Answer:
28
Step-by-step explanation:
x = 2 point questions, y = 3 point questions
x + y = 40
2x + 3y = 92
Solving this we get x = 28, y = 12 so the answer is 28.
Hello there!
The Pythagorean Theorem is:
a² + b² = c²
We have b = 48 and c = 50
Remember: The hypotenuse is always longer.
a² + 48² = 50²
a² + 2304 = 2500
a² = 2500 - 2304
a² = 196
a = √196
a = 14
The missing length is 14.
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Lance is not correct. Although his number does have more decimal places, his number is not greater. Angel has the greatest number in the most valued place, which is the tenths place in this case. We can understand this by knowing that 5>4. So, Angel has more water, and Lance is incorrect.
It is convenient to do part b first, then use that result to do part a.
b. For some pair of points (x1, y1) and (x2, y2), you want to find a point (a, b) such that (a, b) - (x1, y1) = (x2, y2) - (a, b). That is, the differences of coordinates from one end to the center are the same as the differences from the center to the other end.
Adding (a, b) to the above equation gives
2(a, b) - (x1, y1) = (x2, y2)
Adding (x1, y1) then gives
2(a, b) = (x1, y1) + (x2, y2)
Finally, dividing by 2 gives a formula for (a, b):
(a, b) = ((x1, y1) + (x2, y2))/2
The midpoint is the average of the end points.
a. Using the result from part b, the midpoint is
midpoint = ((2, 3) + (6, 7))/2 = (8, 10)/2
midpoint = (4, 5)
