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Colt1911 [192]
3 years ago
7

I need the steps to this problem, please!

Mathematics
1 answer:
FinnZ [79.3K]3 years ago
5 0
Hello Ashley!

This is an isosceles triangle. How do we know? Well, the two little bar they put means that it is isosceles. When you add all the angles together, you MUST find them equal to 180. Another you need to keep in mind is that the angle that are face to face with each other are ALWAYS equal.

Too much talking...we gonna solve the problem.

x + x + 72 = 180
2x + 72 = 180
2x = 180 - 72
2x = 108
x = 108/2
x= 54
That's the answer .

---------------------
What did we say earlier? We said that when we add all the angles together we MUST find them equal to 180. So, we gonna replace x by 54

54 + 54 + 72  = 180
180 = 180
So.. yes we got it right!

54 is the correct answer.

Good luck with your studies!



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The dimensions of the swimming pool and the gym are proportional.
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<h3>The dimensions of the gym floor could be 150 feet by 120 feet</h3><h3>The dimensions of the gym floor could be 225 feet by 180 feet</h3>

<em><u>Solution:</u></em>

Given that,

The dimensions of the swimming pool and the gym are proportional

The pool is 75 feet long by 60 feet wide

To find: set of possible dimensions for the gym

To determine the possible dimensions for the gym, you would use the same number to multiply both 75 and 60

<em><u>One set of dimensions are:</u></em>

75 x 2 = 150

60 x 2 = 120

The dimensions of the gym floor could be 150 feet by 120 feet

<em><u>Other set of dimensions:</u></em>

75 x 3 = 225

60 x 3 = 180

The dimensions of the gym floor could be 225 feet by 180 feet

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Read 2 more answers
How does one find the inverse function of f(x)= <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3x-1%7D" id="TexFormula1" tit
lisabon 2012 [21]

Answer:

\displaystyle f^{-1}(x)=\frac{1+x}{3x}

Step-by-step explanation:

<u>The Inverse of a Function</u>

The procedure to find the inverse of the function is:

* Write the function as a two-variable equation:

\displaystyle y=\frac{1}{3x-1}

* Solve the equation for x.

Multiply by 3x-1

y(3x-1)=1

Divide by y:

\displaystyle 3x-1=\frac{1}{y}

Sum 1:

\displaystyle 3x=\frac{1}{y}+1

Operate the right side:

\displaystyle 3x=\frac{1+y}{y}

Divide by 3:

\displaystyle x=\frac{1+y}{3y}

* Swap the variables:

\displaystyle y=\frac{1+x}{3x}

Write back into function form:

\boxed{\displaystyle f^{-1}(x)=\frac{1+x}{3x}}

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3 years ago
I am redesigning a rectangular prism in geometry where I have to minimize the surface area while maintaining the same volume. I
Romashka [77]

Strategy:

You will need to make use of the formulas for volume and area of the shapes you have chosen.

... volume of a sphere = (4/3)πr³

... area of a sphere = 4πr²

You will have to use the volume equation to find the radius of the sphere with the desired volume. Then use the area formula to verify the area is smaller than for your rectangular prism. (A sphere has the smallest surface area for a given volume of any figure.)

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For your pyramid, it's a bit more complicated. You can use the formula for volume to find a relationship between the side length and the height. Then you can solve for height and put that expression into the equation for surface area. Now, you have an equation for surface area as a function of side length, which you can use to choose side lengths that give surface area in the range you want. You may find a graphing utility to be helpful for this.

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... area of a pyramid = b^2 + 2bs, where s is the slant height: s=√((b/2)^ +h^2)

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The cylinder is solved essentially the same way the pyramid is solved, except the formulas are slightly different.

... volume of a cylinder = πr²h

... area of a cylinder = 2πr² + 2πrh

Numbers:

If I did it right, a pyramid with a base edge length of 4 or 5 inches (or somewhere between) should give a smaller surface area for the volume you want.

For the cylinder, the radius may be around 2 or 2.1 inches.

5 0
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