Dear Angelica, Let the first number be x, the second y and the third z x + y + z = 141 We are told that x = z - 9 so that (z - 9) + y + z = 141 We are also tole that y = 4z Therefore (z...

## William S.'s Resources

If it were not for functions (and our ability to solve them) there would be no space program, no GPS, no computers, no television, no radio and a thousand other things I would hate to live without.

Let's say f(x) = 3x(x - 2)(x + 1) = 0 We know that this is true when x = 0, x = 2 and x = -1 The person who gave you this problem is very kind. It is already factored in such a way that the identity of the zeros is manifestly obvious.

OK, Ali, here's what we know: If x is one of the numbers, then the other is x + 1 So x(x+1) = 4343 Of course I'm assuming here that the two numbers are integers. x2 + x = 4343 or x2 + x - 4343 = 0 This...

Tonya, The formula I'm used to using is A = P[1 + (r/m)]nt P = principal amount (the initial amount you borrow or deposit) r = annual rate of interest (as a decimal) t = number of years the amount is deposited or borrowed for. A = amount...

Dear Dalia, Here we go: P(x)=x4 - 2x3 - 13x2 - 10x P(x) obviously = 0 when x = 0, so there is one of the real zeros. (x = 0) P(x) can be factored into: x(x -5 )(x + 1)(x + 2) from which it is obvious that x...

Dear Dalia, The real roots of P(x) are as follows: x = -(√2 + 1), x = √2 - 1 and x = 4 P(x) can be factored into (x - 4)*(x2 + 2x - 1). From this it is easy to see that x = 4 is one of the real zeros. (x2 + 2x -...

Dalia, There are two and only two rational zeros of this polynomial: x = -2 and x = 4. To these we may also add x= ±√2i but I don't interpret the question of having asked for imaginary roots.

slope = m = (y1 -y2)/(x1 - x2) = [(-4) - 2]/[7 - (-8)] = (-6/15) = -(2/5) It doesn't make any difference which point is (x1, y1) or (x2, y2) as long as you're consistent with yourself. We could just as easily find the slope as follows: m = [2 - (-4)]/[(-8) -...

x2 + x -30 = 0 This expression can be factored into (x + 6)*(x - 5) = 0 which is true when x = -6 or x = 5.

[5x - 1] ≤ 1 -(5x - 1) ≤ 1 ≤ (5x - 1) -(2/5) ≤ x ≤ 0 [(-2/5), 0]

∫ x(x2 + 2)2dx Let u = x2 + 2 du = 2xdx ∫ x(x2 + 2)2dx = (1/2)∫u2du = (1/2)*(u3/3) = (1/6)*(x2 + 2)3 (evaluated between 0 and 1) = (1/6)[(1)2 + 2]3 - (1/6)[(0)2 + 2]3 = (1/6)*(27 - 8) = (19/6)

I sure hope so.

Let T = total cost of table plus chairs. Then T = $419.99 + (6)*(199.99) = $1,619.93 Since $1,619.93 < $2,000.00 you do have enough money to complete the project. $2,000.00 - $1,619.93 = $380.07. The fact that you...

3[2 + 6(4 - 3)] = 3[2 + 6(1)] = 3(8) = 24

A = A0ekt where A0 = 3000, k = 7% (or 0.07) A = (3000 + 630) = 3630 = 3000e[(0.07)t] Our goal is to find t [(3630)/(3000)] = e[(0.07)t] ln{[(3630)/(3000)]} = (0.07)t (0.07)t = 2*ln(11/10) t...

MinHee, I think it would go something like this: $785 - 10% = $706.50 (by virtue of the advanced booking) $706.50 - 5% = $671.18 (because of the coupon) $671...

Valerie, I think the answer is D. I did this by graphing the original equation and adding the constraints onto it, and I'm pretty sure D (2,7) is the answer. I hope some other tutors on this site will weigh in with their answers.

Hi, Valerie, (4^(1/2)) (x^(1/6)) (y^(2/3)) Well, (4^(1/2)) is easy. That's just 2. Now remember: when you multiply you add the exponents, so (x^(1/6)) (y^(2/3)) = x^((1/6) +(2/3)) = x^((1/6) + (4/6)) = x^(5/6) So (4^(1/2))...

-8x - 5y = 10 I. 5x-15y=30 II. Multiply Equation I. by (-3) 24x + 15y = -30 I.' -5x - 15y = 30 Add the two Equations together: x[24...