Evaluate 9 ÷ 3[(18 − 10) − 2^2]. 36 12 0.25 0.75
1 answer:
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Answer:
a.- slope= 36
Interpretation : The cable car travels 36 meter per minute
b.- y = 36x + 100
c.- 640 meters
Step-by-step explanation:
a.-
Find slope using the slope formula :
Plug in the two given points:
Subtract the numbers :
Reduce the fraction : 36
b.-
Using the given y-interspet (100) and the slope create an equation: y = 36x + 100
c.-
Using the equation you created plug in 15 for x to find the
distance: y = 36 (15) + 100
Multiply the numbers : y = 540 + 100
Add the numbers : y = 640
To prove that the diagonals are congruent, you need to formula to compute the distance between two points:
Using that formula, you may prove that , which means that the two diagonals have the same length.
To prove that they are perpendicular, you need the formula to compute the slope of a segment. The slope, knowing the enpoints, is given by
You can use this formula to prove that
In fact, if one slope is the opposite of the reciprocal of the other, the two segments are perpendicular.
Finally, to prove that they bisect each other, you first need to find the point where they meet. First of all, you need to find the line the segments lie on: the formula is
where is one of the points belonging to the line, and you already know how to find the slope. Then, you find the point of intersection, say A, by solving the system involving the two lines:
And use again the formula for the distance between two points to prove that