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(6v - 5b)(3v - 2b)

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d + g = 95 ___ d = 95 - g

2d + 4g = 316

substituting ___ 2(95 - g) + 4g = 316 ___ 190 - 2g + 4g = 316 ___ 2g = 126

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distance / rate = time

a = distance going uphill, returning downhill
b = distance going and returning level
c = distance going downhill, returning uphill

a/2 + b/3 + c/6 + c/2 + b/3 + a/6 = 6

3a + 2b + c + 3c + 2b + a = 36

4(a + b + c) = 36

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e = w + 497

e - 58 = 2(w - 58)

substitute the equivalent value of e from the 1st equation into the 2nd equation to find w

substitute the numerical value of w into the 1st equation to find e

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time = distance / rate

9 / (30 + c) = 1 / (30 - c)

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h + q = 65

.5h + .25q = 26

find the equivalent value for h (or q) in the 1st equation and substitute the value into the second equation

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in the 2 hrs that they work together:

Jane paints 2/5 of the fence (2 hr / 5 hr)

Paul paints 1/3 of the fence (2 hr / 6 hr)

it takes Peter 2 hr to paint the remaining fraction [1 - (2/5) - (1/3)]

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c = r - 6.8

17(r + c) = 26.5(r - c)

substitute the equivalent value of c from the 1st equation into the 2nd equation and solve for r

then substitute the numerical value of r into the 1st equation to find c

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multiply by the LCD (550) ; add the x-terms ; divide to find x

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each term equals the previous term with 10 added

so the nth term is ___ 1 + 10n

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the formula you need is:

the average of the bases , multiplied by the height

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L = W + 10

2L + 2W = 100 ___ substitute the equivalent value for L from the first equation and solve for W

then substitute the numerical value for W into the first equation and find L

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the factors are (p + 3) and (p + 4)

for the product of the factors to be >0 ; either both factors are >0 , OR both factors are <0

p + 3 > 0 ___ p > -3
p + 4 > 0 ___ p > -4

p + 3 < 0 ___ p < -3
p + 4 < 0 ___ p < -4

p must be > -3 AND -4 (which means greater than -3) , OR < -3 AND -4 (which means less than -4)

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1000 * (1 + .08)^60

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A.

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x = amount at 4.5%

(x)(4.5%) + (3000 + x)(6%) = 390

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x = gallons of 4%

(x)(4%) + (39 - x)(1%) = (39)(2%)

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R = H + 6

R + 2 = 2(H + 6 + 2) ___ R + 2 = 2H + 16 ___ substitute the equivalent value of R from the first equation to find H

then substitute the numerical value of H into the first equation to find R

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97/18

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a quarter, two nickels , 5 dimes , 6 pennies

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good solution , and correct

not sure about 3n-4=32 , but you seemed to ignore it

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since zero stories corresponds to zero height , the graph should probably pass through the origin (0,0)

h = (301/23)s + 0 ___ or ___ h = (301/23)s

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the parent(s) are easy to factor in , just concentrate on the boys and girls

the only way for no two boys or two girls to be next to each other is for them to be alternating around the circle

imagine a ring of 5 boys (with spaces) and a ring of 5 girls (with spaces)
___ the rings are intermeshed to make the seating arrangement

how many ways can five things be ordered or arranged sequentially?
___ usually , 5!
___ but a circular arrangement repeats itself as many times as there are positions on the circle
___ so there are 4! (5! / 5) orders for the ring of boys and for the ring of girls
___ there are also 5 ways for the rings to intermesh

so the number of boy-girl arrangements is ___ 4! * 4! * 5

one parent can insert a chair at any of 10 places on the circle
___ so boys and girls and one parent is ___ 4! * 4! * 5 * 10

the second parent would have 11 places to insert a chair
___ so boys and girls and two parents is ___ 4! * 4! * 5 * 10 * 11

the second parent would also allow an adjacent boy and girl to swap positions
so that two boys and two girls
would be separated by parents instead of other boys and girls
___ 10 possible swaps with two positions for the parents
___ the possible arrangements now becomes ___ 4! * 4! * 5 * (10 * 11 + 20)

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if "d+n=47" (which is true), how can "n=d+47" ?

try ___ n = 47 - d

your method is okay

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dividing by 8 ___ x^2 = 1

taking square root ___ x = ±1

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(fraction done by larger pump) + (fraction done by smaller pump) = (whole task)

[5 / (s - 4)] + (5 / s) = 1

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(35 / n) - 2 = 35 / (n + 2)

multiplying by n(n + 2) ___ 35n + 70 - 2n^2 - 4n = 35n

n^2 + 2n - 35 = 0

factoring ___ (n + 7)(n - 5) = 0

n = 5

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Rebecca catches Larry when they have both traveled the same distance

distance equals rate multiplied by time

Rebecca's rate is 25 mph and her time is one hr less than Larry's

Larry's rate is 20 mph

the T in the equations represents Larry's time

depending on your viewpoint, you might say that Rebecca's time to catch Larry doesn't start until Rebecca starts
___ so the answer is either 4 hr or 5 hr

hope this helps

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subtracting 45.4 ___ -2.67 = -.03t

dividing by -.03 ___ 89 = t

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(1 - .002)^h = 1/2

h * log(1 - .002) = log(1/2)

h = [log(1/2)] / [log(1 - .002)]