ANSWER
a. d+4
b. 4d+16
EXPLANATION
The area of the square coaster is represented by:
![{d}^{2} + 8d + 16](https://tex.z-dn.net/?f=%20%7Bd%7D%5E%7B2%7D%20%20%2B%208d%20%2B%2016)
We split the middle term to obtain,
![{d}^{2} + 4d + 4d + 16](https://tex.z-dn.net/?f=%20%7Bd%7D%5E%7B2%7D%20%20%2B%204d%20%2B%204d%20%2B%2016)
We factor by grouping to get,
![d(d + 4) + 4(d + 4)](https://tex.z-dn.net/?f=d%28d%20%2B%204%29%20%2B%204%28d%20%2B%204%29)
![(d + 4)(d + 4) = {(d + 4)}^{2}](https://tex.z-dn.net/?f=%28d%20%2B%204%29%28d%20%2B%204%29%20%3D%20%20%7B%28d%20%2B%204%29%7D%5E%7B2%7D%20)
Since area of a square is l² , it means the side length of the square is
![l = d + 4](https://tex.z-dn.net/?f=l%20%3D%20d%20%2B%204)
b) The perimeter of a square is given by
![P=4l](https://tex.z-dn.net/?f=P%3D4l)
We substitute the length in terms of d, to obtain;
![P=4(d + 4)](https://tex.z-dn.net/?f=P%3D4%28d%20%2B%204%29)
Or
![P=4d + 16](https://tex.z-dn.net/?f=P%3D4d%20%2B%2016)
Answer:
50.27m
2 π r
Step-by-step explanation:
Answer:
- The length of VW = 36 units.
Step-by-step explanation:
We know that a rhombus is a quadrilateral with four sides. All four sides have the same length.
From the diagram, it is clear that
As all the four sides of the rhombus have equal length.
So we can observe
![VW=WX](https://tex.z-dn.net/?f=VW%3DWX)
![6m-12 = 4m+4](https://tex.z-dn.net/?f=6m-12%20%3D%204m%2B4)
Add 12 to both sides
![6m-12+12=4m+4+12](https://tex.z-dn.net/?f=6m-12%2B12%3D4m%2B4%2B12)
![6m=4m+16](https://tex.z-dn.net/?f=6m%3D4m%2B16)
![2m=16](https://tex.z-dn.net/?f=2m%3D16)
Divide both sides by 2
![\frac{2m}{2}=\frac{16}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2m%7D%7B2%7D%3D%5Cfrac%7B16%7D%7B2%7D)
![m=8](https://tex.z-dn.net/?f=m%3D8)
so
The length of VW= 6m-12
= 6(8)-12 ∵ ![m=8](https://tex.z-dn.net/?f=m%3D8)
= 48-12
= 36
Thereofore, the length of VW = 36 units.
![9x^2 - 18 x + 93= -6](https://tex.z-dn.net/?f=9x%5E2%20-%2018%20x%20%2B%2093%3D%20-6)
take away 93 from both sides
![9x^2 - 18 x = - 99](https://tex.z-dn.net/?f=9x%5E2%20-%2018%20x%20%3D%20-%2099)
Divide by 9 through
![x^2 - 2 x = - 11](https://tex.z-dn.net/?f=x%5E2%20-%202%20x%20%3D%20-%2011)
Add (b/2)^2 to form perfect square
![x^2 - 2 x + ( \frac{2}{2} )^2 = - 11 + ( \frac{2}{2} )^2](https://tex.z-dn.net/?f=x%5E2%20-%202%20x%20%2B%20%28%20%5Cfrac%7B2%7D%7B2%7D%20%29%5E2%20%3D%20-%2011%20%2B%20%28%20%5Cfrac%7B2%7D%7B2%7D%20%29%5E2%20)
Form perfect square
![(x - 1)^2 = - 10](https://tex.z-dn.net/?f=%28x%20-%201%29%5E2%20%3D%20-%2010%20)
Square root both sides to find x
![x - 1 = \pm \sqrt{-10}](https://tex.z-dn.net/?f=x%20-%201%20%3D%20%5Cpm%20%20%5Csqrt%7B-10%7D%20)
add 1 on both sides
<h3>hello!</h3>
Plug in the values of x and solve for y:-
y=5+4x
y=5+4(4)
y=5+16
y=21
________________________________
y=5+4x
y=5+5(5)
y=5+20
y=25
_________________________________
y=5+4x
y=5+4(8)
y=5+32
y=37
___________________________________
y=5+4x
y=5+4(10)
y=5+40
y=45
__________________________________
<h3>note:-</h3>
Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)