Renata's recipe for her famous Kale 'n' Clam Quencher calls for kale juice and clam juice in a 3:1 ratio. If Renata pours 18 lit
1 answer:
Answer:
6 liters
Step-by-step explanation:
Given:
Renata's recipe for her famous Kale 'n' Clam Quencher calls for kale juice and clam juice in a 3:1 ratio.
If Renata pours 18 liters of fresh kale juice, how many liters of clam juice should she add to maintain this ratio?
Solution:
Ratio to be maintain by using kale juice and clam juice = 3 : 1 ( given)
Renata pours fresh kale juice = 18 liters
We have to calculate quantity of clam juice should be added to maintain this ratio:-
Let quantity of clam juice should be added =
<u>Ratio to be maintain : : quantity of kale juice : quantity of clam juice</u>
By cross multiplication:
By dividing both sides by 3
Thus, 6 liters of clam juice should she add.
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Answer:
IS a parallelogram
Step-by-step explanation:
The slope formula for the slope of the line between points (x1, y1) and (x2, y2) is ...
m = (y2 -y1)/(x2 -x1)
The distance formula for the length of that same line is ...
d = √((x2 -x1)^2 +(y2 -y1)^2)
Here, you're asked to use each of these formulas 4 times, once for each side of the quadrilateral. I find it convenient to let a calculator or spreadsheet do the repetitive calculations. The result is attached.
The attachment shows that opposites sides have the same length and slope, so are parallel. The quadrilateral is a parallelogram. (The two points used in each calculation are the ones on the result line and the line immediately below. That is why point B is copied to the end of the list.)
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<em>Additional comments</em>
There are much simpler ways to prove the figure is a parallelogram. My favorite is to add the coordinates of the end points of the diagonals:
B +D = (-2+6, -9-3) = (4, -12)
C +E = (0+4, -5-7) = (4, -12)
These values being the same demonstrates the midpoints of the diagonals are coincident. That will only be the case if the quadrilateral is a parallelogram.
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If you must use slope and distance formulas, showing either pair of opposite sides is parallel and have the same length is sufficient to guarantee that the other two sides are also parallel and have the same length. That is, the calculations required in this problem only need to be applied to one pair of opposite sides. (Using a spreadsheet, it's not a lot of extra work to do the calculations for both pairs of opposite sides.)
