What is the measure of [theta]?
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If we need our line to pass through point C, then we have to use the x and coordinates of point C in our new equation. If that line is to be perpendicular to AB, we also need to find the slope of AB and then take its opposite reciprocal. First things first. Point C lies at (6, 4) so we will use x = 6 and y = 4 in our equation in a bit. The coordinates of A are (-2, 4) and the coordinates of B are (2, -8) so the slope between them is 
which is -3. The opposite reciprocal of -3 is 1/3. That's the slope we will use along with the points from C to write the new equation. We will do this by plugging in x, y, and m (slope) into the slope-intercept form of a line and solve for b. 
and 4 = 2 + b. So b = 2. That's the y-intercept, the point on the y axis where the line goes through when x is 0. Therefore, the point you're looking for is (0, 2).
The best approximation to the number of seedlings that are at least 2 inches high in the <u>entire lawn</u> is:
- D. <u>6,400</u>
To identify the total number of seedling in the entire lawn, first you must add all the seedling counted by the researchers:
- Counted seedlings = 82 + 87 + 95 + 99 + 102 + 106 + 111 + 115
- <u>Counted seedlings = 697</u>
Now, you must divide 697 in the number of regions taken by the researchers ( in this case were 8), this to obtain the average:
- Average seedlings by region =
- <u>Average seedlings by region = 87.125</u>
Now, how we know, the entire lawn has a length of 8 feet and a width of 8 feet, it means 64 regions of one feet by one feet, by this reason, we multiply the average of seedlings by the whole regions in the lawn:
- Number of seedlings in the lawn = 87.125 * 64
- <u>Number of seedlings in the lawn = 5576</u>
Taking into account the average of seedlings is 5576, the best approximates of seedlings that are at least 2 inches high in the entire lawn is <u>6400</u>.
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