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bogdanovich [222]
3 years ago
12

Which property of equality would be used to isolate the variable a in this equation?. a – 4 = 12. A. addition property of equali

ty. B. subtraction property of equality. C. multiplication property of equality. D. division property of equality
Mathematics
2 answers:
BARSIC [14]3 years ago
5 0
The property of equality that would be used to isolate the variable "a" in this equation is addition property of equality. he correct option among all the options that are given in the question is the first option or option "A". Adding 4 in both sides of the equation will easily isolate the variable "a". I hope the answer helps you.
Minchanka [31]3 years ago
4 0
A - 4 = 12...add 4 to both sides
a = 12 + 4...addition property of equality
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A truncated cone has horizontal bases with radii 18 and 2. A sphere is tangent to the top, bottom, and lateral surface of the tr
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<h3>Answer:  6 units</h3>

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Explanation:

A truncated cone is where we start with a regular 3D cone and chop off the top. The portion up top is a smaller cone, which we'll ignore. The bottom part is the truncated cone portion.

In the real world, a lampshade is one example of a truncated cone.

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Let x be the radius of the sphere.

We'll be focusing on a vertical cross section of the truncated cone. Refer to figure 1 in the diagram below.

We have the following points

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We'll connect a few of those points forming the dashed lines in figure 1.

To start off, draw a segment from D to G. This forms rectangle BGDE with sides of EB = 2x and BG = 2. The side BC is 18 units, so that must mean GC = BC - BG = 18 - 2 = 16.

Since EB = 2x, this means DG is also 2x.

------------------

Now focus on triangles ABC and AFC. They are congruent right triangles. We can prove this using the HL (hypotenuse leg) theorem. Recall that the radius of a circle is perpendicular to the tangent line, which is why angle AFC is 90 degrees. Angle ABC is a similar story.

Because they are congruent right triangles, this indicates side BC is the same length as side FC. Therefore, FC = 18

Through similar logic, triangles ADE and ADF are congruent as well which leads to ED = FD = 2.

Combine sides FD and FC to get the length of DC

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This is the hypotenuse of the right triangle GCD

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After all that, we have the right triangle GCD with the legs of 2x and 16. The hypotenuse is 20. Refer to figure 2 shown below.

As you can probably guess, we'll use the pythagorean theorem to find the value of x.

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4x^2 = 400-256

4x^2 = 144

x^2 = 144/4

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x = sqrt(36)

x = 6 is the radius of the sphere.

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