Find the missing values in the ratio table. Then write the equivalent ratios in the order they appear in the table.

Mathematics

1 answer:

Wewaii [24]2 years ago

8 0

Calories increase by 25 each.
25, 50, ?, ? = 25, 50, 75, 100

Servings increase by 1/3 each. (1 = 3/3)

1/3, 2/3, 1, 4/3

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Which is the standard form of the equation of the parabola that has a vertex of (3, 1) and a directric of x = -2?

vagabundo [1.1K]

Check the picture below. So,the parabola looks like so, notice the distance "p". since the parabola is opening to the right, then "p" is positive, thus is 5.

$\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
\boxed{(y-{{ k}})^2=4{{ p}}(x-{{ h}})} \\\\
(x-{{ h}})^2=4{{ p}}(y-{{ k}}) \\
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\\\
{{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\$

$\bf -------------------------------\\\\
\begin{cases}
h=3\\
k=1\\
p=5
\end{cases}\implies (y-1)^2=4(5)(x-3)\implies (y-1)^2=20(x-3)
\\\\\\
\cfrac{1}{20}(y-1)^2=x-3\implies \boxed{\cfrac{1}{20}(y-1)^2+3=x}$