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CaHeK987 [17]
3 years ago
9

What is the value of x in the regular polygon below? A. 40 B. 120 C. 60 D. 150

Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
4 0

Answer:

A

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6, thus

sum = 180° × 4 = 720°

Thus each interior angle = 720° ÷ 6 = 120° and therefore

3x = 120 ( divide both sides by 3 )

x = 40 → A

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If rectangle ABCD is rotated counter clock wise 90º about the origin, what will be the coordinates of the vertex D'?
7nadin3 [17]
So, the best way to do this is translate it to clockwise. 90 degrees counterclockwise is equal to 270 degrees clockwise. So, basically, to rotate, you would follow the following format for each point-
(X,Y) -> (-Y,X)
Now, you do it for each of the points.
A= (-5,5), so A' would be (-5,-5)
B= (-1,5), so B' would be (-5,-1)
C= (-5,4), so C' would be (-4,-5)
D= (-1,4) so D' would be (-4,-1)
Notice, how all the points end up in the square below it. Each quadrant has a specific number. The top right is quadrant 1, the top left is quadrant 2, the bottom left is quadrant 3, and the bottom right is quadrant 4. If you are rotating 270 degrees clockwise, you move to the right, like a clock. That puts the new rectangle in quadrant 3. That is a way to check your work.
Now, just so you know for future reference, the following are also different formats for different problems--
A 90 degree Clockwise rotation about the origin will be (X,Y) -> (Y, -X) *Note, -x just stands for the opposite. Say your original x is a negative number. Then the prime (new) x will be positive.
A 180 degree Clockwise rotation about the origin would be (X,Y) -> (-X,-Y) *Note, -y also stands for the opposite.
A 270 degree clockwise rotation about the origin would be (X,Y) -> (-Y,X).
For translating---
90 degrees Clockwise = 270 degrees Counter
270 degrees Clockwise = 90 degrees Counter

Hope this helped!
4 0
3 years ago
The cost of 5 DVDs and a $15
erastovalidia [21]

Answer:

$3

Step-by-step explanation:

the cost of 5 DVDs and a $15

you didn't ask anything

6 0
3 years ago
Read 2 more answers
Simplify using exponent rules.<br><br> (3x^4) (-6x)<br><br><br> (SHOW YOUR WORK)
ehidna [41]

Answer:

Step-by-step explanation:

3x^4(−6x)

=3*x^4*(−6)*x

=−18*x^5

=−18x^5

Hope this helps if I doesn’t helps I will b happy to help u again

4 0
3 years ago
About 11% of people are left-handed. How e = 0.11• 30 e = 3.3 many people would you expect to be left-handed in a class about 3
Marizza181 [45]

Answer:

There are about 3 students that are left handed in a class. First Sara took the percentage of left handed people, 11%,  and multiplied it by the amount of students in the class, 30. She got 3.3 but you can't have 0.3 of a person so she rounded it down to 3.

6 0
3 years ago
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Stanley has $18 to spend on packs of trading cards that cost 1.50 each. The inequality 18x 1.5p represents the number of packs p
aev [14]

Answer:12 packs

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8 0
3 years ago
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