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 >...

FUNCTION HELP PLEASE (answer)

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 >...

use d = rt (d = distance, r = rate of travel = speed, t = time); then "G" catches "D" at t = T, where 9T = 4 + 7T, which can be solved for T to give T = 2 hours

if the hammer is dropped from the roof, which is 25 feet above the ground, then y = -16t^2 + 25, where the origin is at ground level, and where y is the distance of the hammer above the ground at t seconds --- when the hammer hits the ground, at t = T seconds, we have that y = 0 --- in which...

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,...

a cheetah can run (answer)

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...

$6/15 = $2/5 = $4/10, which is less than $5/10

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 +...

The first player could be chosen in 4 ways --- the second player could then be chosen in 3 ways --- the third player could then be chosen in 2 ways --- the fourth player could then be chosen in one way only --- the total number of ways (different orderings) that these four players could be chosen...

let C = number of fish that Cecilia has --- then, O = 2C, where O = number of fish that Oscar has --- and T = O + 8 = 2C + 8, where T = number of fish that Tasha has --- then, C + O + T = C + 2C + (2C + 8) = 148 --- or, 5C + 8 = 148 --- or, 5C = 140 --- or, C = 140/5...

g(x) = 4x - 9; h(x) = x^2 - 4x + 7; g(x) <= f(x) <= h(x); lim(x->4)[g(x)] <= lim(x->4)[f(x)] <= lim(x->4)[h(x)]; 4(4) - 9 <= lim(x->4)[f(x)] <= 4^2 - 4(4) + 7; 16 - 9 <= lim(x->4)[f(x)] <= 16 - 16 + 7; 7 <= lim(x->4)[f(x)] <= 7; therefore,...

17 is prime, that is it can be written only as 17 = 1(17); and 51 is composite (can be written as 51 = 3(17)); therefore, gcf(17,51) = 17

If the 25 kg mass were accelerating downward, that would mean that mg is greater than T (tension), and that we would then have mg - T = ma. However, we are told that the 25 kg mass is decelerating downward at the rate of 5 m/s^2, which can be thought of as accelerating upward at the rate of...

Appilcations of Integration (answer)

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

write the line 3x + 4y = 10 in slope-intercept form: y = -(3/4)x + (5/2) = mx + b, so that m = -(3/4); next, consider the line, y = Mx + B, passing through (-1,-3), perpendicular to the line 3x + 4y = 10, intersecting that line at (c,d); since the line...

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...

just as log(100) = 2, because 10^2 = 100 (10 being the base of the COMMON log), so also we have 10^k = 7

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