a = interest rate of first CD
b = interest rate of second CD
and again, let's say the principal invested in each is $X.
![\bf a-b=3\qquad \implies \qquad \boxed{b}=3+a~\hfill \begin{cases} \left( \frac{a}{100} \right)X=240\\\\ \left( \frac{b}{100} \right)X=360 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{a}{100} \right)X=240\implies X=\cfrac{240}{~~\frac{a}{100}~~}\implies X=\cfrac{24000}{a} \\\\\\ \left( \cfrac{b}{100} \right)X=360\implies X=\cfrac{360}{~~\frac{b}{100}~~}\implies X=\cfrac{36000}{b} \\\\[-0.35em] ~\dotfill\\\\](https://tex.z-dn.net/?f=%5Cbf%20a-b%3D3%5Cqquad%20%5Cimplies%20%5Cqquad%20%5Cboxed%7Bb%7D%3D3%2Ba~%5Chfill%20%5Cbegin%7Bcases%7D%20%5Cleft%28%20%5Cfrac%7Ba%7D%7B100%7D%20%5Cright%29X%3D240%5C%5C%5C%5C%20%5Cleft%28%20%5Cfrac%7Bb%7D%7B100%7D%20%5Cright%29X%3D360%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cleft%28%20%5Ccfrac%7Ba%7D%7B100%7D%20%5Cright%29X%3D240%5Cimplies%20X%3D%5Ccfrac%7B240%7D%7B~~%5Cfrac%7Ba%7D%7B100%7D~~%7D%5Cimplies%20X%3D%5Ccfrac%7B24000%7D%7Ba%7D%20%5C%5C%5C%5C%5C%5C%20%5Cleft%28%20%5Ccfrac%7Bb%7D%7B100%7D%20%5Cright%29X%3D360%5Cimplies%20X%3D%5Ccfrac%7B360%7D%7B~~%5Cfrac%7Bb%7D%7B100%7D~~%7D%5Cimplies%20X%3D%5Ccfrac%7B36000%7D%7Bb%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C)
Cos(2x) = cos^2(x) - sin^2(x) - cos(x)
but sin^2(x) = 1 - cos^2(x)
cos(2x) - cos(x) = cos^2(x) - (1 - cos^2(x) ) - cos(x)
cos(2x) - cos(x) = cos^2(x) - 1 + cos^2(x) - cos(x)
cos(2x) - cos(x) = 2cos^2(x) - 1 - cos(x)
cos(2x) - cos(x) = (2cos(x) + 1)(cos(x) - 1)
I think this is what you have asked for.
By definition, a function is odd if f(-x) = -f(x) for all x in the domain. The answer is choice C
Side note: a function is even if f(-x) = f(x) for all x in the domain
Withdrew 1200
spent 1/5 on travel : 1/5(1200) = 1200/5 = 240
leaving her with : 1200 - 240 = 960
spent 2/3 on hardware : 2/3(960) = 1920/3 = 640
leaving her with : 960 - 640 = 320
320 - lunch = 300.50
320 - 300.50 = lunch
19.50 = lunch <==
Step-by-step explanation:
For the triangle on the bottom right the missing angle is
180- (74+50)= 56°
For the triangle on the bottom left the missing angle is
180- (45+80)= 55°
For the triangle in the middle the missing angle is
180- (54+51)= 75°
For the triangle on top the missing angle is
180- (80+54)= 46°
180- (74+51)= 55°
180- (46+55)= 79°
