west palm beach, florida, gets rain about 16 percent of the time. on how many days out of 400 can residents of west palm beach p
2 answers:
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<u>Given</u>:
Given that the quadrilateral ABCD is inscribed in the circle.
The measure of ∠A is (14z - 7)°
The measure of ∠C is (8z)°
The measure of ∠D is (10z)°
We need to determine the measures of ∠A, ∠B, ∠C and ∠D
<u>Value of z:</u>
We know the property that the opposite angles of a quadrilateral inscribed in a circle are supplementary.
Thus, we have;
Substituting the values, we have;
Thus, the value of z is 8.5
<u>Measure of ∠A:</u>
The measure of ∠A can be determined by substituting the value of z.
Thus, we have;
Thus, the measure of ∠A is 112°
<u>Measure of ∠C:</u>
The measure of ∠C can be determined by substituting the value of z.
Thus, we have;
Thus, the measure of ∠C is 68°
<u>Measure of ∠D:</u>
The measure of ∠D can be determined by substituting the value of z.
Thus, we have;
Thus, the measure of ∠D is 85°
<u>Measure of ∠B:</u>
The angles B and D are supplementary.
Thus, we have;
Substituting the values, we get;
Thus, the measure of ∠B is 95°
a. Rounding to the nearest hundredth means that we only have access to numbers with 2 decimal digits. Our number is enclosed between 45.28 and 45.29. Which one is a better approximation? Well, the one who's closer! To tell how "close" two numbers are, just compute the absolute value of their difference:
So, the distance from 45.29 is less than the distance from 45.28, which makes 45-29 the best approximation.
b. Rounding to the nearest integer means that we can't use decimal digits at all. By the same logic of case (a), we have to choose between 27 and 28: we have
Which makes 27 the best approximation
c. Rounding to the nearest tenth means that we can only use one decimal digit. Again, the logic is always the same: the number lies between 0.2 and 0.3, and we use the same test to check which is a better approximation:
Which makes 0.2 the best approximation.
