Answer:
<h2>x = 35</h2>
Step-by-step explanation:
Because the angles are vertical angles, they must be equal.
3x + 7 = 112
3x = 105
x = 35
Check
3(35) + 7 = 112
112 = 112 Correct
Two supplementary angles always adds up to 180 degrees. If an angle is 67.2 degrees less than the measure of a supplementary angle, an equation can be formed where "A" represents the larger angle, and (A - 67.2) represents the smaller angle.
(A - 67.2)+A=180
(Combine the A's)
2A - 67.2=180
(Add 67.2 to both sides)
2A = 247.2
(Divide by 2 to both sides)
A = 123.6
123.6 degrees is the larger angle.
The smaller angle is represented by (A - 67.2). We now know the value of A so lets plug it in. (123.6 - 67.2) = 56.4. 56.4 is the value of the smaller angle.
We can double check to make sure we got the right answer.
123.6 + 56.4 = 180
Problem One
Call the radius of the second can = r
Call the height of the second can = h
Then the radius of the first can = 1/3 r
The height of the first can = 3*h
A1 / A2 = (2*pi*(1/3r)*(3h)] / [2*pi * r * h]
Here's what will cancel. The twos on the right will cancel. The 3 and 1/3 will multiply to one. The 2 r's will cancel. The h's will cancel. Finally, the pis will cancel
Result A1 / A2 = 1/1
The labels will be shaped differently, but they will occupy the same area.
Problem Two
It seems like the writer of the problem put some lids on the new solid that were not implied by the question.
If I understand the problem correctly, looking at it from the top you are sweeping out a circle for the lid on top and bottom, plus the center core of the cylinder.
One lid would be pi r^2 = pi w^2 and so 2 of them would be 2 pi w^2
The region between the lids would be 2 pi r h for the surface area which is 2pi w h
Put the 2 regions together and you get
Area = 2 pi w^2 + 2 pi w h
Answer: Upper left corner <<<<< Answer
The answer is 36. 36 is two digits, 3 and 2, it is a multiple of 6 and 12: 6 times 6 equals 36 and 12 times 3 equals 36, it is a factor of 108: 36 times 3 equals 108, and 36 has digits that equal to 9: 3 plus 6 equals 9.
You should choose c because it makes the most sense out of all of them
