What is the equation of BD, simplified?

Mathematics

1 answer:

FromTheMoon [43]4 years ago

6 0

Third option is the correct answer.

Answer:

$y = \bigg[ \frac{2b}{(2a - c)} \bigg]x - \bigg[ \frac{2bc}{(2a - c)} \bigg]$

Step-by-step explanation:

$y - y_1 = m(x - x_1) \\ \\ y - 0 = \bigg[ \frac{2b}{(2a - c)} \bigg] (x - c) \\ \\ y = \bigg[ \frac{2b}{(2a - c)} \bigg]x - \bigg[ \frac{2b}{(2a - c)} \bigg]c \\ \\ \purple { \boxed{ \bold{y = \bigg[ \frac{2b}{(2a - c)} \bigg]x - \bigg[ \frac{2bc}{(2a - c)} \bigg]}}} \\$

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the annual interest on 17,000 investment exceeds the interest on an 11,000 investment by 308 . the 17,000is invested at a 0.4% h

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keeping in mind that

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}$

x = percent rate for the 17000 investment.

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so the amount for the 17000 interest will just be (x/100) * 17000, or namely 170x.

and the amount of interest earned for the 11000 is (y/100) * 11000, or just 110y.

now, regardless of what "x" and "y" are, we know that the interest from the 17000 is higher by 308 bucks, therefore 170x = 110y + 308.

we also know that the rate of x is higher as well than y by 0.4%, so then x = y + 0.4.

$\bf \begin{cases} 170x=110y+308\\ \boxed{x}= y +0.4\\[-0.5em] \hrulefill\\ 170\left( \boxed{y+0.4} \right)=110y+308 \end{cases} \\\\\\ 170y+68=110y+308\implies 60y=240\implies y=\cfrac{240}{60}\implies \blacktriangleright y=\stackrel{\%}{4} \blacktriangleleft \\\\\\ x=y+0.4\implies \blacktriangleright x=\stackrel{\%}{4.4} \blacktriangleleft$

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here you have to multiply both sides with 5 to make it a general form ,

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5y = x + 15

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