1. 4x + 8y = 12....divide by 4
x + 2y = 3
2y = -x + 3
y = -1/2x + 3/2...slope is -1/2, y int is 3/2
x + 2y = -3
2y = -x - 3
y = -1/2x - 3/2...slope is -1/2 and y int is -3/2
when the slopes are the same, and the y int are different, then the lines are parallel and never intersect...so they have no solution and are inconsistent
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2. y = 2x - 1...slope is 2 and y int is -1
y = -2x + 5 ...slope is -2 and y int is 5
when the slopes are different and the y int are different, then there is 1 solution making it independent
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3. 4x - 12y = 8...divide by 4
x - 3y = 2
same as other equation meaning the equations are the same line...meaning they have infinite solutions making them dependent
Answer:
6x=54
Step-by-step explanation:
3x - {7-x} =29
open bracket
3x - 7 +x =29
collect like terms and equate
4x =29 +7
4x = 36
divide both sides by 4
x = 9
.
. . 6x= 6 × 9 = 54
6x= 54
Set up your conversion using dimensional analysis. That's just a fancy way of saying set up your values so you cancel what you don't need and keep what you do. If we want to convert miles per hour to feet per second, we need to convert the miles to feet using the fact that there are 5280 feet in 1 mile, and then convert the hours to seconds using the fact that there are 3600 seconds in an hour. Your set up will look like this (it's all about setting up the fractions correctly):
. If you look at that closely, you can see the there is a label of miles on the top in the first fraction and on the bottom in the second fraction. Those cancel each other out by reducing. Then in the bottom of the first fraction there is hours and in the top of the last fraction there is hours. Those cancel out. From top to bottom or bottom to top you can cancel like labels. This leaves us with feet in the top and seconds in the bottom. Now it's a matter of doing the math. You multiply straight across the top and straight across the bottom.
. Simplifying you get 46.933 feet per second.
Answer:
Step-by-step explanation:
Given that there are 3 events as
rolling 3 dice, are the events A: sum divisible by 3 and B: sum divisible 5
The sample space will have
(1,1,1)...(6,6,6)
Sum will start with 3 and end with 18
Sum divisible by 3 are 3,6,9..18
Sum divisible by 5 are 5,10,....15
The common element is 15
Hence these two events are not mutually exclusive.