Plz help me <br> What would be the answer to these three?

What is the equation of a line perpendicular to y= 3/4x +12 that passes through (12, 3)

ycow [4]

Answer:

y=-4/3x-9

=

−

4

3

x

−

9

Step-by-step explanation:

First we need to get the slope of the perpendicular line

The slope of a perpendicular line is equal to the negative inverse of the slope of the given line

y

=

m

x

+

b

y

=

3

4

x

−

2

⇒

m

=

3

4

m

'

=

−

1

m

⇒

m

'

=

−

1

3

4

⇒

m

'

=

−

4

3

Now that we have the slope, we need to find the y-intercept.

To find the y-intercept, we need to plug-in values of

x

and

y

that the line passes through

y

'

=

m

'

x

'

+

b

⇒

y

'

=

−

4

3

x

'

+

b

⇒

7

=

−

4

3

(

−

12

)

+

b

⇒

7

=

16

+

b

⇒

b

=

−

9

Therefore, the equation of the line is

y

=

−

4

3

x

−

9

4 0

3 years ago

Carlo and Anita make mailboxes and toys in their wood shop. Each mailbox requires 1 hour of work from Carlo and 4 hours from Ani

Natali [406]

Answer:

$80

Step-by-step explanation:

Let the number of hours required to make a mailbox = x

Let the number of hours required to make a toy = y

Each mailbox requires 1 hour of work from Carlo and 4 hours from Anita.

Each toy requires 1 hour of work from Carlo and 1 hour from Anita.

The table below summarizes the information for ease of understanding.

$\left|\begin{array}{c|c|c|c}&$Mailbox(x)&$Toy(y)&$Maximum Number of Hours\\--&--&--&------------\\$Carlo&1&1&12\\$Anita&4&1&24\end{array}\right|$

We have the constraints:

$x+y \leq 12\\4x+y \leq 24\\x \geq 0\\y \geq 0$

Each mailbox sells for $10 and each toy sells for $5.

Therefore, Revenue, R(x,y)=10x+5y

The given problem is to:

Maximize, R(x,y)=10x+5y

Subject to the constraints

$x+y \leq 12\\4x+y \leq 24\\x \geq 0\\y \geq 0$

The graph is plotted and attached below.

From the graph, the feasible region are:

(0,0), (6,0), (4,8) and (0,12)

At (6,0), 10x+5y=10(6)+5(0)=60

At (4,8), 10(4)+5(8)=80

At (0,12), 10(0)+5(12)=60

The maximum revenue occurs when they use 4 hours on mailboxes and 8 hours on toys.

The maximum possible revenue is $80.

5 0

4 years ago

Which is inverse f(x)=3x-4

DENIUS [597]

Answer: f^1(x)=x/3+4/3

8 0

4 years ago

Read 2 more answers

What is a unit fraction

amid [387]

A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. A unit fraction is therefore the reciprocal of a positive integer, 1/n. Examples are 1/1, 1/2, 1/3, 1/4 ,1/5, etc.

3 0

3 years ago

Read 2 more answers

there are 18 black socks and 12 Navy socks in your drawer the room is dark and you cannot turn on the light what is the least nu

Natasha_Volkova [10]

Answer:

3/5

Step-by-step explanation:

To have the best chance of pulling a pair with the same color you should try to get a pair of black socks. There is a 3/5 chance of pulling a black sock so this means for every 5 socks you pull you get 3 black socks or 2 navy socks. Either way you will get a pair of socks with the same color. (Double check to make sure I'm correct)

4 0

3 years ago

Read 2 more answers

Plz help me What would be the answer to these three?