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muminat
2 years ago
13

What is the inverse of the function f(x) = x - 12?

Mathematics
1 answer:
ludmilkaskok [199]2 years ago
7 0

Answer: \displaystyle f(x)^{-1}=x+12

Step-by-step explanation:

     First, we will rewrite the function in terms of <em>y</em> as in y = x - 12.

     Second, we will swap the x and y values.

y = x - 12

x = y - 12

     Third, we will solve for y. In other words, we will isolate the <em>y</em> variable and get it "by itself" on one side of the equal sign.

x = y - 12

x + 12 = y

y = x + 12

      Lastly, we will change y back into terms of the function, but the inverse.

\displaystyle f(x)^{-1}=x+12

<em>Learn more about the </em><em>inverse of a function</em><em> here:</em>

<em>brainly.com/question/940569</em>

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Is my answer correct?
kumpel [21]

Answer:

yes

Step-by-step explanation:

YOU DID IT'S A GOOD DAY

4 0
2 years ago
I NEED HELP PLEASE!!!! Given a real world problem, can you find the unit rate?
Yuliya22 [10]

Here is an example:

Josh bought 7 apples for $21.

21/7 is 3, so one apple costs $3. This is the unit rate.

21/7 simplifies to 3/1, that’s another way to think about it. Simplify the fraction until the denominator is 1.

Hope this helps! Tell me if you have any questions!

3 0
3 years ago
What is the area of the shaded region in the figure below ? Leave answer in terms of pi and in simplest radical form
ser-zykov [4K]

Answer:

Step-by-step explanation:

That shaded area is called a segment. To find the area of a segment within a circle, you first have to find the area of the pizza-shaped portion (called the sector), then subtract from it the area of the triangle (the sector without the shaded area forms a triangle as you can see). This difference will be the area of the segment.

The formula for the area of a sector of a circle is:

A_s=\frac{\theta}{360}*\pi r^2 where our theta is the central angle of the circle (60 degrees) and r is the radius (the square root of 3).

Filling in:

A_s=\frac{60}{360}*\pi (\sqrt{3})^2 which simplifies a bit to

A_s=\frac{1}{6}*\pi(3) which simplifies a bit further to

A_s=\frac{1}{2}\pi which of course is the same as

A_s=\frac{\pi}{2}

Now for tricky part...the area of the triangle.

We see that the central angle is 60 degrees. We also know, by the definition of a radius of a circle, that 2 of the sides of the triangle (formed by 2 radii of the circle) measure √3. If we pull that triangle out and set it to the side to work on it with the central angle at the top, we have an equilateral triangle. This is because of the Isosceles Triangle Theorem that says that if 2 sides of a triangle are congruent then the angles opposite those sides are also congruent. If the vertex angle (the angle at the top) is 60, then by the Triangle Angle-Sum theorem,

180 - 60 = 120, AND since the 2 other angles in the triangle are congruent by the Isosceles Triangle Theorem, they have to split that 120 evenly in order to be congruent. 120 / 2 = 60. This is a 60-60-60 triangle.

If we take that extracted equilateral triangle and split it straight down the middle from the vertex angle, we get a right triangle with the vertex angle half of what it was. It was 60, now it's 30. The base angles are now 90 and 60. The hypotenuse of this right triangle is the same as the radius of the circle, and the base of this right triangle is \frac{\sqrt{3} }{2}. Remember that when we split that 60-60-60 triangle down the center we split the vertex angle in half but we also split the base in half.

Using Pythagorean's Theorem we can find the height of the triangle to fill in the area formula for a triangle which is

A=\frac{1}{2}bh. There are other triangle area formulas but this is the only one that gives us the correct notation of the area so it matches one of your choices.

Finding the height value using Pythagorean's Theorem:

(\sqrt{3})^2=h^2+(\frac{\sqrt{3} }{2})^2 which simplifies to

3=h^2+\frac{3}{4} and

3-\frac{3}{4}=h^2 and

\frac{12}{4} -\frac{3}{4} =h^2 and

\frac{9}{4} =h^2

Taking the square root of both the 9 and the 4 (which are both perfect squares, thankfully!), we get that the height is 3/2. Now we can finally fill in the area formula for the triangle!

A=\frac{1}{2}(\sqrt{3})(\frac{3}{2}) which simplifies to

A=\frac{3\sqrt{3} }{4}

Therefore, the area in terms of pi for that little segment is

A_{seg}=\frac{\pi}{2}-\frac{3\sqrt{3} }{4}, choice A.

8 0
3 years ago
In a square, one pair of opposite sides was made 50% longer and the other pair of opposite sides was made 50% shorter
omeli [17]
Sorry, maybe is too late for you, But the answer is:
For example: 4 x 4=16cm² if <span> one pair of opposite sides was made 50% longer and the other pair of opposite sides was made 50% shorter
It became: 6 x 2=12cm</span>²
12/16=0.75
So, the 75% <span>of the square’s area is the area of the new rectangle.</span>
8 0
3 years ago
What is the volume of a cone that has a radius of 12 m and a height of 3 m?
vfiekz [6]
452.16 m^3
1/3 = 0.333333333
0.333333333 * 3.14 = 1.046666667
1.046666667 * 144 =150.72
150.72 * 3 = 452.16
5 0
3 years ago
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