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2 years ago

PLEASE HELPPPPP ME PLEASE I DONT KNOW WHAT TO DO ☹️#7

Mathematics

1 answer:

nirvana33 [79]2 years ago

8 0

Given:

The function is:

$f(x)=-2x+5$

To find:

The inverse of the given function, then draw the graphs of function and its inverse.

Solution:

We have,

$f(x)=-2x+5$

Step 1: Substitute $f(x)=y$ .

$y=-2x+5$

Step 2: Interchange x and y.

$x=-2y+5$

Step 3: Isolate variable y.

$2y=5-x$

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

Step 4: Substitute $y=g(x)$ .

$g(x)=\dfrac{5-x}{2}$

Hence, the inverse of the given function is $g(x)=\dfrac{5-x}{2}$ and the graphs of these functions are shown below.

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3 years ago

Read 2 more answers

Please help me with this

horrorfan [7]

Answer:

$\dfrac{4000\pi}{3}$ ft³

Step-by-step explanation:

First, let's figure out how to get the volume of a sphere from its surface area. If r is the radius of our sphere, then

The formula for a sphere's surface area is $A = 4\pi r^2$

The formula for a sphere's volume is $V=\frac{4}{3}\pi r^3$

So to get from area to volume, we have to divide the area by 3 and then multiply it by r. Mathematically:

$V=\frac{A}{3}r$

Before we solve for V though, we need to find the radius of our sphere. Thankfully, we're given the surface area - $400\pi$ ft² - so we can use the area formula to find that radius:

$A=4\pi r^2=400\pi\\r^2=100\\r=10$

And now that we have our radius, we can put it into our volume formula to find

$V=\frac{A}{3} r=\frac{400\pi}{3}(10)=\frac{4000\pi}{3}$ ft³

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3 years ago

-4x - 6y = 6 4x + 6y = -4

Sloan [31]

Step-by-step explanation:

$-4x - 6y = 6$

$4x + 6y = -4$

To solve a system of equations, we can add the two equations and solve for one of the remaining variables -- let's try to eliminate the $x$ variable when we add the two equations together.

Right now, there's a $-4x$ term in the first equation, and a $4x$ term in the second equation, so if we add those together, we'll be able to eliminate the $x$ variable altogether and solve for $y$ .

However, when we also have a $-6y$ term in the first equation and $6y$ term in the second equation, so adding these together will also eliminate the $y$ term, leaving a $0$ on the left-hand side of the equation.

If we add the two numbers on the right side of the equation, we get $-2$ , which does not equal $0$ , meaning there are no solutions to this system of equations.