Answer:
26, 68 and 84
Step-by-step explanation:
Let the angle that is three times smaller than another be X.
Since the angle sum of a triangle is 180 degrees, we can form the following equation:
X + 3X + (3X- 16) = 180
Now we can simplify this equation:
7X - 16 = 180
7X = 196 (add 16 to both sides)
X = 196/7
X = 28
Therefore, the smallest angle is 28 degrees.
And from here we can figure out the other angles as they are 3x28 and 3x28 - 16.
So the three angles are 28 degrees, (3x28-16) 68 degrees, and (3x28) 84 degrees.
Answer:
24 units
Step-by-step explanation:
Perimeter of Polygon PQRSTU = sum of all its side lengths = PQ + QR + RS + ST + TU + PU
PQ = |-4 -(-2)| = 2 units
QR = |4 - 2| = 2 units
RS = |-2 - 2| = 4 units
ST = |2 -(-2)| = 4 units
TU = |2 -(-4)| = 6 units
PU = |4 - (-2)| = 6 units
Perimeter of Polygon PQRSTU = 2 + 2 + 4 + 4 + 6 + 6 = 24 units
Answer:
Step-by-step explanation:
![\frac{15}{\sqrt{31} - 4}\\\\=\frac{15}{\sqrt{31} - 4} \times \frac{\sqrt{31} + 4}{\sqrt{31}+ 4} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ rationalizing \ the \ denominator \ ]\\\\=\frac{15( \sqrt{31} + 4 )}{(\sqrt{31})^2 - (4)^2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ (a-b)(a+b) = a^2 - b^2 \ ]\\\\=\frac{15 ( \sqrt{31} + 4)}{31 - 16}\\\\=\frac{15 (\sqrt{31} + 4)}{15}\\\\= \sqrt{31} + 4](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7B%5Csqrt%7B31%7D%20-%204%7D%5C%5C%5C%5C%3D%5Cfrac%7B15%7D%7B%5Csqrt%7B31%7D%20-%204%7D%20%5Ctimes%20%5Cfrac%7B%5Csqrt%7B31%7D%20%2B%204%7D%7B%5Csqrt%7B31%7D%2B%204%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%20%20%5B%20%20%5C%20rationalizing%20%5C%20the%20%5C%20denominator%20%5C%20%5D%5C%5C%5C%5C%3D%5Cfrac%7B15%28%20%5Csqrt%7B31%7D%20%2B%204%20%29%7D%7B%28%5Csqrt%7B31%7D%29%5E2%20-%20%284%29%5E2%7D%20%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%20%5C%20%5C%20%5C%20%5B%20%5C%20%28a-b%29%28a%2Bb%29%20%3D%20a%5E2%20-%20b%5E2%20%5C%20%5D%5C%5C%5C%5C%3D%5Cfrac%7B15%20%28%20%5Csqrt%7B31%7D%20%2B%204%29%7D%7B31%20-%2016%7D%5C%5C%5C%5C%3D%5Cfrac%7B15%20%28%5Csqrt%7B31%7D%20%2B%204%29%7D%7B15%7D%5C%5C%5C%5C%3D%20%5Csqrt%7B31%7D%20%2B%204)
Answer:
y=7/10+3/10
Step-by-step explanation:
