A party-favor bag must have a volume of 140 cubic inches and the dimensions that are shown below. The equation x cubed + 6 x squared minus 27 x = 140 can be used to find x. A bag has a height of x + 9 inches, a width of x minus 3 inches, and a length of x inches. What are the dimensions of the party-favor bag? Use a graphing calculator and a system of equations to find the answer.

The dimensions of the the party favor bag are;

Height = 14 inches

Width = 2 inches  

Length = 5 inches

Step-by-step explanation:

The given parameters are;

x³ + 6·x² - 27·x = 140

The dimensions of the party-favor bag are;

Height = (x + 9) inches

Width = (x - 3) inches

Length = x inches

The given equation can be rewritten as follows;

x³ + 6·x² - 27·x - 140 = 0

Using an online application, we have;

x³ + 6·x² - 27·x - 140 = 0 = (x + 4)·(x - 5)·(x + 7)

Therefore, x = -4, 5, or -7

Which gives x = 5, as the length of the party favor bag, x inches, cannot be negative;

Therefore, the dimensions of the the party favor bag are;

Height = (x + 9) inches = (5 + 9) inches = 14 inches

Width = (x - 3) inches = (5 - 3) inches = 2 inches  

Length = x inches = 5 inches.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.