Answer:
16.5 square feet
Step-by-step explanation:
The logo consists of
- rectangle with sides of 3 ft and 1.5 ft;
- trapezoid with bases 3 ft, 4 ft and height of 3 ft;
- triangle with base of 1.5 ft and height of 2 ft.
<u>The area of rectangle:</u>
![A_{rectangle}=1.5\ ft\times 3\ ft=4.5\ ft^2](https://tex.z-dn.net/?f=A_%7Brectangle%7D%3D1.5%5C%20ft%5Ctimes%203%5C%20ft%3D4.5%5C%20ft%5E2)
<u>The area of trapezoid:</u>
![A_{trapezoid}=\dfrac{3\ ft+4\ ft}{2}\times 3 \ ft=3.5\ ft\times 3 \ ft=10.5 \ ft^2](https://tex.z-dn.net/?f=A_%7Btrapezoid%7D%3D%5Cdfrac%7B3%5C%20ft%2B4%5C%20ft%7D%7B2%7D%5Ctimes%203%20%5C%20ft%3D3.5%5C%20ft%5Ctimes%203%20%5C%20ft%3D10.5%20%5C%20ft%5E2)
<u>The area of triangle:</u>
![A_{triangle}=\dfrac{1}{2}\times 1.5\ ft\times 2 \ ft=1.5\ ft^2](https://tex.z-dn.net/?f=A_%7Btriangle%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%201.5%5C%20ft%5Ctimes%202%20%5C%20ft%3D1.5%5C%20ft%5E2)
Hence, <u>the area of logo:</u>
![A=A_{rectangle}+A_{trapezoid}+A_{triangle}=4.5\ ft^2+10.5\ ft^2+1.5\ ft^2=16.5\ ft^2](https://tex.z-dn.net/?f=A%3DA_%7Brectangle%7D%2BA_%7Btrapezoid%7D%2BA_%7Btriangle%7D%3D4.5%5C%20ft%5E2%2B10.5%5C%20ft%5E2%2B1.5%5C%20ft%5E2%3D16.5%5C%20ft%5E2)
Answer:
x = 72
Step-by-step explanation:
By exterior angle theorem:
x° + (x + 10)° = 154°
(x + 10 + x) ° = 154°
(2x + 10)° = 154°
2x + 10 = 154
2x = 154 - 10
2x = 144
x = 144/2
x = 72
Answer:
Infinitely many solutions.
Step-by-step explanation:
x-2y=-3
14y-7x=21
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simplify 14y-7x=21 into 2y-x=3
x-2y=-3
2y-x=3
--------------
x=2y+(-3)
x=2y-3
2y-(2y-3)=3
2y-2y+3=3
0+3=3
infinitely many solutions
Y= 3/2x + 2
If you do rise/run from (-2,-1) the y-intercept will be 2