Explanation:
a. The line joining the midpoints of the parallel bases is perpendicular to both of them. It is the line of symmetry for the trapezoid. This means the angles and sides on one side of that line of symmetry are congruent to the corresponding angles and sides on the other side of the line. The diagonals are the same length.
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b. We observe that adjacent pairs of points have the same x-coordinate, so are on vertical lines, which have undefined slope. KN is a segment of the line x=1; LM is a segment of the line x=3. If the trapezoid is isosceles, the midpoints of these segments will be on a horizontal line. The midpoint of KN is at y=(3-2)/2 = 1/2. The midpoint of LM is at y=(1+0)/2 = 1/2. These points are on the same horizontal line, so the trapezoid <em>is isosceles</em>.
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c. We observed in part (b) that the parallel sides are KN and LM. The coordinate difference between K and L is (1, 3) -(3, 1) = (-2, 2). That is, segment KL is the hypotenuse of an isosceles right triangle with side lengths 2, so the lengths of KL and MN are both 2√2.
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For part (c), we used the shortcut that the hypotenuse of an isosceles right triangle is √2 times the leg length.
Answer:
1 whole one and a third of one.
Step-by-step explanation:
1 1/3 of a granola bar
Answer: 0.22
Step-by-step explanation:
We know that the best point estimate for the difference between two population mean is the difference between their sample means.
Given : For the 39 randomly selected upperclassmen, the sample mean was 0.12 and sample standard deviation was 0.42. For the 35 randomly selected underclassmen, the sample mean was 0.34 and the sample standard deviation was 0.87.
Let A denotes the population of upperclassmen and B denotes the population of underclassmen .
Then, the point estimate of the difference in the population mean volunteered between underclassmen and upperclassmen will be :-
Hence, the point estimate of the difference in the population mean volunteered between underclassmen and upperclassmen =0.22
Answer:
Part 1) The y-intercept is the point 
Part 2) The x-intercepts are the points 
Step-by-step explanation:
we have
This is a vertical parabola open upward
step 1
Find the y-intercept
we know that
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
The y-intercept is the point (0,-3)
step 2
Find the x-intercepts
we know that
The x-intercept is the value of x when the value of y is equal to zero
so
For y=0
solve for x
Adds 3 both sides
take square root both sides
so
The x-intercepts are the points
Answer:
Step-by-step explanation:
The two legs of an iscosles right triangle are equal. The sides opposite each 45 degree angle are equal.
6^2 + 6^2 = x^2
36 + 36 = x^2
x^2 = 72
sqrt(x^2) = sqrt(72)
x = 6√2
