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Answers by Herb K.

if the original function is y = f(x), then      (a)  if y = f(x) + k;   translate vertically upward, if k > 0; translate vertically downward if k <0      (b)  if y = f(x-a);  translate horizontally to the right, if a >...

if the number of numbers in the data set is odd (e.g., 5), then the median will be a value on the data set --- example: 2, 5, 8, 9, 10 --- the median is the middle number, i.e., 8, which is a number in the data set --- if, on the other hand, the number of numbers in the data set is even (e.g,...

let C = speed of cheetah; let  L = speed of lion --- then C = L + 20 --- also, from distance = speed (time), we have time = distance/speed --- so that, 7/C = 5/L --- or C =(7/5)L --- then, (7/5)L = L + 20 --- or, (2/5)L = 20 --- or, L = (5/2)20 --- or, L = 50 --- and C = L + 20...

if 2 out of 5 sheep are white, then 3 out of 5 sheep are black --- thus, the ratio of black sheep (B) to white sheep (W) is B/W = 3/2 --- also, B = W + 8 --- or (W + 8)/W = 3/2 --- or, cross multiplying, 3W = 2(W + 8) --- or, W = 16, and B = W + 8 = 16 + 8 = 24 --- then, B +...

average value of a function, f(x), over an interval [a,b], is given by (1/(b - a))[integral from a to b of f(x)dx], which in this case, a=0 and b=6, becomes [1/(6 - 0)]S(0,6)x^2 dx = (1/6)[x^3/3](0,6) = (1/18)[6^3 - 0^3] = (1/18)(6)(36) = 36/3 = 12

Consider: 4(30) = 120 then, consider various ways to multiply two numbers together to get 120: 1       120           note:  1 + 120 = 121 2         60          ...

(x+3)(x^2+4x-5) (answer)

if you are being asked to multiply, then use Distributive Property:  (x + 3)(x^2 + 4x - 5) = x(x^2) + x(4x) + x(-5) + 3x^2 + 3(4x) + 3(-5) = x^3 + 4x^2 - 5x + 3x^2 + 12x - 15 = x^3 + 7x^2 + 7x - 15   if, on the...