width = W length = L= 2W-6   P = 2L+2W 84=2(2W-6) + 2W 84= 4W -12 + 2W 84 = 6W -12 84+12 = 6W 96 = 6W W=16   Solution W=16 L = 2(16)-6 = 32-6 = 26

30+ 1/4S >=80 1/4S >= 80-30 1/4 S >= 50 S >= 200 per week

If you apply the discount first: 39.99(1-.20)-10 =39.99(.8)-10 =31.99-10 =21.99   If you apply the gift card first: (39.99-10.00)(1-.20) =(29.99)(.8) =23.99   You should apply the 20% discount first.  The lowest final price is \$21.99.

The Santa's are proportional, so the ratio of chocolate to inches is the same.  Therefore, you can solve this using equivalent fractions.   4 oz./2 in.= x oz./5 in.   Cross multiply and solve for x.   x= 10 ounces.   The new Santa needs 10...

paycheck=.1sales +2000 x=sales         y=paycheck 0                  2000 100              2010 200              2020 300      ...

R = C/(X/1000)  Solve for X R = C (1000/X)  multiply by the reciprocal R = 1000C/X RX = 1000C  Multiply both sides by X. X = 1000C/R   X = (1000)(12)/3.028139   X =  3,962

Solve the first equation for y: 3x + 2y = 4 2y = 4 - 3x y = (4 - 3x ) / 2   Substitute (4 - 3x) / 2 for y in the second equation. 5x - 4[(4 - 3x) / 2] = 3 5x - 2(4 - 3x) = 3 5x - 8  + 6x = 3 11 x = 11 x = 1 Use this value for x to solve...

This equation has two answers. Any real number times 0 equals 0.  This is called the zero property of multiplication. Therefore either (c-25) has to equal zero, or (c+50) has to equal zero. SOLUTION:  (c-25)(c+50)= 0 (c-25) = 0 C-25+25 = 0+25   (add...

0 = -1,500,000 + 97,000/.11-g 0=.11-g/.11-g(-1,500,000 + 97,000/.11-g)  remove the fraction be multiplying by .11-g/.11-g 0=-1,500,000(.11-g) + 97,000 0 = -165,000 + 1,500,000g + 97,000   distributive property -1,500,000g = -165,000 + 97,000   ...

PV1 = x PV2 = 15000-x r1=.04 r2=.035 FV = PV1(1+r1) + PV2(1+r2) 15575 = 1.04x + 1.035(15000-x) 15575 = 1.04x + 15525 - 1.035x 50 = .005x x = \$10,000 = PV1 \$15,000-x = \$5000 = PV2

number of adults = x number of children = x+44 number of seniors = total number of tickets - adults - children = 718-x-(x+44)=674-2x Ticket sales = \$21*adults + \$6*children +\$14*seniors 9486 = 21x + 6(x+44) + 14(674-2x) 9486 = 21x + 6x + 264...

x3+2x2-5x-10 factor by grouping and use distributive law: (x3+2x2)-(5x+10) x2(x+2)-5(x+2) (x2-5)(x+2) (x+√5)(x-√5)(x+2)

4m3+5m2-8m-10=0 (4m3+5m2)-(8m+10)=0 m2(4m+5)-2(4m+5)=0 (m2-2)(4m+5)=0 (m+√2)(m-√2)(4m+5)=0 m+√2=0    m-√2=0   4m+5=0 m=√2, -√2 and -5/4

3(-x-4) =2x+3(x-5) -3x-12 = 2x =3x -15      expand by multiplying out the expression in () -3x-12 = 5x-15 -3x+3x-12 = 5x+3x-15  add 3x to both sides -12+15 = 8x-15+15      add 15 to both sides 3 = 8x 3/8...