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SR

Sandra R.

Algebra

1 week, 1 day ago

In 2017, the top-selling frozen pizza brands, DiGiorno and Red Baron, together had sales of $1586.9 million. Red Baron’s sales were $442.3 million less than DiGiorno’s. What were sales in millions for each brand?

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Answer

In 2017, the top-selling frozen pizza brands, DiGiorno and Red Baron, together had sales of $1586.9 million. Red Baron’s sales were $442.3 million less than DiGiorno’s. What were sales in millions for each brand?

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Video Transcript

for this problem. We want to find the area of the right isosceles triangle formed by the X axis. Why access and the line passing through A B. Now below is the illustration of the given problem. Now let's say that this distance here is X. So since we haven't I saw slowly strangled, then the length of this base will be equal to the length of this height. So this one is also X. And if this is X then the points here Are for the first one that will be zero x. And This one here will be X0. Now we know that the area of a triangle Is equal to 1/2 times the base times the height. And based on this figure, our base and height are the same soul. This is equal to 1/2 times X times X. Or that's X squared over two. Next I want to find an expression for X. That will be in terms of A and B. Now to do this we use the fact that this blue line passes through A. B. And we can form an equation in terms of X. A and B. Using the idea of the slope of a line. Now we recall that the slope of a line. This is just the change in why that's a difference. But to me and it's A Y said to and why someone over the change in X. That will be the change or the difference between except to minus except one. Now let's say this is our X of one weiss of one and this is our X. Up to I said to then the slope of this line is equal to What's up to minus weiss of one over X. Up to minus except one. That's going to be zero -X over x minus zero. And this is equal to let's say this is our except one weiss of one instead and you will form the equation the right hand side, that's zero minus B over x minus A. So this is true because if you pick any point in this line and find the slope, the slopes will always be equal. Now, solving for X in this equation we have -1. This is equal to negative B over x minus A. And multiplying both sides of this equation by x minus A. This will give us negative X plus A equal to negative B. Or that the same as X equal to A plus B. So this area here, which is equal to X squared over two. This is equal to the square of A plus B. All over to And that's the area of our right isosceles triangle.

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