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
yes
10² = 10 × 10 = 100
divide 100 by her daily average of 20
= 5
She should be able to read 100 pages in 5 days
Answer:
m = 4.5
Step-by-step explanation:
m is the variable for slope (just for validation)
y = 25 + 4.5 (x - 5)
Expand,
y = 25 + 4.5x - 22.5
Collect like terms,
y = 4.5x + 2.5
The slope of the gradient is always the coefficient of x
Therefore, m = 4.5
Hope this helped!! :)
Answer:
The answer to your question is below
Step-by-step explanation:
To solve this problem, for a and c, just look in the x-axis the value given and find the value of a and c in the y-axis.
To solve this problem, for b and d, just look in the y-axis the value given and find the value of b and d in the x-axis.
f(2) = -3 a = -3
f(b) = 0 b = -4
f(-2) = -1 c = -1
f(d) = -6 d = 8