## Jonathan F.'s Resources Let's make each an equation. The variables:   x = number of hours y = total number of calories burned   The jogger's equation: y = 225 + 250x The walker's equation: y = 275 + 200x   The number already burned is a constant (just a number, like... First, break 75 into its prime factors: 3, 5, 5. Right now, you have 3 · 5 · 5 under the radical sign. If you have a pair, you can simplify, by putting one of its members (a 5) in front of the radical sign, and removing the other one, since the square root of 52 is 5. The 3 remains... You have a cube root in your denominator. Conjugates only apply to square roots and complex numbers! Don't use them with cube roots, etc.!   1 ------------- 1 - cbrt(3)   What if you could make a difference of two cubes out of that denominator? After all, a cube... This is simply subtracting fractions with like denominators. 5/(x+4) - x/(x+4) = (5-x)/(x+4)   Also, make sure that you specify the domain restriction: x ≠ -4, because if x = -4, then the denominator will be 0, which you cannot have. "Extrema" is the plural; "extremum" is the singular. You have 1 extremum or 2+ extrema. First, you need to find the slope ("m"), which is the change in "y" over the change in "x".   m = (y2 - y1) / (x2 - x1) m = [8 - (-3)] / (8 - 5) m = 11/3   Slope-intercept form is y = mx + b. You now have "m", so: y =... 40 miles per gallon = 40 miles per 1 gallon = 40 miles / 1 gallon. If he can drive 40 miles on 1 gallon of gas, how many miles can he drive on 8.9 gallons of gas?   40 miles * 8.9 gallons = 356 miles ---------- 1 gallon   The "gallons" in the top and bottom... 2n/5 ... let's say that each "n" is a pizza. If you have 2 pizzas, and divide them equally amongst 5 people, each person gets 2/5 of a pizza. Therefore, 2n/5 can be expressed as (2/5)n.   (-n/6) ... again, let's say that each "n" is a pizza. If you have 1 pizza,... This is an algebra word problem. The trick to these is to express them symbolically, using x's. After that, they become regular algebra problems to be solved.   The washer costs 3 times as much as the dryer. Let's say that the dryer's cost is "x", and therefore, the washer's... Exponentiation is just repeated multiplication. Here, you will be multiplying fractions. x2 = x * x   (4/a)2 = (4/a) * (4/a) = 16/a2 This is an "age problem". The trick to these is to express them symbolically, using x's. After that, it becomes a regular algebra problem to be solved.   NOW: John is 4 times as old as Martha. Let's say that Martha's present age is "x", and therefore, John's present... You need common denominators. To subtract (2x+3)/5 from 6x, you need both to be over the same denominator. Look at 6x as "6x / 1". To get the least common denominator, find the least common multiple (LCM) of your denominators (for 1 and 5, this is 5).   To put (2x+3)/5... A network printer is a printer that is connected to a network. Normally, a printer is connected to one computer, which means that you have to use that computer, in order to print to that printer. However, every computer would then need its own local printer. Sharing a printer over a network...