Is the equation true, false, or open?<br> 5x+2=6x+11

Find the slope of the line that passes through the two points.<br> (12,-5) and (10,-4)

hichkok12 [17]

Given parameters:

First point = (12, -5)

Second point = (10, -4)

Unknown:

Slope of the line = ?

Slope is simply the vertical rise divided by the horizontal distance.

Slope = $\frac{Rise }{horizontal distance}$

Simply to find slope;

Slope = $\frac{y_{2} - y_{1} }{x_{2} - x_{1} }$

First point = (12, -5), x₁ = 12 and y₁ = -5

Second point = (10, -4), x₂ = 10 and y₂ = -4

Input the parameters:

Slope = $\frac{-4 -(-5)}{10 - 12}$

= $\frac{-4 + 5}{-2}$

= - $\frac{1}{2}$

The slope of the line is - $\frac{1}{2}$

7 0

3 years ago

What is the area of the parallelogram below if b=6.1? Round your answer to the nearest tenth.

Alisiya [41]

The answer to this is 48.8

6 0

2 years ago

The following table represents Tracie's earnings:

ozzi

In the table it shows that 1 hour corresponds to $25. Or if you want to check it, simply take any value and divide it by its corresponding hour ( ex. 50/2 or 75/3) Hope this helps!

3 0

3 years ago

Read 2 more answers

A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$