Total pay before deductions is known as

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

charle [14.2K]

ANSWER

See below

EXPLANATION

Given

$f(x) = \frac{ {x}- 9 }{x + 5}$

and

$g(x) = \frac{ - 5x - 9}{x - 1}$

$(f \circ \: g)(x)= \frac{ (\frac{ - 5x - 9}{x - 1})- 9 }{(\frac{ - 5x - 9}{x - 1} )+ 5}$

$(f \circ \: g)(x)= \frac{ \frac{ - 5x - 9 - 9(x - 1)}{x - 1}}{\frac{ - 5x - 9 + 5(x - 1)}{x - 1} }$

Expand:

$(f \circ \: g)(x)= \frac{ \frac{ - 5x - 9 - 9x + 9}{x - 1}}{\frac{ - 5x - 9 + 5x - 5}{x - 1} }$

$(f \circ \: g)(x)= \frac{ \frac{ - 5x - 9x + 9 - 9}{x - 1}}{\frac{ - 5x + 5x - 5 - 9}{x - 1} }$

$(f \circ \: g)(x)= \frac{ \frac{ - 14x }{x - 1}}{\frac{ -14}{x - 1} }$

Since the denominators are the same, they will cancel out,

$(f \circ \: g)(x)= \frac{ - 14x}{ - 14} = x$

8 0

3 years ago

Can someone please help me with this problem!

Anna71 [15]

Answer:

11 yards

Step-by-step explanation:

The volume of a cone formula is:

$V=\frac{1}{3}\pi r^2 h$

Where V is the volume,

r is the radius (half of diameter)

h is the height

Given,

h = 15

V = 475.17

We find the radius (r) first by substituting given values:

$V=\frac{1}{3}\pi r^2 h\\475.17=\frac{1}{3}\pi r^2 (15)\\475.17=5\pi r^2\\r^2=30.25\\r=5.5$

The radius (r) is 5.5 yards

We need the diameter, which is DOUBLE THE RADIUS, so diameter would be:

Diameter = 5.5 * 2 = 11 yards

8 0

3 years ago

What is the area of the figure?

Bad White [126]

20m ^2

Explanation:
The top part be be cut into 2 2•2 triangles. A = 4 for both of them
And the rest is a 4•4 square, so A = 16.
4 + 16 = 20

Hope this helps!

5 0

3 years ago

Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the ai

ss7ja [257]

Answer:

The probability that the plane is oveloaded is P=0.9983.

The pilot should take out the baggage and send it in another plain or have less passengers in the plain to not overload.

Step-by-step explanation:

The aircraft will be overloaded if the mean weight of the passengers is greater than 163 lb.

If the plane is full, we have 41 men in the plane. This is our sample size.

The weights of men are normally distributed with a mean of 180.5 lb and a standard deviation of 38.2.

So the mean of the sample is 180.5 lb (equal to the population mean).

The standard deviation is:

$\sigma=\frac{\sigma}{\sqrt{N}} =\frac{38.2}{\sqrt{41}}=\frac{38.2}{6.4} =5.97$

Then, we can calculate the z value for x=163 lb.

$z=\frac{x-\mu}{\sigma}=\frac{163-180.5}{5.97}=\frac{-17.5}{5.97}= -2.93$

The probability that the mean weight of the men in the airplane is below 163 lb is P=0.0017

$P(\bar X$

Then the probability that the plane is oveloaded is P=0.9983:

$P(overloaded)=1-P(X$

The pilot should take out the baggage or have less passengers in the plain to not overload.

7 0

4 years ago

A submersible traveling at a depth of 250 feet dives at an angle of 15 degrees with respect to a

kipiarov [429]

Answer:

$\boxed{\text{652 ft}}$

Step-by-step explanation:

The submersible is diving at a down angle of 15° along the hypotenuse AC of triangle ABC.

Its horizontal track along the surface AB is 1500 ft.

$\begin{array}{rcl}\tan A & = &\dfrac{BC}{AC}\\\\\tan 15^{\circ} & = & \dfrac{a}{1500}\\\\0.2679 & = & \dfrac{a}{1500}\\\\a & = & 1500 \times 0.2679\\& = & \textbf{402 ft}\\\end{array}$

The submersible was already at a depth of 250 feet when it began the dive.

New depth = 250 + 402 = 652 ft

$\text{The depth after the dive is }\boxed{\textbf{652 ft}}$

6 0

3 years ago