Prove: The opposite sides of a parallelogram are equal.
1 answer:
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Answer:
Option D
Step-by-step explanation:
Out of all given options, Option D (the parallelogram) will tessellate the easiest.
Option B's shape (the Trapezoid) is also possible. However, it would take a little more work for it to tessellate. The trapezoid provided would not tessellate alone.
Option A and Option C's shape wouldn't tessellate because it would leave a gap. To add, Option C's shape is nearly impossible to tessellate.
Answer:
length of rectangle = 5
width of rectangle = 5
Area of rectangle = 25
Step-by-step explanation:
Since the length of the rectangle is "x", and the value of the area is given by the product of the length "x" times the width "10-x", indeed, the area "y" of the rectangle is given by the equation:
Now, they tell us that the area of the rectangle is such that coincides with the maximum (vertex) of the parabola this quadratic expression represents. So in order to find the dimensions of the rectangle and therefore its area, we find the x-coordinate for the vertex, and from it, the y-coordinate of the vertex, which is the rectangle's actual area.
Recall that the formula for the x of the vertex of a quadratic of the form :
is given by the formula:
which in our case gives:
Therefore, the length of the rectangle is 5, and its width (10-x) is also 5.
The area of the rectangle is therefore the product of these two values: 5 * 5 = 25
Which should coincide with the value we obtain when we replace x by 5 in the area formula: