Theorem — a mathematical statement that is proved using rigorous mathematical reasoning. In a mathematical paper, the term theorem is often reserved for the most important results.
Postulate — a statement that is assumed to be true without proof. These are the basic building blocks from which all theorems are proved
Answer:
m=15
Step-by-step explanation:
BODMAS
6m+6+7-3m=-32
collect like terms
6m-3m+6+7=-32
3m+13=-32
3m=-32-13
3m=45
m=45/3
m=15
Answers:
- Part A) There is one pair of parallel sides
- Part B) (-3, -5/2) and (-1/2, 5/2)
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Explanation:
Part A
By definition, a trapezoid has exactly one pair of parallel sides. The other opposite sides aren't parallel. In this case, we'd need to prove that PQ is parallel to RS by seeing if the slopes are the same or not. Parallel lines have equal slopes.
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Part B
The midsegment has both endpoints as the midpoints of the non-parallel sides.
The midpoint of segment PS is found by adding the corresponding coordinates and dividing by 2.
x coord = (x1+x2)/2 = (-4+(-2))/2 = -6/2 = -3
y coord = (y1+y2)/2 = (-1+(-4))/2 = -5/2
The midpoint of segment PS is (-3, -5/2)
Repeat those steps to find the midpoint of QR
x coord = (x1+x2)/2 = (-2+1)/2 = -1/2
y coord = (x1+x2)/2 = (3+2)/2 = 5/2
The midpoint of QR is (-1/2, 5/2)
Join these midpoints up to form the midsegment. The midsegment is parallel to PQ and RS.
Answer:
There are 96 ways different 4 digit numbers which can be made from these 5 digits.
Step-by-step explanation:
There are 5 different digits. The first one must be
1 3 5 or 7
So you can have 4 for the first one. Now the zero can be put into the mix.
4 * 4 * 3 * 2
96
Answer:
It would take 15 students 6 days to weed the school compound
Step-by-step explanation:
This first step to solving this question is to break down the given rates.
We are told that 10 students take 9 days to weed the school compound. From here we can simplify this by figuring out how long it would take 1 student to weed the compound. Having less people would mean taking a longer time.
1 person is a 1/10 of 10 people. Since we have 10x less people, it should take 10x as long. Therefore it would take 1 person 9x10=90 days to weed a school.
Now the question asks how long it would take 15 people. 15 people is 15x as many as 1 person, so it should take 15x less time to weed the compound. 90/15 = 6
It would take 15 students 6 days to weed the school compound.
Similarly you could have just divided 9 by 1.5 as 15 is 1.5x10, but it is easier to explain the process using the above method.
Hope this helped!