The perimeter of a figure is the sum of the lengths of the sides used to make the given figure. The perimeter of the shape ABCD is 19.1(5.099+4.4721+5.099+4.4721).
<h3>What is the perimeter?</h3>
The perimeter of a figure is the sum of the lengths of the sides used to make the given figure.
The perimeter of the shape can be found by finding the length of the different sides, therefore,
![AB = \sqrt{(5-0)^2+(-1-0)^2} = \sqrt{26} = 5.099](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%285-0%29%5E2%2B%28-1-0%29%5E2%7D%20%3D%20%5Csqrt%7B26%7D%20%3D%205.099)
![BC = \sqrt{(3-5)^2+(-5+1)^2} = \sqrt{20} = 4.4721](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B%283-5%29%5E2%2B%28-5%2B1%29%5E2%7D%20%3D%20%5Csqrt%7B20%7D%20%3D%204.4721)
![CD = \sqrt{(-2-3)^2+(-4+5)^2} = \sqrt{26} = 5.099](https://tex.z-dn.net/?f=CD%20%3D%20%5Csqrt%7B%28-2-3%29%5E2%2B%28-4%2B5%29%5E2%7D%20%3D%20%5Csqrt%7B26%7D%20%3D%205.099)
![AD=\sqrt{(-2-0)^2+(-4-0)}=\sqrt{20} = 4.4721](https://tex.z-dn.net/?f=AD%3D%5Csqrt%7B%28-2-0%29%5E2%2B%28-4-0%29%7D%3D%5Csqrt%7B20%7D%20%3D%204.4721)
Hence, the perimeter of the shape ABCD is 19.1(5.099+4.4721+5.099+4.4721).
Learn more about perimeter here:
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To get the value of 1/10 of 9 inches, simply multiply 1/10 by 9
value = (1/10)(9) = 9/10 = 0.9 inches
Answer:
(1,3)
Step-by-step explanation:
The given function is
![y = - 2 {x}^{2} + 4x + 1](https://tex.z-dn.net/?f=y%20%3D%20%20-%202%20%7Bx%7D%5E%7B2%7D%20%20%2B%204x%20%2B%201)
Factor 2 from the first two terms
![y = - 2( {x}^{2} - 2x) + 1](https://tex.z-dn.net/?f=y%20%3D%20%20-%202%28%20%7Bx%7D%5E%7B2%7D%20%20%20-%202x%29%20%2B%201)
Add and subtract the square of half the coefficient of x.
![y = - 2( {x}^{2} - 2x + 1 - 1) + 1](https://tex.z-dn.net/?f=y%20%3D%20%20-%202%28%20%7Bx%7D%5E%7B2%7D%20%20%20-%202x%20%2B%201%20-%201%29%20%2B%201)
Let us create perfect square trinomial
![y = - 2( {x}^{2} - 2x + 1 ) + - 2 \times - 1 + 1](https://tex.z-dn.net/?f=y%20%3D%20%20-%202%28%20%7Bx%7D%5E%7B2%7D%20%20%20-%202x%20%2B%201%20%29%20%2B%20%20-%202%20%5Ctimes%20%20-%201%20%2B%201)
This implies that:
![y = - 2( {x - 1)}^{2}+ 3](https://tex.z-dn.net/?f=y%20%3D%20%20-%202%28%20%7Bx%20-%201%29%7D%5E%7B2%7D%2B%20%203)
Therefore the vertex is (1,3).
We got this by comparing to
![y = a( {x - h)}^{2} + k](https://tex.z-dn.net/?f=y%20%3D%20a%28%20%7Bx%20-%20h%29%7D%5E%7B2%7D%20%20%2B%20k)
Answer:
Step-by-step explanation:
Givens
x = the larger number
y = the smaller number
Equations
x+y =95
x + 2y = 120
Solution
x+y =95
x + 2y = 120
x + y = 95 Subtract
y = 25
x + y = 95
x + 25 = 95
x + 25 -25 = 95 - 25
x = 70
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I did the problem before I realized that I could have stopped after equations.
The answer is the middle choice.