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A more direct approach.   Let l be the dimension parallel to the barn's wall. l + 2w = 100   Total length of fencing used.  Notice there's only one l. l = 100 - 2w   A =  lw = (100-2w)(w) = -2w2+100w This parabola describes area versus...

"Grade" is most often seen in situations where it refers to the slope of the ground.  A highway sign warning for a steep hill may reference a 10% grade.  You can also snoop around for home building or landscaping applications where it may be referenced as inches per foot. ...

Solve for x, a/x+a + b/x-b = (a+b)/(x+c)   This one is a bit too messy to type out without a real equation editor, but here's how to proceed.   (I assumed that the x+a and x-b should have been in parentheses.)   Find a common denominator...

Here's the hard way: Starting with A: A    AB       ABC       ABD       ABE    AC       ACD       ACE    AD       ADE B   ...

I played with this for a while too, and wasn't able to reach any of the given choices. I decided to just check using some known angle to see if any of the choices would work. Using a calculator and 30 degrees, none of the choices has the same calculated value as the original formula. Check...

Put your numbers in order (27, 27, 57, 57, 59, ...) Divide them into 4 same-sized groups. There are 24 numbers in the dataset, so it divides into 4 groups with 6 values in each one.   Since the dividing lines between fourths (quarters) all lie between two numbers (for...

First, area is measured in square units.  You're asked to find an area.   The question is then, what area is inclosed in a square area.  You can find the dimensions of the square from the amount of fencing required to go around the square and to divide it into 4 sub-squares...

"Similar" means one is a scale model of the other.   If you increase all dimensions of ANY plane figure by a factor, the ratio of the areas is that factor squared!   Large dimension is 4x the small one. The ratio is 16:1.   Try it with a couple...

A = number with \$20 bonus B = number with \$50 bonus   The average bonus is the total of all bonuses divided by the number of employees.   (20A + 50B) / 20 = 38 A + 2.5B = 38 A + B = 20   A + 2.5B = 38 A +    1B...

V = x3 x = 1/4   You can just multiply fractions like this: 1/4 x 1/4 x 1/4 = (1 x 1 x 1) / (4 x 4 x 4)                        = 1/64   or you can cube the fraction like this: (1/4)3 = 13/43 =...

The trick to this mixture problem is to calculate the amount of chlorine in each component and in the final mixture. Then you can write the second equation that you need.   A = amount of 6% solution B = amount of 18% solution   Total of A and B is 8 liters A +...

The trick to this one is recognizing that consecutive odd numbers increase by 2 for each step.  (Would be the same for even numbers!)   Call the first one n, the second (n+2) and the third (n+4).  Now you can write an equation.   Now look for things you...

The increase in the water level is the amount of volume that the nugget added, the same as if you had just added water.   Subtract: 225 - 80 = 145 ml

I like to tell people to look for pieces that you can write expressions for, then re-read the problem to see how to put them together.   Arthur weighs 21 lbs more than lily. A = L + 21   four times lily's weight 4L   114 lb less than four times...

Pr(T) would be the probability of getting tails. The probability of getting heads OR tails is 100%, or 1.0, so Pr(H) = 1.0 - 0.6 = 0.4. That's 4 out of 10.   How many heads out of 85 tosses? 0.4 * 85 = 34

This is a system of equations: 3b + 4e = 12.33 4b + 3e = 14.13   Multiply the top equation by 4 and the bottom one by 3:   12b + 16e = 49.32 12b +   9e = 42.39 _______________   Subtract     0 +   7e = 6.93   e...

3 - 1 / (x-1) = 3x/(x-2)   The first step is to eliminate the denominators.  To do this multiply both sides by (x-1) * (x-2) One of these factors will cancel out in each of the fractional terms.   (3)(x-1)(x-2) - (1)(x-2) = (3x)(x-1)   Now it's a matter...

This may be easier to follow.  Do the synthetic division normally, but leave it in terms of a.  We know the remainder must be zero because (x-3) is a factor.   3   |   1     a            -5          ...

The key to starting this one is recognizing that you can factor the difference of two squares.   Taking the first part of the relationship: a+b =  a^2 - b^2   (you goofed on the sign here!)   You can factor the difference of two squares, so: a+b...

The end of the question is missing.  I'm assuming that it ask how many people earned more than \$60,000.   We know how many people were surveyed: 1200.  2 1/2% of those people earn more than \$60,000.  The question is, "How many people is that?"  Stated differently,...