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Nadya [2.5K]
3 years ago
7

Which option correctly shows how this formula can be rearranged to isolate x^2?

Mathematics
1 answer:
Dimas [21]3 years ago
4 0

Answer:

A

Step-by-step explanation:

We have:

\displaystyle m=\frac{x_1-x_2}{y_1-y_2}

And we want to isolate x₂.

So, let’s first remove the denominator by multiplying both sides by it:

\displaystyle m(y_1-y_2)=\frac{x_1-x_2}{y_1-y_2}(y_1-y_2)

The right side will cancel. This will leave:

\displaystyle m(y_1-y_2)=x_1-x_2

Now, we can subtract x₁ from both sides. So:

\displaystyle m(y_1-y_2)-x_1=-x_2

Finally, we will multiply both sides by -1. So:

\displaystyle x_2=-m(y_1-y_2)+x_1

Hence, our answer is A.

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The cost, C, to produce b baseball bats per day is modeled by the function C(b) = 0.06b2 – 7.2b + 390. What number of bats shoul
kozerog [31]

Check the picture below, that's just an example of a parabola opening upwards.

so the cost equation C(b), which is a quadratic with a positive leading term's coefficient, has the graph of a parabola like the one in the picture, so the cost goes down and down and down, reaches the vertex or namely the minimum, and then goes back up.

bearing in mind that the quantity will be on the x-axis and the cost amount is over the y-axis, what are the coordinates of the vertex of this parabola?  namely, at what cost for how many bats?

\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ C(b) = \stackrel{\stackrel{a}{\downarrow }}{0.06}b^2\stackrel{\stackrel{b}{\downarrow }}{-7.2}b\stackrel{\stackrel{c}{\downarrow }}{+390} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)

\bf \left( -\cfrac{-7.2}{2(0.06)}~~,~~390-\cfrac{(-7.2)^2}{4(0.06)} \right)\implies (60~~,~~390-216) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (\stackrel{\textit{number of bats}}{60}~~,~~\stackrel{\textit{total cost}}{174})~\hfill

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3 years ago
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The ratio of boys to girls in a class is 5:4. There are 36 Students in the class.How many students are girls
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Answer:

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Step-by-step explanation:

boys : girls : total

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