Add. Write the sum in simplest form. 12 1/3 + 6 2/6 =
2 answers:
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ANSWER TO QUESTION 1
We multiply through by the Least Common Multiple which is 2.
We expand brackets to obtain,
Grouping like terms, have
Whenever you solve an equation and you get the above result, you don't have to get confuse.
It simply means the question does not have a UNIQUE solution.
That any real number will number will satisfy the above equation.
Hence,
ANSWER TO QUESTION 2
We factor x to obtain;
We divide both sides by (a+b)
We multiply through by the Least Common Multiple which is 2.
We expand brackets to obtain,
Grouping like terms, have
Whenever you solve an equation and you get the above result, you don't have to get confuse.
It simply means the question does not have a UNIQUE solution.
That any real number will number will satisfy the above equation.
Hence,
ANSWER TO QUESTION 2
We factor x to obtain;
We divide both sides by (a+b)
The graph of y = 2(x - 3)² + 2 can be seen in the attached picture. This problem can be solved through the concept of parabola and transformation.
<h3>Further explanation</h3><u>The Problem:</u>
Which is the graph of y = 2(x - 3)² + 2?
<u>Question-1:</u>
How to make a graph y = 2 (x - 3) ² + 2 through the concept of a parabola.
<u>The Process:</u>
The equation of a parabola is given by .
Keep in mind the following points:
- vertex point at (h, k)
- axis of symmetry at x = h
- a > 0 the parabola opens upward
- a < 0 the parabola opens downward
- the y-intercept is
at x = 0.
From our case it can be concluded as follows:
- the graph of y = 2(x - 3)² + 2 opens upward
- vertex point at (3, 2)
- axis of symmetry at x = 3
- the y-intercept is 2(3²) + 2 = 20 or in coordinates of (0, 20)
<u>Question-2:</u>
How to make the graph of y = 2(x - 3)² + 2 through the transformation.
<u>The Process:</u>
To plot the graph of y = 2(x - 3) ² + 2 we apply for the following transformation order:
Step-1: clearly, to obtain the graph of y = (x - 3)² we shift the graph of y = x² to the right 3 units.
Step-2: to obtain the graph of y = 2(x - 3)², we stretch the graph of y = (x - 3)² by a factor of 2 (in other words, multiply each y-coordinate by 2).
Step-3: finally, to obtain the graph of y = 2(x - 3)² + 2 we shift the graph of y = 2(x - 3)² upward 3 units.
Thus the construction of the graph y = 2 (x - 3) ² + 2 is completed.
The graph of y = 2(x - 3) ² + 2 is drawn by the combination of shifting the graph of y = x² to the right 3 units and upward 2 units, and also stretch by a factor of 2. Between vertical shift and stretch steps, it is the same whatever steps are taken first.
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Notes
- The transformation of graphs is changing the shape and location of a graph.
- There are four types of transformation geometry: translation (or shifting), reflection, rotation, and dilation (or stretching/shrinking).
- In this case, the transformation is shifting horizontally and vertically and also stretching vertically.
In general, given the graph of y = f(x) and v > 0, we obtain the graph of:
by shifting the graph of
upward v units.
by shifting the graph of
That's the vertical shift, now the horizontal one. Given the graph of y = f(x) and h > 0, we obtain the graph of:
by shifting the graph of
by shifting the graph of
Hence, the combination of vertical and horizontal shifts is as follows:
The plus or minus sign follows the direction of the shift, i.e., up-down or left-right .
Notice the following definitions for stretch and shrink.
- In general, given the graph of
, we obtain the graph of
by stretching
or shrinking
the graph of
- In general, given the graph of
by stretching
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