m=# of members 30m=(m-10)*40 30m=40m-400 30m-40m=-400 -10m=-400 m=40 members to begin with 40*$30=$1200
m=# of members 30m=(m-10)*40 30m=40m-400 30m-40m=-400 -10m=-400 m=40 members to begin with 40*$30=$1200
d=r*t 354=r*3+(r+14)*3 354=3r+3r+42 354-42=6r 312=6r r=312/6 r=52 mph r+14=66 mph
this is an example of inverse proportionality 8=k/520 k=8*520 k=4160 days=4160/832 (520+312=832) days=5 or,... xy has to be constant 520*8=832*d 4160=832*d 4160/832=d 5=d again
the distance traveled does not matter because they are the same coming and going let's choose 120 miles for our distance d=r*t 120=60*t (going) t=2 hours 120=40*t (returning) t=3 hours total distance=rate*total time (120+120)=rate*(2+3) 240=rate*5 rate=240/5 rate=48...
2i(5-i)^2 2i(25-10i+i2) 2i(25-10i-1) (i2=-1) 2i(24-10i) 48i-20i2 48i+20 3(5+2i^3)-i(7i^2+4i) 3(5-2i)-i(-7+4i) because i^3=i*i^2=i*(-1)=-i 15-6i+7i-4i2 15-6i+7i+4 because i^2=-1 19+i ...
54-n=36 54-n+n=36+n 54+0=36+n 54-36=36+n-36 54-36=n+36-36 54-36=n+0 18=n
part 1... 13 diamonds+3 kings (the king of diamonds is included in the 13 diamonds and you can't count it twice) 16/52=4/13 or... 13 diamonds+4 kings-1 king of diamonds=16 again part 2... jack of hearts, jack of diamonds, queen of hearts, queen of diamonds,...
135=3*3*3*5 225=3*3*5*5 GCF=3*3*5=45 3 stacks of rice with 45 bags in each stack and 5 stacks of wheat with 45 bags in each stack
x=original cost a 20% discount means you paid only 80% $24 is 80% of what number ? 24=80%*x 24=0.8*x 240=8x 240/8=x x=$30 for the original cost
x^3+10x^2+25x=0 x(x^2+10x+25)=0 x(x+5)^2=0 -5 is the multiple zero (x+5=0 and x=-5) and the multiplicity is 3 (1+2=3, the exponent of x is 1)
[(30)(8.4)-S]/29=8.5 [252-S]=246.5 252-246.5=S 5.5=S [(30)(8.4)-L]/29=8.2 [252-L]=237.8 252-237.8=L 14.2=L 14.2-5.5=8.7 which is E
x^2+8x+15 what 2 numbers multiply to make 15 and add to make 8? 3 and 5 (x+3)(x+5)
(-8a^3b)^(1/3) is the numerator -8 is -2 cubed take out -2 and a from the radicand leaving b inside (-2a)*(3√b) is the numerator (27b^10)^(1/3) is the denominator 27 is 3 cubed and b^10=b^9*b take out 3 and b^3 from the radicand leaving b inside (3*3*3=27 and b3*b3*b3=b9) 3b3*(3√b)...
d=rt 168=(r-w)*2 252=(r+w)*2 simplify 84=r-w 126=r+w add 210=2r r=210/2 r=105 miles per hour is the speed of the helicopter in still air the rate of the wind is 21 mph
18 cups for 20 dogs and 12 cats a dog eats 3 times as much as a cat 20*3+12*1=72 servings for 20 dogs and 12 cats 18/72=1/4 cup 1/4 cup for each cat and 3/4 cup for each dog 12 dogs eat 12*(3/4) cups 20 cats eat 20*(1/4) cup 12*(3/4)=9 cups 20*(1/4)=5 cups 9+5=14...
distance=rate*time total distance=rate*total time You can't add the two rates and divide by two because the time going and the time coming back are different. The distance does not matter because it is the same coming and going. Because the distance does not matter, we can use an...
115.3º go counterclockwise 360º and then go counterclockwise 115.3º to get 115.3+360=475.3º add another 360º to get 360+475.3=835.3º go clockwise 360-115.3=244.7º to get -244.7º go clockwise another 360 to get -360+(-244.7)=-604.7º
distance=rate*time freight train d=25*t passenger train d+280=60*t (the passenger train has to travel the extra 280 miles that the freight train has already traveled since the freight is 280 miles ahead of the passenger) substitute 25t+280=60t 280=60t-25t 280=35t t=280/35 t=8...
distance=rate*time d=r*(2.7) for Eugene d=(r+16.1)*2 for Jose 2.7r=2(r+16.1) 2.7r=2r+32.2 0.7r=32.2 7r=322 r=46 km per hour for Eugene r+16.1=46+16.1=62.1 km per hour for Jose
m=mother's age s=son's age m=s2 m-1=7(s-1) substitute s2-1=7(s-1) s2-1=7s-7 s2-1-7s+7=0 s2-7s+6=0 factor (s-6)(s-1)=0 s-6=0 s=6 m=62=36 the mother is 36 and the son is 6 one year ago their ages were 35 and 5 and 35 is 7*5