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A 6 ounce serving of grapefruit juice contains 171 grams of water. How many grams of water are in 20 ounces of grapefruit juice?
2 answers:
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Answer:
The correct option is;
A. 453
Step-by-step explanation:
The given numbers are not related by factors, because the factors of 779 are 1, 19, 41, and 779
Similarly the factors of 926 are 1, 2, 463, 926
Therefore, the numbers are related by direct association of each digit of the central number to each of the three numbers on the vertices of the triangle as follows;
For the first triangle, we have the numbers at the vertices are; at the top, 14, at the bottom left is 21, and at the bottom right is 36, we have;
Top number divided by 2 gives 14/2 = 7
Bottom left number divided by 3 gives 21/3 = 7
Bottom right number divided by 4 gives 36/4 = 9
From which we have the number at the center which is 779
Similarly, for the second triangle, we have the numbers at the vertices are; at the top, 18, at the bottom left is 6, and at the bottom right is 24, we have;
Top number divided by 2 gives 18/2 = 9
Bottom left number divided by 3 gives 6/3 = 2
Bottom right number divided by 4 gives 24/4 = 6
From which we have the number at the center which is 962
Therefore, when we have, the numbers at the vertices as follows;
At the top, 8, at the bottom left is 15, and at the bottom right is 12, we have;
Top number divided by 2 gives 8/2 = 4
Bottom left number divided by 3 gives 15/3 = 5
Bottom right number divided by 4 gives 12/4 = 3
From which we have the number at the center is 453.
Step-by-step explanation:
A lot of times, one of the hardest parts of proving anything is figuring out exactly what you're trying to prove. Fortunately for us, we already have it laid out. We're trying to prove the Pythagorean theorem, which says that on a right triangle with legs a and b and a hypotenuse c, the sides are related by the equation
This particular proof uses similarity, cleverly splitting the original right triangle into three - the original, and two smaller ones. One fact about similar triangles that helps us is that <em>corresponding sides are proportional</em>. This fact is used for the second step of the proof:
and
For our proof, we're going to try to go off of this fact to build back the Pythagorean theorem. We'll need an a², a b², and a c² for that, and we can get the first two by cross multiplying each equations, giving us two new ones:
and
.
This is Statement 3, and we go to it through Multiplication. Next, we can add the two equations together to get the left side of the Pythagorean theorem, factoring a c out of the right side to give us:
This is Statement 4, and we used the Addition property of equality to get it.
Now, looking at the original figure, we can see that the lengths d and f add together to give us a c. We can express that fact with the equation
This is Statement 5, given to us through the Segment addition postulate. Finally, we can use our equation from statement 5 to substitute f + d for c in our equation from Statement 4, giving us the Pythagorean theorem:
This is Statement 6, our final statement, and it uses the Substitution property of equality to finish our proof.