Answer:
(-4,-3)
Step-by-step explanation:
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.
<h3>
Answer: 445.20 dollars</h3>
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Explanation:
There are two approaches.
The slightly longer approach will have us take 6% of 420 to get 0.06*420 = 25.20
So 25.20 is the amount of tax you pay on top of the original $420. The total bill is 420+25.20 = 445.20 dollars
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The shortcut is to multiply 420 by 1.06 to get 420*1.06 = 445.20
The 1.06 multiplier indicates an increase of 6%
We can think of it it as 1.06 = 1 + 0.06 = 100% + 6%
