Mark is right on with his solution. I just want to show you that patterns exist in mathematics. If you recognize them it can make your work a lot easier. However, remember that you must show your work for your teacher.
1/2 + 1/4 + 1/8 + 1/16 + + 1/512=?
1/2 + 1/4=3/4
1/2...

the train travels for 1.5 hours at 90 km/hr for a distance of 135 km
the train travels for 2 hours at 110 km/hr for a distance of 220 km
distance=rate*time
total distance=rate*total time
355=rate*3.5
3550=rate*35
rate=3550/35
rate=101.42857 km/hr is the average...

let d=# of days
let m=amount of money spent per day
d*m=1200
d=1200/m
(d+2)(m-50)=1200
dm+2m-50d-100=1200
substitute 1200/m for d
(1200/m)(m)+2m-(50)(1200/m)-100=1200
1200+2m-(60,000/m)=1300
multiply both sides by m
1200m+2m2-60,000=1300m
2m2+1200m-1300m-60,000=0
2m2-100m-60,000=0
divide...

44/2=22 which is half of the perimeter
write the prime factorization of 112
112=2*56=2*2*28=2*2*2*14=2*2*2*2*7=(2*2*2)*(2*7)=8*14 and 8+14=22
the rectangle is 8m by 14m

Look at the previous problem that Paul M. did for you. It is the same type of problem. The answer is a slight variation of the above answer. You are adding 3 to each term to get the next term instead of adding 4 to each term. Give it a try. You can do it !

let x=the price of the fourth item
1.5+3+4+x=(1.5)(3)(4)(x)
8.5+x=18x
8.5=18x-x
8.5=17x
85=170x
x=85/170
x=0.5
x=$0.50 is the price of the fourth item

equiangular or equilateral triangles have three lines of symmetry

the answer is "parallel" but that is not listed
if you must use one of the words listed the answer would be coplanar

7x-3y=10
-3y=10-7x
3y=7x-10
y=(7/3)x-(10/3)
the slope of a perpendicular line is the negative reciprocal of the slope of the line it is perpendicular to
therefore, -3/7 is the slope which is C.

area=912 and perimeter=134
in a problem like this the simplest thing to do is...
134/2=67 (half of the perimeter)
factor 912
2*2*2*2*3*19=(2*2*2*2*3)*(19)=48*19 and 48+19=67
the lawn is 19 by 48 (the length plus the width equals half of the perimeter)

each square has a side length of √6400=80 cm
draw two squares side by side
80 80
80 80
80 80
6*80=480...

an=a1+(n-1)d is the Arithmetic Sequence Formula
an=1200+(n-1)(-50)
an=1200-50n+50
an=1250-50n

2/(y+1)+3/(y-1)
[2(y-1)+3(y+1)]/(y+1)(y-1)
(2y-2+3y+3)/(y+1)(y-1)
(5y+1)/(y+1)(y-1) or (5y+1)/(y2-1) because (y+1)(y-1)=y2-1

20+30=50 total students
50*56=2800 total points
30*60=1800 total points for girls
2800-1800=1000 total points for boys
1000/20=50 mean for boys

how many ways can you choose 10 houses out of 20 ?
for each group of 10 houses the first person gets, the second person gets the remaining 10 houses
use n!/r!(n-r)! where n=20 and r=10
20!/10!(20-10)!
20!/(10!)(10!)
(20*19*18*17*16*15*14*13*12*11)/(10*9*8*7*6*5*4*3*2)
simplify...

draw a diagram
P-P-P-P-P-P-P-P-P-P-P-P-P
there is a post at each end and 11 posts in between
the 11 posts divides the 48 feet into 12 equal pieces (48/12=4)
each post will be 4 feet from the previous one
you asked "how far is each post from the...

k=# of knives
s=# of spoons
f=# of forks
327=k+s
348=k+f
he lost 10% of the forks so he has 90% of the forks left; 90%f=0.9f
he lost 3 spoons so he has s-3 spoons left
the number of forks and spoons are the same
0.9f=s-3
s=0.9f+3
substitute...

f(x)=5x+2, g(x)=x2+1
g(f(x))=?
replace the x in g(x) with 5x+2
g(5x+2)=(5x+2)2+1
=25x2+20x+4+1
=25x2+20x+5 which is D.

ax=bx+c is the equation that has one solution
ax-bx=c
(a-b)x=c
x=c/(a-b)
ax+b=ax+b has infinitely many solutions
ax+b-b=ax
ax=ax
x=x
ax+b=ax+c
ax-ax+b=c
b=c is a false statement so there are no solut...

12x2+mx+5=0
the roots are in the ratio 3:2, so the roots are 3x and 2x
the sum of the roots is -b/a
3x+2x=-m/12
5x=-m/12
the product of the roots is c/a
(3x)(2x)= 6x2
6x2=5/12
5x=-m/12
60x=-m
x=-m/60
6(-m/60)2=5/12
6(m2/3600)=5/12
m2/600=5/12
m2=(600)(5/12)
m2=50*5
m2=250
m=√250
m=5√10
using...