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In a triangle, the measure of an angle is in the same order of size as the length of the opposite side. The smallest angle is opposite the shortest side. The largest angle is opposite the longest side. The middle-sized angle is opposite the middle-sized side.
Also, in a triangle, the sum of the measures of the interior angles is 180.
We can now calculate the measures of the three angles by writing and solving an equation.
m<A + m<B + m<C = 180
9x - 7 + 7x - 9 + 28 - 2x = 180
Collect like terms on the left side.
9x + 7x - 2x - 7 - 9 + 28 = 180
14x + 12 = 180
Subtract 12 from both sides.
14x = 168
x = 12
Now that we know x, we can find the measure of each angle.
m<A = 9x - 7 = 9(12) - 7 = 108 - 7 = 101
m<B = 7x - 9 = 7(12) - 9 = 84 - 9 = 75
m<C = 28 - 2x = 28 - 2(12) = 28 - 24 = 4
(Quick check: Add the angles measures: 101 + 75 + 4 = 180. The sum is 180 as it should be.)
Now that we know the angle measures, the opposite sides are in the same order of size.
AB < AC < BC
The sides are, in increasing order of length:
AB, AC, BC
Answer:
6.2 kilograms/ deciliters
Step-by-step explanation:
megagrams to kilograms
1 megagram = 1000 kilograms
hectoliter to deciliter
1 hectoliter = 1000 deciliter
Using conversion factors
6.2megagrams 1000 kilgrams 1 hectoliter
---------------------- * ----------------------- * -------------------------
hectoliter 1 megagram 1000 deciliters
Canceling like terms
6.2 kilograms/ deciliters
Answer:
3 in
Step-by-step explanation:
The volume of the large sphere is ...
V = (4/3)πr³ = 288π . . . cubic inches
The volume of the smaller sphere is ...
288π -252π = 36π . . . cubic inches
The ratio of volumes of the smaller sphere to the larger is the cube of the ratio of radii. The radius of the smaller sphere will be ...
(6 in)∛(36π/(288π)) = (6 in)∛(1/8) = 3 in . . . . small sphere radius