Answer:
The number of Pencils purchased and the cost of pencils has a proportional relationship.
Step-by-step explanation:
In order to figure out if a proportional relationship between two variable exists,
- All you need is to check if relationships between two variables have equivalent ratios.
- If the ratios between two variables is same, it means a proportional relationship between two variable exists.
Lets take a simple example:
As
2/10 = 9/45 is a TRUE proportion.
The reason is that both fractions reduces to 1/5, and
because 10 × 9 = 2 × 45.
So
In the equation it needs to be determined whether the number of Pencils purchased and the cost of pencils represent a proportional relationship?
When we are given that:
In other words each pencil costs $0.25.
As each pencil costs $0.25, it means:
2 pencils cost $0.5, 3 pencils cost $0.75, and 4 pencils cost $1 and so on.
Thus
Cost ÷ No of Pencils Purchased = 0.25 ÷ 1 = 0.5 ÷ 2 = 0.75 ÷ 3 = 1 ÷ 4
And the ratio is same.
i.e. cost per pencil = 0.25 : 1
As all of the ratios are same, we can determine that it has a proportional relationship.
Therefore, the number of Pencils purchased and the cost of pencils has a proportional relationship.
<h2>90 sq in</h2>
Step-by-step explanation:
The total area in the figure can be divided into two areas.
The is the area of the rectangle.
The is the area of the adjacent triangle to the rectangle.
Total area=90
6*30 = 180
8*20 = 160
9*10 = 90
180+160+90 = 430 stickers
(2a + 3b)^2 = 4a^2 + 12ab + 9b^2 =
((4a^2 - 6ab + 9b^2) + 18ab) = 144
4a^2 - 6ab + 9b^2 = 144 - 18 ab
8a^3 + 27b^3 = (2a + 3b)(4a^2 - 6ab + 9b^2)
8a^3 + 27b^3 = (2a + 3b)*(144 - 18ab)
8a^3 + 27b^3 = 12 * (144 - 18ab)
= 12 * ( 144 - 18*6) since ab = 6
= 12 * (144 - 108)
= 12 * (36)
= 432 <<<<==== answer