What is the solution to the following inequality?
-4.2(1 + 2x) < - 23.55 +4.5x

Step-by-step explanation:

-4.2*(1 +2x) < -23.55 + 4.5

Use distributive property

-4.2*1 + 2x *(-4.2) < -23.55 + 4.5x

-4.2 - 8.4x < -23.55 + 4.5x

Add 8.4 x to both sides

-4.2 < -23.55 + 4.5x + 8.4x

-4.2 < -23.55 + 12.9x

Add 23.55  to both sides

-4.2 + 23.55 < 12.9x

19.35  < 12.9x

Divide both sides by 12.9

19.35/12.9 < x

1.5 < x

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages