1. a website sells sweaters. the amount of sales p(c) varies directly with the number of customers c. ten customers bought a total of $455 worth of sweaters. which equation can be used to find the sales for c customers? a. p(c) = 45.5c b. p(c) = 455c c. p(c) = 4550/c d. p(c) = 455/c 2. the time it takes to wash all the windows on a large building w(x) varies inversely with the number of workers assigned to the job x. it takes 6 hours to complete the job when 4 workers are assigned to it. which equation can be used to find the time to complete the job when x workers are assigned to it? a. w(x) = 1.5x b. w(x) = 24x c. w(x) = 10/x d. w(x) = 24/x

1. A) P(c) = 45.5c

2. B) W(x) = 24x

Step-by-step explanation:

1) If the amount of sales p(c) varies directly with the number of customers c, mathematically we have;

p(c) = kc where k is the constant of proportionality

Since ten customers bought a total of $455 worth of sweaters,

p(c) = $455 and c = 10

Substituting this values in the equation we have to get k

$455= 10k

k = $455/10

k = $45.5... (1)

To find the sales p(c) for c customers, we substitute the value of k in the formula

p(c) = kc

p(c) = $44.5c (A)

b) If the time it takes to wash all the windows on a large building W(x) varies inversely with the number of workers assigned to the job x, we will have,

W(x) = k/x (since it is inverse)

If it takes 6 hours to complete the job when 4 workers are assigned to it, the equation becomes;

6= k/4

k = 24... (1)

The equation that can be used to find the time to complete the job when x workers are assigned to it will be;

W(x) = kx

Since k = 24, we will substitute it in the formula to have;

W(x) = 24x which is the required equation (B)

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer:   (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))