By doubling each dimension the area of a parallelogram increased from 36 square centimeters to 144 square centimeters. find the
1 answer:
The percentage of increase in area will be 300%
<em><u>Explanation</u></em>
By doubling each dimension, the area of a parallelogram increased from 36 square centimeters to 144 square centimeters.
So, the increased area = Final area - Initial area = (144 - 36)cm² = 108 cm²
Now, for finding the percentage of increase, first we need to <u>divide "the increased area" by the "initial area" and then multiply by 100% </u>
Thus, the percentage of increase in area %
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Answer:
(1, 3)
Step-by-step explanation:
You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola. The first few steps are as follows. Set the parabola equal to 0 so you can solve for the vertex. Separate the x terms from the constant by moving the constant to the other side of the equals sign. The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out). Let's start there. The first 2 steps result in this polynomial:
. Now we factor out the -2:
. Now we complete the square. This process is to take half the linear term, square it, and add it to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. We add 1 into the set of parenthesis. But we actually added into the parenthesis is +1(-2). The -2 out front is a multiplier and we cannot ignore it. Adding in to both sides looks like this:
. Simplifying gives us this:
On the left we have created a perfect square binomial which reflects the h coordinate of the vertex. Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:
From this form,
you can determine the coordinates of the vertex to be (1, 3)
Check the picture below.
notice, the dashed line is the "continuation" of the graph, however, for the constraints in the piece-wise, is excluded.
notice, the dashed line is the "continuation" of the graph, however, for the constraints in the piece-wise, is excluded.