What’s the slope of x-5y=15

Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Select t

nignag [31]

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

$y = mx + b$

Where:

m: It's the slope

b: It is the cut-off point with the y axis

On the other hand we have that if two lines are perpendicular, then the product of their slopes is -1. So:

$m_ {1} * m_ {2} = - 1$

The given line is:

$5x-2y = -6\\-2y = -6-5x\\2y = 5x + 6\\y = \frac {5} {2} x + \frac {6} {2}\\y = \frac {5} {2} x + 3$

So we have:

$m_ {1} = \frac {5} {2}$

We find $m_ {2}:$ $m_ {2} = \frac {-1} {\frac {5} {2}}\\m = - \frac {2} {5}$

So, a line perpendicular to the one given is of the form:

$y = - \frac {2} {5} x + b$

We substitute the given point to find "b":

$-4 = - \frac {2} {5} (5) + b\\-4 = -2 + b\\-4 + 2 = b\\b = -2$

Finally we have:

$y = - \frac {2} {5} x-2$

In point-slope form we have:

$y - (- 4) = - \frac {2} {5} (x-5)\\y + 4 = - \frac {2} {5} (x-5)$

ANswer:

$y = - \frac {2} {5} x-2\\y + 4 = - \frac {2} {5} (x-5)$

3 0

3 years ago

Read 2 more answers

the base of the Eiffel tower has a square with an area of 15625 square feet what is the length of the side of the base

tigry1 [53]

77374747484847373848484848

6 0

3 years ago

14. The maximum capacity for seating in a theater is 500 people. The theater sells two types of

Eva8 [605]

Taking into account the definition of a system of linear equations, the amount of adult tickets sold is 356 and the amount of child tickets sold is 144.

<h3>System of linear equations</h3>

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

<h3>Amount of ticket sold</h3>

In this case, a system of linear equations must be proposed taking into account that:

"x" is the amount of adult tickets sold.
"y" is the amount of child tickets sold.

The maximum capacity for seating in a theater is 500 people. If they sold out on a certain showtime, this is represented by x+y=500.

On the other side, the theater sells two types of tickets, adult tickets for $7.25 each and child tickets for $4 each and the made a total of $3,157. This is represented by 7.25x +4y=3157.

So, the system of equations to be solved is

$\left \{ {{x+y=500} \atop {7.25x+4y=3157}} \right.$

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable x from the first equation you get:

x=500 - y

Substituting this expression in the second equation you get:

7.25× (500 -y) +4y=3157

7.25×500 - 7.25y +4y=3157

3625 - 7.25y +4y=3157

- 7.25y +4y=3157 -3625

-3.25y= -468

y= (-468)÷ (-3.25)

Substituting this value in the expression x=500 - y you get:

x=500 - 144

Remembering that "x" is the amount of adult tickets sold and "y" is the amount of child tickets sold, you get that the amount of adult tickets sold is 356 and the amount of child tickets sold is 144.

Learn more about system of equations:

<u>brainly.com/question/14323743</u>

<u>brainly.com/question/1365672</u>

<u>brainly.com/question/20533585</u>

<u>brainly.com/question/20379472</u>

5 0

2 years ago

2 in., 3 in., 6 in.<br> can a triangle have sides with the given lengths

Rainbow [258]

Answer:

No because the 6+4 does not equal 36.

Step-by-step explanation:

first make the hypotenuse 6 the other two are sides A and B

Use the pythagorean theorem: 3^2+2^2+6^2

6+4=36

3 0

3 years ago

The following formula relates 3 equantities: force(F),mass(m),and acceleration(a)

weqwewe [10]

We know, Force = mass × acceleration

( i ) :

Given,
Force = 25 units
Mass = 10 units
Acceleration = ?

Solution,

Applying the formula of force,
➡ Force = mass × Acceleration

⏩ 25 = 10 × acceleration

⏩ 25 / 10 =acceleration

⏩ 2.5 units = acceleration

( ii ) :

Given,
Force = 25 units
Acceleration = 5 units
Mass =?

Solution :

Applying formula,
➡ Force = mass × acceleration

⏩ 25 = 5 × mass

⏩ 25 / 5 = mass

⏩ 5 units = mass

$\:$

5 0

3 years ago