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Answers by Gene G.

The equals sign should not be there! You're supposed to solve the inequality.  It's a lot like solving an equation. You need to get the x by itself on the left side of the inequality symbol. x/5 < 4 multiply both sides by 5 x < (4)(5) x < 20   ...

Both expressions are equal to y, so equate the two to each other and solve for x. 2x-4 = 2cos2π/3x-4 cos2π = 1 2x-4 = 2/(3x-4)  multiply both sides by (3x-4) (2x-4)(3x-4) =  2 6x2-20x+16 =2 6x2-20x+14 = 0 Simplify 3x2-10x+7 = 0 Use AC...

input out put (answer)

a) A(w) = 258 258 = 600 - 19w,    solve for w -342 = -19w 18 = w   b) w =  5 A(5) = 600 - (19)(5) A(5) = 600 - 95 A(5) = 505  

slope of a line (answer)

The point-slope form is: y-y1 = m(x-x1)   Substitute -4 for m, -2 for x1 and 3 for y1.  (-2,3) is an (x,y) coordinate pair. y-3 = -4[x-(-2)] y-3 = -4(x+2)   David got it wrong.  He swapped the x and y. NOTE: This is a really common error!  Since...

Newspapers... (answer)

A Venn diagram will help you visualize this.  A, I, and C You'll have three overlapping circles with regions where they overlap. AI, AC, CI, and ACI. ACI is 15, the number that applied to all three.   Just looking at A: The total for A is 70. 40 applied only...

I spotted the terms x^4 - y^2 as the difference of two squares. Factor that, then see if you can regroup and find a new common factor. It turns out that you can.   Regroup: (x^4 - y^2) + (2x^3 - 2xy) Factor (x^2-y)(x^2+y) + (2x)(x^2-y) There is now...

Simplification (answer)

Break it into pieces that you can write expressions for. Since there are more than 40 hours worked in the week, the full basic wage is (40)(80). The excess hours to be paid at $120/hr is (H-40). The overtime pay is thus (H-40)(120) The 25% tax on the total leaves 75%, so (0.75) times...

Draw a diagram of the garden and sidewalk. The garden is a rectangle 20 x 30 feet. The outline of the sidewalk is a rectangle outside the garden with dimensions: (2x+20) by (2x+30) Where x is the width of the sidewalk. X gets added to both ends of each dimension, so it adds...

July 2012 15 (answer)

Since the numbers of men and women are the same in each village, we only need three variables A, B, and C for the number of men OR women in each.  The populations of the villages are 2A, 2B and 2C.   The number of men in village A plus the number of women in village B equal the...

Word problem (answer)

The trick to this type of mixture problem is calculating the amount of pure acid in the components and the mixture.   The final mixture is 90L of 51% solution. (0.51)(90) = 45.9 L of acid   A = volume of pure acid B = volume of 10% acid   1.00A +...

I don't have time to finish this right now, but here's hard part.   0.07B +0.05C + 0.09M = 8940  total income generated B + C + M = 122000                total invested   B + C = M, so M is half of the...

HELP PLEASE!!! (answer)

T = Taylor's rate = 1/132 jobs per hour M = Michelle's rate = ?   The trick is to add their rates of work, and figuring out how to use that.   Jobs completed in time t is  J = (rate)*t   For Taylor alone, the rate is 1/132 and the time is 132. 1...

2x^5+20x=--14x^3 (answer)

2x^5 + 20x = 14x^3 2x^5 - 14x^3 + 20x = 0 Factor out 2x (2x)(x^4 - 7x^2 + 10) = 0   2x = 0 x = 0   Now factor the remainder. Recognize that x^4 is (x^2)^2. You can work with it as is, or you can substitute u for x^2 to make it look like...