Which expression is the simplest form of -(3x+y)+2x-4y)?
1 answer:
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Given:
One linear function represented by the table.
Another linear function represented by the graph.
To find:
The greater unit rate and greater y-intercept.
Solution:
Formula for slope (unit rate):
From the given table it is clear that the linear function passes through (0,5) and (5,15). The function intersect the y-axis at (0,15), so the y-intercept is 15.
So, the unit rate of first function is 2.
From the given graph it is clear that the linear function passes through (0,6) and (-4,0). The function intersect the y-axis at (0,6), so the y-intercept is 6.
So, the unit rate of first function is .
Now,
And,
Therefore, the greater unit rate of the two functions is 2. The greater y-intercept of the two functions is 15.
Answer:
The Pythagorean identity states that
Using that we can rewrite the left denominator as:
Which can be factored as
The numerator we can expand as:
On the right hand side, let's multply numerator and denominator with (1 - sin t):
The total formula then becomes:
There you go... left and right are equal.