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4 years ago

If z is directly proprotional to x and z = 12 when x = 3, find the value of x when z = 18

Mathematics

1 answer:

elixir [45]4 years ago

3 0

Answer:

Step-by-step explanation:

z is directly proportional to x

z = kx, where k is coefficient

If z = 12 when x = 3

Then we have

12 = 3k
k = 4

So the coefficient is 4

When z = 18, we have

18 = 4x
x = 18/4
x = 4.5

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Answer:

a. $x=4\sqrt{3}$

b. $m\angle B =60\°$

Step-by-step explanation:

a. The sides of an Equilateral triangle are all equal.

Then, in this case:

$AB=BC=CA=8$

Based on this, you can identify that AD divides the side BC into two equal parts and the triangle into two equal Right triangles. Then:

$CD=BD=\frac{8}{2}=4$

Knowing the length CD, you can find "x" using the Pythagorean Theorem. This is:

$a^2=b^2+c^2$

Where "a" is the hypotenuse and "b" and "c" are the legs.

In this case:

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Substituting values and solving for "x", you get:

$8^2=x^2+4^2\\\\\sqrt{8^2-4^2}=x\\\\x=4\sqrt{3}$

b. By definition, the measure of each interior angle of an Equilateral triangle is 60 degrees. Therefore:

$m\angle B =60\°$

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