The width w of a rectangular swimming pool is x+4 the area of the pool is 2x^3-29x+12 what is an expression for the length of the pool?

Step-by-step explanation:

** CORRECTIONS: Q1: It's 2x^3-29x+12; Q2,3,4,5,6: All conditions have ≠ symbol; Q7: it's (12x^2+32x+16); Q10: Option D should be divided by x^4; **

(1) Given:

Width = W = x+4

Area = A =

Length = L = ?

Since the pool is rectangular in shape:

area = width * length

A = W * L

Substitute:

The long division is attached with the answer (below in the picture). Hence the correct answer is  (Option C)

(2) Given expression:

Where x ≠ 6. (Option B)

(3) Given :

Now simplify:

Where x ≠ -1/8 (Option A)

(4) Given:

Simplify:

Where x ≠ -1 (Option A)

(5) Given:

Simplify:

where x≠6 (Option C)

(6) Given:

Simplify:

Where a ≠ 0 (Option C)

(7) Mathematically:

Simplify:

(Option C)

(8) Simplify:

(Option A)

(9) Simplify:

(Option A)

(10) Given:

Simplify:

(Option D)

(11) Given:

Simplify:

(Option C)

(12) Simplify:

(Option A)

(13) Simplify:

(Option A)

(14) Simplify:

(Option B)

(15) Simplify:

(Option D)

(16) Given:

4/x + 5/x = -3

Simplify:

(4+5)/x = -3

-3x = 9

x = -3 (Option C)

(17) Simplify:

(Option D)

(18) Simplify:

(Option C)

(19) Dorothy's rate (alone) will be:

Rosanne's rate (alone) will be:

If both work together, add both the rates:

(in 1/hours)

To find the hours, flip the rate:

hours (Option B)

(20) As pressure (p) is inversely proportional with volume (v):

p = k/v (where k is constant of proportionality)

k = pv

Find constant using initial values:

k = (104)(108)

k = 11232

Now new pressure is:

p = k/v = 11232/432 = 26 Pa (Option A)

(21)

x: 1,3,5,10

y: 4,12,20,40

Direct variation is the value of y increases with x. So,

y = 4x

If x = 1,y=4(1)=4

If x = 3,y=4(3)=12

If x = 5,y=20

If x = 10,y=40 (Option A)

(22)

If x=-16,4(-16) + 64 = 0;denominator will become zero,which means that there will be discontinuity at x = -16. Hence, x=-16 (Option C) should be excluded.

the answer is 175.4379

step-by-step explanation: