Answer: Any of the following angles are <u>not</u> congruent to angle 5.
- angle 2
- angle 4
- angle 6
- angle 8
The only exception being that if angle 5 is 90 degrees, then so are the remaining four angles shown above (in fact, all 8 angles are right angles).
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Explanation:
Angles 2 and 5 are supplementary since line p is parallel to line r. This means angle 2 and angle 5 add to 180 degrees. The two angles are only congruent if both are right angles (aka 90 degree angles); otherwise, they are not congruent angles.
Angle 2 = angle 4 because they are vertical angles. So because these two angles are congruent, and angle 2 does not have the same measure as angle 5, this consequently leads to angle 4 also not being the same measure as angle 5 (unless both are right angles).
Angle 2 = angle 8 because they are alternate interior angles. Following the same logic path as the last paragraph, we see that angles 8 and angle 5 aren't the same measure. Or we could note that angle 5 and angle 8 form a straight angle, so they must add to 180 degrees. The two angles are only congruent if they were 90 degrees each, or otherwise not congruent at all.
Similar logic can also show that angle 6 is not congruent to angle 5.
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An alternative path is to find all the angles that are always congruent to angle 5 and they are...
- angle 1 (corresponding angles)
- angle 3 (alternate interior angles)
- angle 7 (vertical angles)
And everything else is not congruent to angle 5.
The income of the amusement park is a function of the price of the ticket
The entry price that will result in no income is $24
<h3>How to determine the entry price that results in no income</h3>
The expression for the income is given as:
When the income is 0, we have the following equation
Factor out 4x
Split the equation
4x = 0 or 24 - x = 0
Solve for x
x = 0 or x = 24
This means that, the entry price that will result in no income is $24
Read more about income and expenses at:
brainly.com/question/13628349
Answer:
7/12
Step-by-step explanation:
To subtract fractions, you must make all of the fractions have a common denominator. We can set both of the denominators as 12. To achieve this, you must multiply both sides of 2/3 by 4. This will change the denominator of the fraction, while keeping the fraction equal to 2/3. Doing this will give us 8/12. Now we can subtract. Since the denominators are the same, we only subtract the numerators. Since 8-1 is 7, our answer is 7/12. The denominator does not change.
If these permutations were in a line, then the equation would be n!. But since we are dealing with a circle, it's a little bit different, given that there is no specific beginning or end. This means that <span>you could rotate the circle around n different ways and still have the same circular permutation. Thus, this would be the expression you are looking for:
n!/n, which can be simplified as (n-1)!
The correct answer is the second option.</span>
