In circle E, and are diameters. Angle BCA measures 53°. Circle E is shown. Line segments A C and B D are diameters. Lines are dr
2 answers:
Answer:
Step-by-step explanation:
Givens
- AC and BD are diameters.
- Angle BCA measures 53°.
Notice that line segment BE is congruent to line segment CE, because they are the radius of the circumference. That means the triangle that contains these sides is isosceles.
, by definition of triangles isosceles.
Then,
, by sum of internal angles.
And,
, by vertical angles definition.
But, we know that the measured of a subtended arc is equal to its angle.
Therefore,
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x + 6y = 12
You want the y-value to be on one side of the equation, so you have to subtract the x-value from both sides.
6y = -x + 12
Next, you divide both sides by 6, so that the y-value will be by itself.
y = - + 2
We know that the slope or the 'm' value is located before the x-value based on y = mx +b, therefore the slope is -
The letters of the word BOOKKEEPER can be arranged in 151,200 ways.
The group can be arranged in 8640 ways with all students of the same major together.
Explanation
There are 10 letters in the word bookkeeper. There is 1 B; 2 O's; 2 K's; 3 E's; 1 P; and 1 R.
An arrangement of n total objects where n₁ is one kind, n₂ is another, etc. is given by:
Keeping all of the students of each major together makes each one essentially a "unit." With this in mind, there are 3 units, that can be arranged in 3!=6 ways.
Within the English unit, the students can be arranged in 3!=6 ways.
Within the anthropology unit, the students can be arranged in 2!=2 ways.
Within the history unit, the students can be arranged in 5!=120 ways.
This gives us 6(6*2*120) = 8640
The group can be arranged in 8640 ways with all students of the same major together.
Explanation
There are 10 letters in the word bookkeeper. There is 1 B; 2 O's; 2 K's; 3 E's; 1 P; and 1 R.
An arrangement of n total objects where n₁ is one kind, n₂ is another, etc. is given by:
Keeping all of the students of each major together makes each one essentially a "unit." With this in mind, there are 3 units, that can be arranged in 3!=6 ways.
Within the English unit, the students can be arranged in 3!=6 ways.
Within the anthropology unit, the students can be arranged in 2!=2 ways.
Within the history unit, the students can be arranged in 5!=120 ways.
This gives us 6(6*2*120) = 8640