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Serggg [28]
10 months ago
5

Solve. 3 Inx= - 12 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. (Type

an integer or a decimal. Round to the nearest thousandth. Use a comma to separate answers.) O B. The solution is not a real number.

Mathematics
1 answer:
faust18 [17]10 months ago
4 0

Problem

Solution

We have the following equation given:

3 ln x= -12

We can divide both sides of the equation by 3 and we got:

ln x= -12/3

ln x = -4

Now we can apply the inverse operation of the ln who is exponentiation with base euler (e) and we have:

e^(ln x) = e^(-4)

If we simplify we got:

x= e^(-4) = 0.018

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In a triangle find the Remote exterior angle given the remote interior angles are 27 and 53
Varvara68 [4.7K]

Answer:We can use equations to represent the measures of the angles described above. One equation might tell us the sum of the angles of the triangle. For example,

x + y + z = 180

We know this is true, because the sum of the angles inside a triangle is always 180 degrees. What is w? We don't know yet. But, we may observe that the measure of angle w plus the measure of angle z = 180 degrees, because they are a pair of supplementary angles. Notice how Z and W together make a straight line? That's 180 degrees. So, we can make a new equation:

w + z = 180

Then, if we combine the two equations above, we can determine that the measure of angle w = x + y. Here's how to do that:

x + y + z = 180 (this is the first equation)

w + z = 180 (this is the second equation)

Now, rewrite the second equation as z = 180 - w and substitute that for z in the first equation:

x + y + (180 - w) = 180

x + y - w = 0

x + y = w

Interesting. This tells us that the measure of the exterior angle equals the total of the other two interior angles. In fact, there is a theorem called the Exterior Angle Theorem which further explores this relationship:

Exterior Angle Theorem

The measure of an exterior angle (our w) of a triangle equals to the sum of the measures of the two remote interior angles (our x and y) of the triangle.

Let's try two example problems.

Example A:

If the measure of the exterior angle is (3x - 10) degrees, and the measure of the two remote interior angles are 25 degrees and (x + 15) degrees, find x.

First example of finding an exterior angle

To solve, we use the fact that W = X + Y. Note that here I'm referring to the angles W, X, and Y as shown in the first image of this lesson. Their names are not important. What is important is that an exterior angle equals the sum of the remote interior angles.

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Select the correct answer.
Irina18 [472]
D. About 122 units I just took the test
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