Reducing
9x + -31 = 43
Rearranging the components:
-31 + 9x = 43
Finding the solution
-31 + 9x = 43
Isolating the variable 'x'.
Shift all terms with x to one side,
Add '31' to both sides of the equation.
0 + 31 + 9x = 43 + 31
Summing up similar items:
-31 + 31 = 0
0 + 9x = 43 + 31
9x = 43 + 31
Summing similar items:
43 + 31 = 74
9x = 74
Split each side by '9'
x = 8.222222222
Simplifying
x = 8.222222222
The asymptote of g(x) represents the asymptote of f(x) shifted six units upwards.
Let s denote the count of shirts and h the count of hats.
According to the provided information, the talent show organizers have a budget of $1800 to purchase merchandise clothing for sale at the event. The price for shirts is $10 each, while hats are priced at $8.
The expense for s shirts is given by
, and the cost for h hats is described by
. The combined cost for s shirts and h hats must not surpass 1800, which can be expressed as:

Additionally, they plan to acquire at least five times more shirts than hats. This implies that the quantity of shirts should be at least five times that of hats. This can be represented as:

Therefore, the second inequality should be
making option C the correct answer.
Given :
∠m1 = ( 7x - 19 )°.
∠m2 = ( x + 5 )°.
To Find :
The value of x .
Solution :
As the relationship between angle ∠m1 and ∠m2 isn't specified,
let's presuppose that the sum of ∠m1 and ∠m2 equals 180°.
Thus,

Angle ∠m2 = (24.25 + 5 )° = 29.25°.
Consequently, ∠m2 is 29.25°.
Hence, this solution meets the requirements.
The sphere's radius is calculated as 18 divided by 2, giving 9 cm.
Using the formula for the volume of a sphere, we find it to be 4/3 πr^3, resulting in 4/3 x π x (9)^3 which equals 972 π cubic centimeters.
If we halve the diameter, the new volume can be calculated as: 4/3 x π x (9/2)^3 equals 4/3 x π x (9)^3 x (1/2)^3, simplifying down to 1/8 of 972.
Thus, the new volume will only be 1/8 of the original volume.