This question is solved applying the formula of the area of the rectangle, and finding it's width. To do this, we solve a quadratic equation, and we get that the cardboard has a width of 1.5 feet.
Area of a rectangle:
The area of rectangle of length l and width w is given by:
![A = wl](https://tex.z-dn.net/?f=A%20%3D%20wl)
w(2w + 3) = 9
From this, we get that:
![l = 2w + 3, A = 9](https://tex.z-dn.net/?f=l%20%3D%202w%20%2B%203%2C%20A%20%3D%209)
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
.
This polynomial has roots
such that
, given by the following formulas:
In this question:
![w(2w+3) = 9](https://tex.z-dn.net/?f=w%282w%2B3%29%20%3D%209)
![2w^2 + 3w - 9 = 0](https://tex.z-dn.net/?f=2w%5E2%20%2B%203w%20-%209%20%3D%200)
Thus a quadratic equation with ![a = 2, b = 3, c = -9](https://tex.z-dn.net/?f=a%20%3D%202%2C%20b%20%3D%203%2C%20c%20%3D%20-9)
Then
![\Delta = 3^2 - 4(2)(-9) = 81](https://tex.z-dn.net/?f=%5CDelta%20%3D%203%5E2%20-%204%282%29%28-9%29%20%3D%2081)
![w_{2} = \frac{-3 - \sqrt{81}}{2*2} = -3](https://tex.z-dn.net/?f=w_%7B2%7D%20%3D%20%5Cfrac%7B-3%20-%20%5Csqrt%7B81%7D%7D%7B2%2A2%7D%20%3D%20-3)
Width is a positive measure, thus, the width of the cardboard is of 1.5 feet.
Another similar problem can be found at brainly.com/question/16995958
Answer:
400 total .... 120 officers
Step-by-step explanation:
.7 X = 280
x=400
Answer: ![1 \frac{2}{12}\ ft](https://tex.z-dn.net/?f=1%20%5Cfrac%7B2%7D%7B12%7D%5C%20ft)
Step-by-step explanation:
The height of Denise castle is ![1 \frac{7}{12}=\frac{12\times 1+7}{12}=\frac{19}{12}\ ft](https://tex.z-dn.net/?f=1%20%5Cfrac%7B7%7D%7B12%7D%3D%5Cfrac%7B12%5Ctimes%201%2B7%7D%7B12%7D%3D%5Cfrac%7B19%7D%7B12%7D%5C%20ft)
height of her sister ![\frac{5}{12}\ ft](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B12%7D%5C%20ft)
Difference between the height of the castle
![\Rightarrow \frac{19}{12}-\frac{5}{12}=\frac{14}{12}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B19%7D%7B12%7D-%5Cfrac%7B5%7D%7B12%7D%3D%5Cfrac%7B14%7D%7B12%7D)
In mixed fraction it is ![\frac{14}{12}\ or\ 1 \frac{2}{12}\ ft](https://tex.z-dn.net/?f=%5Cfrac%7B14%7D%7B12%7D%5C%20or%5C%201%20%5Cfrac%7B2%7D%7B12%7D%5C%20ft)
<span>If you would like
to know what is the difference between 8743 and 7621, you can calculate this
using the following steps:<span>
difference
between </span></span>8743 and 7621<span>:
8743 - 7621 = 1122
<span>The
correct result would be b</span>. 1122.</span>
Answer:
a31 = 11
Step-by-step explanation:
a31 is the 3rd row the 1st column
a31 = 11