linear system.
Answer:
Yes
Step-by-step explanation:
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Answer:
The anwser you are looking for is number 2
Step-by-step explanation:
Answer: 4=40 ! Its a pattern
Answer:
1. shifts the graph right 2 units
2. y = -2(x -3)² +7
Step-by-step explanation:
1) Replacing x with x-h in any function shifts the graph h units to the right. Here, you have replaced x with (x-2), so the graph will be shifted 2 units to the right.
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3) The vertex form of the equation of a parabola is ...
y = a(x -h)² +k . . . . . . . . for vertex (h, k) and vertical scale factor 'a'
Here, the vertex is (h, k) = (3, 7), and the parabola opens downward. This tells us the sign of 'a' is negative.
The graph is not so clear that it is easy to read the value of 'a' directly from it, but there are several clues.
The zeros of the above function are found at h±√(k/a). This graph shows the zeros to be located such that √(7/a) is slightly less than 2. This means the magnitude of 'a' will be slightly more than 7/2² = 1.75. The y-intercept of the function is 7-9a. It is less than -7, but probably more than -14. This puts bounds on 'a':
-14 < 7-9a < -7
-21/9 < -a < -14/9 ⇒ -2.33 < -a < -1.56
If we assume that 'a' is an integer value, we have bounded its magnitude as being between 1.75 and 2.33, so a=-2 is a reasonable choice.
The equation of the graph may be ...
y = -2(x -3)² +7