Answer:
Step-by-step explanation:
so his class lasts 2 5/6 hrs...and he has already been in there for 1 2/5 hr
so the time he has left can be found by subtracting the time he has been there from the total time of the class
2 5/6 - 1 2/5....
(2 - 1) = 1 : (5/6 - 2/5 = 25/30 - 12/30 = 13/30)
so he has 1 13/30 hrs left <====
Answer:
1) b = 7.4 yds
2) c = 14.9 yds
Step-by-step explanation:
1) 3^2 + b^2 = 8^2
9 + b^2 = 64
b^2 = 64 - 9
b = sqrt 55
b = 7.4 yd
2) 15^2 + 2^2 = c^2
225+4=c^2
Sqrt(221) = c
C = 14.9
Check the picture below.
let's notice that the angle at K is an inscribed angle with an intercepted arc
![\bf \stackrel{\textit{using the inscribed angle theorem}}{K=\cfrac{\widehat{LI}+\widehat{IJ}}{2}}\implies 9x+1=\cfrac{(10x-1)+59}{2} \\\\\\ 9x+1=\cfrac{10x+58}{2}\implies 18x+2=10x+58\implies 8x+2=58 \\\\\\ 8x=56\implies x=\cfrac{56}{8}\implies x=7 \\\\[-0.35em] ~\dotfill\\\\ K=9x+1\implies K=9(7)+1\implies \boxed{K=64}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Busing%20the%20inscribed%20angle%20theorem%7D%7D%7BK%3D%5Ccfrac%7B%5Cwidehat%7BLI%7D%2B%5Cwidehat%7BIJ%7D%7D%7B2%7D%7D%5Cimplies%209x%2B1%3D%5Ccfrac%7B%2810x-1%29%2B59%7D%7B2%7D%20%5C%5C%5C%5C%5C%5C%209x%2B1%3D%5Ccfrac%7B10x%2B58%7D%7B2%7D%5Cimplies%2018x%2B2%3D10x%2B58%5Cimplies%208x%2B2%3D58%20%5C%5C%5C%5C%5C%5C%208x%3D56%5Cimplies%20x%3D%5Ccfrac%7B56%7D%7B8%7D%5Cimplies%20x%3D7%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20K%3D9x%2B1%5Cimplies%20K%3D9%287%29%2B1%5Cimplies%20%5Cboxed%7BK%3D64%7D)
now, let's notice something again, the angle at L is also an inscribed angle, intercepting and arc of 97 + 59 = 156, so then, by the inscribed angle theorem,
∡L is half that, or 78°.
now, let's take a look at the picture down below, to the inscribed quadrilateral conjecture, since ∡J and ∡I are both supplementary angles, then
∡I = 180 - 64 = 116°.
∡J = 180 - 78 = 102°.
I'm not good with any math that is above per algebra sorry.
Answer:
200cm^2
Step-by-step explanation:
When we need to find length of a rectangle we need to divide area by breadth.
Length of a rectangle = Area ÷ breadth.
ℓ = A ÷ b.
Similarly, when we need to find breadth of a rectangle we need to divide area by length.
Breadth of a rectangle = Area ÷ length.