If it takes one person 4 hours to paint a room and another person 12 hours to
paint the same room, working together they could paint the room even quicker, it
turns out they would paint the room in 3 hours together. This can be reasoned by
the following logic, if the first person paints the room in 4 hours, she paints 14 of
the room each hour. If the second person takes 12 hours to paint the room, he
paints 1 of the room each hour. So together, each hour they paint 1 + 1 of the 12 4 12
room. Using a common denominator of 12 gives: 3 + 1 = 4 = 1. This means 12 12 12 3
each hour, working together they complete 13 of the room. If 13 is completed each hour, it follows that it will take 3 hours to complete the entire room.
This pattern is used to solve teamwork problems. If the first person does a job in A, a second person does a job in B, and together they can do a job in T (total). We can use the team work equation.
Teamwork Equation: A1 + B1 = T1
Often these problems will involve fractions. Rather than thinking of the first frac-
tion as A1 , it may be better to think of it as the reciprocal of A’s time.
World View Note: When the Egyptians, who were the first to work with frac- tions, wrote fractions, they were all unit fractions (numerator of one). They only used these type of fractions for about 2000 years! Some believe that this cumber- some style of using fractions was used for so long out of tradition, others believe the Egyptians had a way of thinking about and working with fractions that has been completely lost in history.
Answer:
X = -2
Step-by-step explanation:
1/2 X (5X-8) = -9
multiply both sides of the equation by 2
2 X 1/2 X (5X - 8) = 2 X (-9)
1 X (5X - 8) = 2 X (-9)
Reduce the numbers with the greatest common divisor 2
5 x -8 = 2 x (-9)
5 x -8 = -18
Move constant to the right by adding its opposite to both sides
5X -8 + 8=-18 + 8
Then eliminate the opposites
5X = -18 + 8
Calculate the sum
5X = -10
Divide both sides of the equation by 5
5X DIVIDE 5 = -10 DIVIDE BY 5
X = -10 DIVIDE BY 5
X = -2
Answer:
c
d
Step-by-step explanation:
Answer:
C. The chance to be selected into the sample was the same for all veterinarians
1. y = -x - 2...slope here is -1. A parallel line will have the same slope
y = mx + b
slope(m) = -1
(2,-2)...x = 2 and y = -2
now we sub and find b, the y int
-2 = -1(2) + b
-2 = -2 + b
-2 + 2 = b
0 = b
so ur parallel equation is : y = -x
=========================
2. -1 = -3/2(2) + b
-1 = -3 + b
-1 + 3 = b
2 = b
parallel equation is : y = -3/2x + 2
==========================
3. parallel equation is : x = 4
==========================
4. 3 = 1/2(-2) + b
3 = -1 + b
3 + 1 = b
4 = b
parallel equation is : y = 1/2x + 4
===========================
5. y + 0 = 2(x - 5)
y = 2x - 10 <== parallel line
============================
6. neither
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7. if ur second equation is : 2x + y = 7, then the lines are parallel
============================
8. neither
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9. sometimes
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10. never
