Answer:
The length of each side of the 9 in
Step-by-step explanation:
The volume of the gift box is 972 in. The height of the gift box is 12 inches
and the area of the base is 81 in².
We want to determine the length of each side of the square base if the base shape is a square.
Recall that, the area of a square is
It was given that, the area of this base is 81 in²
Take positive square root:
Solution:
Given expression is
To find the inverse of y.
⇒
Do cross multiplication.
⇒ y = –6 × 3
⇒ y = –18
Inverse of y means reverse the function.
We know that inverse of y is .
⇒
Hence, inverse of y is
Problem #2
We must find the solution to the following system of inequalities:
(1) We solve for y the first inequality:
Now, we multiply both sides of the inequality by (-1), this changes the signs on both sides and inverts the inequality symbol:
The solution to this inequality is the set of all the points (x, y) over the line:
This line has:
• slope m = 3/2,
,• y-intercept b = -2.
(2) We solve for y the second inequality:
The solution to this inequality is the set of all the points (x, y) below the line:
This line has:
• slope m = -1/3,
,• y-intercept b = 2.
(3) Plotting the lines of points (1) and (2), and painting the region:
• over the line from point (1),
,• and below the line from point (2),
we get the following graph:
AnswerThe points that satisfy both inequalities are given by the intersection of the blue and red regions:
