x^2+8x+15 what 2 numbers multiply to make 15 and add to make 8? 3 and 5 (x+3)(x+5)
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
2^(1-x)=8^(3x+1) 8=2^3 2^(1-x)=(2^3)^(3x+1) 2^(1-x)=2^(3*(3x+1)) 2^(1-x)=2^(9x+3) since the bases are the same the exponents are equal to each other (1-x)=(9x+3) 1-x=9x+3 1=9x+x+3) 1=10x+3 1-3=10x -2=10x x=-2/10 x=(-1/5)...
A=(pi)*r^2 1386=(22/7)(r^2) multiply both sides by (7/22) (7/22)(1386)=(7/22)(22/7)(r^2) 7*63=r^2 7*7*3*3=r^2 (7*63=441 which is 21*21) (21)^2=r^2 r=21 cm
I posted a comment but it didn't show up so I'll explain it here. The letter u is the 21st letter. S=21(21+1)/2=231 and 231-21=210, or t is the 20th letter and S=20(20+1)/2=210. The last t is in position 210. The u's are in positions 211-231. This means that c) 215 and d) 229 are...
Here's another solution. I think the amount of each solution is missing. 7:3 means 7/10=70% milk 3:2 means 3/5=60% milk assume each solution is 100 liters 70%(x)+60%(100-x)=66 2/3%(100) because 2:1 means 2/3=66 2/3 % milk 0.7x+0.6(100-x)=66 2/3 0.7x+60-0.6x=66...
if you flip a coin once, there are 2 possibilities, H or T (2^1) if you flip a coin twice, there are 4 possibilities, HH,HT,TH,TT (2^2=4) three times, 2^3=8 4 times, 2^4=16 5 times, 2^5=32 6 times, 2^6=64 7 times, 2^7=128 total possibilities; this is the denominator how...
(1/2)/8=(1/2)*(1/8)=1/16 received by each think of it this way... if you had a whole cake each person would get 1/8 of the cake, but you only have half of a cake so everybody gets 1/2 of what they would have gotten so each person gets 1/2 of 1/8 which is 1/16
let x=the first number x+8=the second number (the second is 8 more than the first) (1/2)(x-3)=the third number (to go from the first to the third you have to subtract 3 from the first and then take half of what's left-it says "the first is 3 more than twice the third") add...
(1/10)^5=(1/100,000) the probability of rolling a 4 is 1/10 each time you roll the die and you roll the die 5 times the first roll has no effect on the second roll, the second roll has no effect on the third roll, etc
(x-4)(x+5)=0 x^2-4x+5x-20=0 x^2+x-20=0 5x^2+5x-100=0
distance=rate*time 2340=r*4+(r+35)*4 2340=4r+4r+140 2340=8r+140 2340-140=8r 2200=8r r=2200/8 r=275 mph r+35=310 mph
[(x/4)-(4/x)]/[1-(4/x)] [(x^2-16)/4x]/[(x-4)/x] [(x-4)(x+4)/4x]*[x/(x-4) simplify (x+4)/4 (x^(-2)-y^(-2))/(x^(-1)) (x^(-2))/(x^(-1))-(y^(-2)/x^(-1)) x/(x^2)-x/(y^2) (1/x)-(x/y^2), or if you want a single fraction... (y^2-x^2)/xy^2