Part 1
Focus on triangle ABC.
Since AB is a diameter of the circle, this means angle ACB is 90 degrees. Refer to Thale's Theorem. Or you could use the inscribed angle theorem. Thale's theorem is a special case of the inscribed angle theorem.
Minor arc CB is 48 degrees. Use the inscribed angle theorem to see that angle CAB is 48/2 = 24 degrees.
Therefore, angle CBA = 90 - (angle CAB) = 90 - 24 = 66 degrees
<h3>
Answer: 66</h3>
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Part 2
Inscribed angle CBA was found to be 66 degrees back in part 1.
This doubles to 132 degrees to represent minor arc AC.
Or you could note that:
minor arc AC = 180 - (minor arc CB) = 180 - 48 = 132
Inscribed angle BCD is 48 degrees. This doubles to 96 degrees when using the inscribed angle theorem, and this is the measure of minor arc CBD.
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Here's what we know about the arc measures of the circle
- minor arc AC = 132 degrees
- minor arc CB = 48 degrees
- minor arc BD = 96 degrees
These three arcs, along with minor arc AD, will add up to get a full 360 degree circle. Check out the diagram below.
Adding those 3 pieces gets us 132+48+96 = 276
This means minor arc AD has to be 360 - 276 = 84 degrees
Then use the inscribed angle theorem one more time to divide the minor arc AD in half to get the inscribed angle ACD
84/2 = 42
<h3>
Answer: 42</h3>
Answer:A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of a to b is written a to b,ab,ora:b. ... When a ratio is written in fraction form, the fraction should be simplified. If it is an improper fraction, we do not change it to a mixed number.
Step-by-step explanation:
A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of a to b is written a to b,ab,ora:b. ... When a ratio is written in fraction form, the fraction should be simplified. If it is an improper fraction, we do not change it to a mixed number.
Answer:
The correct answer is A) 4/663.
Step-by-step explanation:
First you find the probability of drawing a queen when drawing a single card from a deck of 52 cards. Since there are 4 queens(the queen of diamond, the queen of hearts, the queen of spades, and the queen of clubs) in a deck of 52 cards, the probability of drawing a queen when drawing a single card from a deck of 52 cards is 4/52.
Next you find the probability of drawing a king when drawing a single card from a deck of 51 cards(since you did not replace the first card you drew). Since there are 4 kings(the king of diamond, the king of hearts, the king of spades, and the king of clubs) in a deck of cards, the probability of drawing a king when drawing a single card from a deck of 51 cards is 4/51.
Then you multiply the two probabilities to determine the probability of drawing a queen then a king. So,
4/52 x 4/51 =
4 x 4/52 x 51 =
16/2652
Finally, simplify the fraction. The greatest number that can go into both the numerator and denominator is 4. So divide both the numerator and denominator by 4. When you do this, you get the following:
16 divided by 4 = 4 as the numerator and
2652 divided by 4 = 663 as denominator.
So, the final answer is 4/663.
Answer:
x=14
PN=MN=85
Step-by-step explanation:
It is an isosceles triangle because PQ=MQ and QN is perpendicular to PM. PN=MN
8x-27=6x+1
2x=28
x=14
PN=MN=85
Answer:
21..........
Step-by-step explanation:
