Question

A) For all values of x for which these

expressions are defined, perform the indicated
operation and express in simplest form.
1) x + 22
2)
+
X
6
x+29
1,
b) The distance an object falls is given by the
formula d = gt². Find d, to the nearest
tenth, when g = 9.8 and t = = 41⁄2.

Answer 1

a)

(x+2)/6

To add (x + 2)/6 + x/(6), you first need to find a common denominator, which is 6.

(x + 2)/6 + x/(6) = (x + 2 + 6x)/6

= (7x + 2)/6

Therefore, (x + 2)/6 + x/(6) simplifies to (7x + 2)/6.

(x+29)/(x+22)

To add (x + 29)/(x + 22) + 1, you need to find a common denominator, which is (x + 22).

(x + 29)/(x + 22) + 1 = (x + 29)/(x + 22) + (x + 22)/(x + 22)

= (2x + 51)/(x + 22)

Therefore, (x + 29)/(x + 22) + 1 simplifies to (2x + 51)/(x + 22).

b)

Given that d = gt^2, g = 9.8 and t = 4.5, we can substitute these values into the formula to find the distance, d.

d = (9.8) × (4.5)^2

= (9.8) × (20.25)

= 198.45

To the nearest tenth, d is equal to 198.5. Therefore, the distance an object falls is 198.5 units.

Explanation: