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3 years ago

Find an equation of the line. Write the equation using function notation. Through (3, -3); perpendicular to 5y= x-10

1 answer:

3 0

$\bf 5y=x-10\implies y=\cfrac{x-10}{5}\implies \stackrel{slope}{y=\stackrel{\downarrow }{\cfrac{1}{5}}x-2} \\\\\\ \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{1}{5}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{5}{1}}\qquad \stackrel{negative~reciprocal}{-\cfrac{5}{1}\implies -5}}$

so we're really looking for the equation of a line whose slope is -5 and runs through 3, -3.

$\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-3})~\hspace{10em} slope = m\implies -5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-3)=-5(x-3) \\\\\\ y+3=-5x+15\implies \stackrel{y}{f(x)}=-5x+12$

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Answer:the number one

Step-by-step explanation:

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3 years ago

Which table shows a proportional relationship between x and y? Plz Help

Nastasia [14]

Answer:

The proportional table in the attached figure

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Verify each table

Find the value of the constant of proportionality k for each ordered pair of a table.

$k=\frac{y}{x}$

If all the values of k are the same, then the table represent a proportional relationship between x and y

Table 1

For x=1, y=2 ----> $k=\frac{2}{1}=2$

For x=2, y=4 ----> $k=\frac{4}{2}=2$

For x=3, y=8 ----> $k=\frac{8}{3}=2.7$

The values of k are not equal

This table not represent a proportional relationship between x and y

Table 2

For x=0, y=4

The line not passes through the origin

This table not represent a proportional relationship between x and y

Table 3

For x=0, y=0 ----> is OK the line passes though the origin

For x=1, y=1 ----> $k=\frac{1}{1}=1$

For x=2, y=4 ----> $k=\frac{4}{2}=2$

The values of k are not equal

This table not represent a proportional relationship between x and y

Table 4

For x=1, y=4 ----> $k=\frac{4}{1}=4$

For x=2, y=8 ----> $k=\frac{8}{2}=4$

For x=3, y=12 ----> $k=\frac{12}{3}=4$

The values of k are the same

This table represent a proportional relationship between x and y

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4 years ago

What is the vertex of the graph of y = x^2 + 4x?

Sidana [21]

The answer is (-2,-4)

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4 years ago

GUYSSSSS!!!! PLEASE I NEED HELP RIGHT NOWW!!! HELP PLEASE!

nikdorinn [45]

Answer:

$\angle ABC=20^{\circ}$

Step-by-step explanation:

Since each side of a line is 180 degrees, we can write the following system of equations:

$\begin{cases}2x+12y+x+2y=180,\\x+2y+8y-4x=180\end{cases},\\\begin{cases}3x+14y=180,\\-3x+10y=180\end{cases}$

Add both equations to solve for $y$ :

$24y=360,\\y=\frac{360}{24}=15$

Now substitute $y=15$ into $3x+14y=180$ to solve for $x$ :

$3x+14(15)=180,\\3x=-30,\\x=-10$

Finish by substituting both variables to solve for $\angle ABC$ :

$\angle ABC=x+2y,\\\angle ABC=-10+2(15),\\\angle ABC=-10+30=\boxed{20^{\circ}}$

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3 years ago

1. How does the scope of practice help regulate the health care field?

Lubov Fominskaja [6]

Answer:

Scope of practice describes the procedures, actions, and processes that a healthcare practitioner is permitted to undertake in keeping with the terms of their professional license.

Step-by-step explanation:

By implementing the law which restricts certain people to work under what they excel they are low chances of making errors in their respective field . and this leads to increase in the proper medical treatment and this would regulate the health care field. suppose if a person with tooth pain comes to neurologist ,according to scope of practice restricted to treat him which results in the neurologist making error in treating dental problem is decreased and he might consult better dentist.

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3 years ago