1. Simplify
[3x^2-27]/[7]
2. Simplify
[7t+28]/[7t]
3. Out of a sample of 230 nails, 6 were rejected because of defective heads. How many defective heads would you expect to find out of a sample of 920 nails? Reduce all fractions to lowest terms.
4. A telephone pole casts a shadow 12 feet long at the same time that a man 6 feet tall casts a shadow of 3.6 feet. How tall is the pole? Reduce all fractions to lowest terms.
5. Simplify
[6t+12]/[t^2-t-6]
6. Simplify
[a-8]/[a+7]
7. Solve for x
[x^2-x=6]
8. Simplify
[2x^2+x-3]/[3x^2-5x+2]
9. Solve
[4x+1]/[3] =[x-5]/[2]
Thanks... these are sample questions in my friends homework and she just doesnt understand it since shes been sick and missing class. Thanks if you can help with the answers. We don't need to hear that she needs to do her own homework, she's already trying and failing at getting the answers right.
Thanks, Emily 1. [3x^2-27]/[7]= 3[x^2-9]/7=3/7[x+3][x-3]
2. [7t+28]/[7t]= 7[t+4]/[7t]= [t+4]/t
3. out of 230, 6 are rejected
therefore out of 920, 920*6/230= 24 nails are rejected
4. since the man is 6 ft tall and casts a shadow of 3.6 ft, the telephone being twice the height of the man will cast a shadow of 3.6*2=7.2 ft tall
5. [6t+12]/[t^2-t-6]=6[t+2]/[t^2-3t+2t-6]=6...
which is 6/[t-3]
6 [a-8]/[a+7] is not further solvable
7 [x^2-x=6] therefore x^2-x-6=0 therefore x^2-3x+2x-6=0
therfore x[x-3]+2[x-3]=0 therfore [x+2][x-3]=0 meaning x=3 or
x= -2
8. [2x^2+x-3]/[3x^2-5x+2]= [2x^2+3x-2x-3]/[3x^2-3x-2x+2]=
[x(2x+3)-(2x+3)]/[3x(x-1)-(x-1)]=[(x-1)(...
2x+3/3x-1
9 [4x+1]/[3] =[x-5]/[2] is nothing but 4x/3+1/3=x/2-5/2
grouping the x terms together gives us 4x/3-x/2= -5/2-1/3
on simplification gives us 5x/6= -17/6
therefore x= -17/5
Hope this helps this r kiddo problems ask ur friend to put a bit more effort 1. 3(x^2 - 9)/7 = 3(x+3)(x-3)/7
2. 7(t+4)/7t = (t+4)/t
3. 920*6/230=24
4. 12*3.6/6 = 7.2
5. 6(t+2)/(t-3)(t+2) = 6/(t-3)
6. (a-8)/(a+7)
7. x^2-x-6 = 0 ; (x-3)(x+2)=0
8. (2x+3)(x-1)/(3x-2)(x-1) = (2x+3)/(3x-2)
9. 2(4x+1)=3(x-5); 8x+2=3x-15 ; 5x=-17; x=-17/5 1) [3x^2-27]/[7]
= 3(x^2 -9)/7
= 3(x+3)(x-3)/27
2) [7t+28]/7t
= 7t/[7t] +28/[7t]
= 1 + 4/t
3) Fraction of Bad nails is 6/230 = 3/115
Bad nails in 920 is 920 *3/115 = 184*3/23= (184/23 )* 3= 8*3=24. So you expect 24 bad nails.
4) Ratio of actual man height/shadow of man's height is the same as the ratio of actual pole height (let this be x)/ shadow of pole
6/3.6 = x/12
60/36= 10/6=5/3=x/12
therefore x= 6*12/3.6= 6*10*12/36= 1*10*12/6= 1*10*2= 20ft
5) [6t+12]/[t^2-t-6]
[(6(t+2)]/[(t-3)(t+2)]
t+2 will cancel leaving
6/[t-3]
6) [a-8]/[a+7]
cannot be simplified more than this.
7) [x^2-x=6] take 6 from both sides
x^2 - x-6= 0
(x-3)(x+2)= 0
Therefore (x-3)= 0 and (x+2)= 0
Therefore x= -2 and +3.
8) [2x^2+x-3]/[3x^2-5x+2]
= [(2x +3)(x-1)]/[(3x-2)(x-1)]
(x-1) cancels out.
= [(2x+3)]/[(3x-2)]
9) [4x+1]/[3] =[x-5]/[2]
2[4x+1]= 3[x-5]
= 8x + 2 = 3x -15
= 5x = -17
x= -17/5.
That's a lot of hard work. | 