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22.01.2020 •
Mathematics
Concrete consists of six parts gravel to one part cement. a builder makes up 140kg of concrete mixture. what is the weight of gravel used in this mixture?
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Ответ:
120kg
Step-by-step explanation:
The ratio of gravel to cement is 6:1
Then add them up which is 7
The do 140 divided by 7 which is 20
Then do 6 times 20 which is 120
Then do 1 times 20 which is (obviously)20
Then add 20 and 120 which makes 140
Hope it helps!
Ответ:
Part 1) They are perpendicular because they have slopes that are opposite reciprocals of −2 and one half.
Part 2) The coordinates of the end of the stencil are (9,3)
Step-by-step explanation:
Part 1)
step 1
Find the slope of segment AB
we have
Segment AB falls on line
> isolate the variable y
Divide by 4 both sides
so
The slope of segment AB is m=1/2
step 2
Find the slope of segment CD
we have
Segment CD falls on line
> isolate the variable y
Divide by 2 both sides
so
The slope of segment CD is m=-2
step 3
Compare the slopes
mAB=1/2
mCD=-2
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal each other (the product is equal to -1)
(1/2) and -2 are opposite reciprocal
therefore
Segment AB and segment CD are perpendicular
Part 2)
Let
A(1,-1) and B(3,0)
Find the x-distance between point A and B
dx=(3-1)=2 units
we know that
The point (3,0) s 1:3 of the way to where she wants the end of the stencil
Multiply by 3 the x-distance between point A and B
3(2)=6 units
The x-coordinate of the end of the stencil will be 6 units plus the x-coordinate point (3,0)
x-coordinate=6+3=9
Find the y-distance between point A and B
dy=(0+1)=1 units
we know that
The point (3,0) s 1:3 of the way to where she wants the end of the stencil
Multiply by 3 the y-distance between point A and B
3(1)=3 units
The y-coordinate of the end of the stencil will be 3 units plus the y-coordinate point (3,0)
y-coordinate=3+0=3
therefore
The coordinates of the end of the stencil are (9,3)