Answer:
17.75°
Step-by-step explanation:
Since it is a right triangle, we can use pythagorean theorem to find the unknown side, side opposite of the angle "?".
Let that side be "x", so we can write (using pythagorean theorem):
![x^2+20^2=21^2\\](https://tex.z-dn.net/?f=x%5E2%2B20%5E2%3D21%5E2%5C%5C)
Now, solving for x:
![x^2+20^2=21^2\\x^2+400=441\\x^2=41\\x=\sqrt{41}](https://tex.z-dn.net/?f=x%5E2%2B20%5E2%3D21%5E2%5C%5Cx%5E2%2B400%3D441%5C%5Cx%5E2%3D41%5C%5Cx%3D%5Csqrt%7B41%7D)
Now we use Law of Cosines to solve for the angle "?".
Law of Cosines: ![p^2=a^2+b^2-2abCosP](https://tex.z-dn.net/?f=p%5E2%3Da%5E2%2Bb%5E2-2abCosP)
Where
p is the side opposite to angle
P is the angle (we want to solve for)
a, and b are the two sides given
Thus, we have:
![p^2=a^2+b^2-2abCosP\\(\sqrt{41})^2=21^2+20^2-2(21)(20)CosP\\41=841-840CosP\\840CosP=800\\CosP=0.9524\\P=Cos^{-1}(0.9524)\\P=17.75](https://tex.z-dn.net/?f=p%5E2%3Da%5E2%2Bb%5E2-2abCosP%5C%5C%28%5Csqrt%7B41%7D%29%5E2%3D21%5E2%2B20%5E2-2%2821%29%2820%29CosP%5C%5C41%3D841-840CosP%5C%5C840CosP%3D800%5C%5CCosP%3D0.9524%5C%5CP%3DCos%5E%7B-1%7D%280.9524%29%5C%5CP%3D17.75)
1 inch = 0.0833 ft
So if it were 20 inches, one would multiply 0.0833 by 20 to get the amount of ft
If it were 42 inches one would multiply 0.0833 by 42 to get the amount of ft
Whatever the amount of inches multiply it by 0.0833 to find the ft
Slope: (y2-y1)/(x2-x1)
(7-2)/(7-4) = 5/3
Solution: the slope is 5/3
32.75 + 39.88 = 72.63
72.63 x 114% = 72.63 x 1.14 = $82.7982 or $82.80 to the nearest cent.
114% is all of the cost of the meal plus 14 % extra for the tip. See how muliplying by 1.14 includes the $72.63 (this saves the step of adding it on at the end if you were only to find 14% of $72.63)
Answer:
0.189
4.525
Step-by-step explanation:
v/1 + 2/v + 4v/3 = 11
we can eliminate denominators if we distribute 3v to each term:
3v(v/1 + 2/v + 4v/3) = 3v(11)
3v² + 6 + 4v² = 33v
7v² - 33v + 6 = 0
factor this trinomial:
there are no factors of 6 that would add to -33 so we can use the quadratic formula to solve: (-b ± √b²-4ac) / 2a
a = 7
b = -33
c = 6
[33 ± √(-33)² - 4(7)(6)] / 2(7)
(33 ± √1089 - 168) / 14
(33 ± √921) / 14
(33 ± 30.35) / 14
(33+30.35) / 14 = 4.525
(33-30.35) / 14 = 0.189