Write a integer for the situation a deposit of $145.50<br> Helpppp fast pleaseeeee

Consider the function f(x)= 2/5x-4

Gre4nikov [31]

Answer: a) $\frac{5}{2}x+10=f^{-1}(x)=g(x)$

Step-by-step explanation:

Since we have given that

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

a.) Find the inverse of f(x) and name it g(x).

Let f(x) = y

So, it becomes

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

Switching x to y , we get

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

$5x=2y-20\\\\5x+20=2y\\\\\frac{5x+20}{2}=y\\\\\frac{5}{2}x+10=y\\\\\frac{5}{2}x+10=f^{-1}(x)=g(x)$

b) . Use composition to show that f(x) and g(x) are inverses of each other.

$\mathrm{For}\:f=\frac{2}{5}x-4\:\\\\\mathrm{substitute}\:x\:\mathrm{with}\:g\left(x\right)=\frac{5}{2}x+10\\\\=\frac{2}{5}\left(\frac{5}{2}x+10\right)-4\\\\=x$

Similarly,

$\mathrm{g\left(x\right)=\frac{5}{2}x+10,\:f\left(x\right)=\frac{2}{5}x-4,\:g\left(x\right)\circ \:f\left(x\right)}\\\\\mathrm{For}\:g=\frac{5}{2}x+10\:\mathrm{substitute}\:x\:\mathrm{with}\:f\left(x\right)=\frac{2}{5}x-4\\\\=\frac{5}{2}\left(\frac{2}{5}x-4\right)+10\\\\=x$

so, both are inverses of each other.

c) Draw the graphs of f(x) and g(x) on the same coordinate plane.

As shown below in the graph , Since for inverse function we need an axis of symmetry i.e. y=x

And both f(x) and g(x) are symmetry to y=x.

∴ f(x) and g(x) are inverses of each other.

5 0

4 years ago

Make a frequency table to show the following test times (in minutes) for a reading test. 81, 63, 61, 58, 72, 70, 79, 68, 82, 64,

kodGreya [7K]

Sorry about my handwriting. this is what your graph should look like

3 0

4 years ago

PLS HELPPPPP THANK UUU

Julli [10]

C. x=3/2 y=1/2

Hope this helps!

3 0

3 years ago

Ruben bought 6 new books for his collection. This increased his collection by 12%. How many books did he have before his purchas

Norma-Jean [14]

Answer: The required number of books that Ruben had before purchases is 50.

Step-by-step explanation: Given that Ruben bought 6 new books for his collection that increased his collection by 12%.

We are to find the number of books that Ruben had before purchases.

Let x denotes the number of books that Ruben had before purchases.

Then, according to the given information, we have

$x+6=x+12\%\times x\\\\\\\Rightarrow 6=\dfrac{12}{100}x\\\\\\\Rightarrow 6=\dfrac{3x}{25}\\\\\\\Rightarrow 3x=150\\\\\Rightarrow x=\dfrac{150}{3}\\\\\Rightarrow x=50.$

Thus, the required number of books that Ruben had before purchases is 50.

4 0

3 years ago

Hey anyone know this ?

Sergeu [11.5K]

Answer:

It's an equilateral triangle so the measure of each angle here=60 degrees

s..4x degree=15*4

hence, the value of X=15

<h2>Have a good day Ahead:)</h2>

6 0

3 years ago

Write a integer for the situation a deposit of $145.50 Helpppp fast pleaseeeee