Consider the line 7x + 5y = 5.

Mathematics

1 answer:

Anna71 [15]3 years ago

3 0

Answer:

M perpendicular line = 5 is the numerator and 7 is the denominator

M parallel line = negative then 7 as the numerator and 5 as your denominator

Step-by-step explanation:

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A parabolà can be drawn given a focus of (7,9) and a

NeTakaya

from the provided focus point and directrix, we can see that the focus point is above the directrix, meaning is a vertical parabola and is opening upwards, thus the squared variable will be the "x".

keeping in mind the vertex is half-way between these two fellows, Check the picture below.

$\bf \textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill$

$\bf \begin{cases} h = 7\\ k = 7\\ p = 2 \end{cases}\implies 4(2)(y-7)=(x-7)^2\implies 8(y-7)=(x-7)^2 \\\\\\ y-7=\cfrac{1}{8}(x-7)^2\implies \boxed{y=\cfrac{1}{8}(x-7)^2+7}$

6 0

4 years ago

A baseball team has 4 pitchers, who only pitch, and 16 other players, all of whom can play any position other than pitcher. F

ivolga24 [154]

Answer:

2,075,673,600 batting orders may occur.

Step-by-step explanation:

The order of the first eight batters in the batting order is important. For example, if we exchange Jonathan Schoop with Adam Jones in the lineup, that is a different lineup. So we use the permutations formula to solve this problem.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!}$