3(x+6) <= x+5 3x+18 <= x+5 2x <= -13 x <= -6.5 Any number less than or equal to -6.5

x=Bessy’s amount of money y=Bob’s amount of money   x=8y (Bessy has 8 Times as much money as Bob)   x+4=4(y+4) (Bessy will have 4 times much money as Bob if each makes \$4)   Two equations, two variables   x=8y x+4=4(y+4)   Substitute   8y+4=4(y+4) 8y+4=4y+16 4y=12 y=3 x=8*3=24   Bessy...

Car   d=distance car travels when police catches up v=speed of car=31 t=time it takes for police to catch car   d=vt d=31t   Police   d=distance car travels when police catches up t=time it takes for police to catch car Vi=initial...

Let's go step by step:   100 stolen ---- \$100 down Thief gives 100 bill to pay for 70 dollars worth of products ---- back even Give back \$30 in change ---- \$30 loss

Lines that are parallel have the same slopes.  The slope is the number in front of x, so the slope of y = 3x-4 is 3.  So our new line's slope will also be 3   Then we can use the point-slope formula for a line:   y - y1 = m(x-x1) where m is the slope and (x1,y1)...

f = number of \$5 bills t = number of \$10 bills   f + t = 15 5f + 10t = 130   t = 15-f   5f + 10(15-f) = 130 5f + 150 - 10f = 130 -5f = -20 f = 4 t = 11   There are 11 \$10 bills and 4 \$5 bills.

x = amount invested at 6% y = amount invested at 9%   x+y = 25,000   interest income from 6% investment: .06x interest income from 9% investment: .09y   total interest income = 1,860 = .06x + .09y   two equations, two variables   x+y=25000...

A = P(1+r/n)^(nt)   A = new amount P = principal (original amount) r = annual interest rate (as a decimal) n = number of compounding periods / year t = number of years   P = 1000 r = .06 n = 4 (compounding quarterly) t = 1/4 (3 months = 1/4...

(x-1)-2 = 25   (x-1)-2 is the same as 1/(x-1)2   1/(x-1)2=25   1=25(x-1)2   1/25 = (x-1)2   1/5 = √(x-1)2   + or - 1/5 = x-1   x-1 = 1/5 or x-1 = -1/5   x = 1 1/5 or x = 4/5

The problem does not mention compounding interest, so we can assume simple interest.   Interest = Principal * Rate * Time   12%: I12=x*.12*1=.12x   6%: I6=(6300-x)*.06*1=378-.06x   Total Yield = I12+I6=660   .12x+378-.06x=660...

False, that is called the Poisson distribution

Use an exponential decay equation:   A(t) = Ao e^(-kt) where Ao is the starting amount   at time t = 3 hours, we have half of what we started with, so 0.5Ao:   .5Ao = Aoe^(-k*3) .5=e^(-3k) ln(.5)=-3k k=ln(.5)/-3 k=.231   A(t) =...

sin2x = sinx   use the identity: sin2x=2sinxcosx   2sinxcosx = sinx   2sinxcosx - sinx = 0   sinx(2cosx-1) = 0   sinx = 0  OR   2cosx-1=0   sin x = 0 when x is an integer multiple of pi, or x = npi (n = 0, +-1,...

5x2y - 3xy2 = 14   (2,1):   5(2)2(1) - 3(2)(1)2 = 14 5(4)(1) - 3(2)(1) = 14 20 - 6 = 14 14 = 14   d/dx (5x2y - 3xy2 = 14)   5x2(dy/dx) + 10xy - [3x(2y dy/dx) + 3y2] = 0   5x2(dy/dx) + 10xy - 6xy(dy/dx) - 3y2...

We can factor 9-x on the bottom as (3-√x)(3+√x).   Then we can cancel out the 3-√x s. We are left with 1/(3+√x). Now if we plug in 9 for x. We get a value of 1/6, so it is continuous at x=9.

We can rewrite the term of the infinite series like this:   2 * (4/5)^n   Whenever you have a number raised to n like this [r^n], it's a geometric series.  A geometric series converges when the absolute value of the number being raised to a power is less than 1.  It...

To find max and min, we need the first derivative.   f(x) = xsqrt(x2+4) = x(x2+4)1/2   f ' (x) = x*1/2(x2+4)-1/2 * 2x + (x2+4)1/2 * 1 = x2/sqrt(x2+4) + sqrt(x^2+4)   = x2/sqrt(x2+4) + (x2+4)/sqrt(x2+4) =...

Formula for sum of geometric series:   Sum = a/(1-r)   where a is the first term and r is what we multiply by each time.   a = 32   To find r: -8/32 = -1/4; 2/-8 = -1/4.  So r = -1/4   Sum = 32/(1-(-1/4)) = 32/(1+1/4) = 32/(5/4)...

For interest compounding continuously, we need this formula:   A = Pert   A is Amount at some time t P is the initial amount r is the interest rate (as a decimal) t is number of years     For our problem, we would plug in:   A...

The problem discusses two conditions about the field: the area and the length of fencing.  First, the entire field has an area of 1,000,000 ft^2.  Since we don't know the dimensions yet, let's call those x and y.  Since it's a rectangle, the area equation would be:   1,000,000...