13.33333333333333333333333333333333 infinity
Answer:
The width of rectangle w = 4 units
Step-by-step explanation:
We are given:
Width of rectangle = w
Length of rectangle = w+ 4
Area of rectangle = 32 units
We need to find width of the rectangle
The formula used is: ![Area\:of\:rectangle=Length\times Width](https://tex.z-dn.net/?f=Area%5C%3Aof%5C%3Arectangle%3DLength%5Ctimes%20Width)
Putting values and finding width of rectangle
![Area\:of\:rectangle=Length\times Width\\32=(w+4)\times w\\32=w^2+4w\\w^2+4w-32=0](https://tex.z-dn.net/?f=Area%5C%3Aof%5C%3Arectangle%3DLength%5Ctimes%20Width%5C%5C32%3D%28w%2B4%29%5Ctimes%20w%5C%5C32%3Dw%5E2%2B4w%5C%5Cw%5E2%2B4w-32%3D0)
We need to solve this quadratic equation to find width (w)
We will use factorisation and break the middle term.
![w^2+4w-32=0\\w^2+8w-4w-32=0\\w(w+8)-4(w+8)=0\\(w-4)(w+8)=0\\w-4=0\:or\:w+8=0\\w=4\:or\:w=-8](https://tex.z-dn.net/?f=w%5E2%2B4w-32%3D0%5C%5Cw%5E2%2B8w-4w-32%3D0%5C%5Cw%28w%2B8%29-4%28w%2B8%29%3D0%5C%5C%28w-4%29%28w%2B8%29%3D0%5C%5Cw-4%3D0%5C%3Aor%5C%3Aw%2B8%3D0%5C%5Cw%3D4%5C%3Aor%5C%3Aw%3D-8)
Since width of rectangle can't be negative, so rejecting w=-8
Therefore, the width of rectangle w = 4 units
Y = kx
Y is the total cost
The number of dvds is x
The cost of each one ($12) is k
y = $12x
Or instead of Y you can but T for total cost
t = $12x
Answer:
Straight line graph with positive gradient (slope)
y-intercept: (0, -3)
x-intercept: (12, 0)
Step-by-step explanation:
is a linear function
The line intercepts the y-axis when x = 0:
![y=\dfrac14(0)-3=-3](https://tex.z-dn.net/?f=y%3D%5Cdfrac14%280%29-3%3D-3)
Therefore, the y-intercept is (0, -3)
The line intercepts the x-axis when y = 0:
![\implies \dfrac14x-3=0\\\\\implies \dfrac14x=3\\\\\implies x=12](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac14x-3%3D0%5C%5C%5C%5C%5Cimplies%20%5Cdfrac14x%3D3%5C%5C%5C%5C%5Cimplies%20x%3D12)
Therefore, the x-intercept is (12, 0)