Answer:
19 units
Step-by-step explanation:
Plot points A(5,2), B(-1,4), C(-2,1) and D(4,-1) on the coordinate plane. Find lengths of all sides as distances between two points:
![AB=\sqrt{(-1-5)^2+(4-2)^2}=\sqrt{6^2+2^2}=\sqrt{36+4}=\sqrt{40}=2\sqrt{10}\ units\\ \\BC=\sqrt{(-2-(-1))^2+(1-4)^2}=\sqrt{1^2+3^2}=\sqrt{1+9}=\sqrt{10}\ units\\ \\CD=\sqrt{(4-(-2))^2+(-1-1)^2}=\sqrt{6^2+2^2}=\sqrt{36+4}=\sqrt{40}=2\sqrt{10}\ units\\ \\DA=\sqrt{(5-4)^2+(2-(-1))^2}=\sqrt{1^2+3^2}=\sqrt{1+9}=\sqrt{10}\ units](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%28-1-5%29%5E2%2B%284-2%29%5E2%7D%3D%5Csqrt%7B6%5E2%2B2%5E2%7D%3D%5Csqrt%7B36%2B4%7D%3D%5Csqrt%7B40%7D%3D2%5Csqrt%7B10%7D%5C%20units%5C%5C%20%5C%5CBC%3D%5Csqrt%7B%28-2-%28-1%29%29%5E2%2B%281-4%29%5E2%7D%3D%5Csqrt%7B1%5E2%2B3%5E2%7D%3D%5Csqrt%7B1%2B9%7D%3D%5Csqrt%7B10%7D%5C%20units%5C%5C%20%5C%5CCD%3D%5Csqrt%7B%284-%28-2%29%29%5E2%2B%28-1-1%29%5E2%7D%3D%5Csqrt%7B6%5E2%2B2%5E2%7D%3D%5Csqrt%7B36%2B4%7D%3D%5Csqrt%7B40%7D%3D2%5Csqrt%7B10%7D%5C%20units%5C%5C%20%5C%5CDA%3D%5Csqrt%7B%285-4%29%5E2%2B%282-%28-1%29%29%5E2%7D%3D%5Csqrt%7B1%5E2%2B3%5E2%7D%3D%5Csqrt%7B1%2B9%7D%3D%5Csqrt%7B10%7D%5C%20units)
The perimeter of the rectangle ABCD is
![AB+BC+CD+DA=2\sqrt{10}+\sqrt{10}+2\sqrt{10}+\sqrt{10}=6\sqrt{10}\approx 18.97\ units\approx 19\ units](https://tex.z-dn.net/?f=AB%2BBC%2BCD%2BDA%3D2%5Csqrt%7B10%7D%2B%5Csqrt%7B10%7D%2B2%5Csqrt%7B10%7D%2B%5Csqrt%7B10%7D%3D6%5Csqrt%7B10%7D%5Capprox%2018.97%5C%20units%5Capprox%2019%5C%20units)
To solve using completing square method we proceed as follows:
x^2-10x+8=0
x^2-10x=-8
but
c=(b/2)^2
c=(10/2)^2=25
thus we can add this in our expression to get
x^2-10x+25=8+25
factorizing the LHS we get:
(x-5)(x-5)=33
(x-5)^2=33
getting the square roots of both sides we have:
x-5=+/-√33
x=5+/-√33
Answer:
Kristina will!
Step-by-step explanation:
Both Krista and Kevin found the right answer to Stacey’s question. Stacey will invest $108 in company A if she invests $24 in company B.
Step B would be correct because you trying to find the total number of hours she reads in 8 days and not the difference. <span />
Answer:
smaller number is 10
larger number is 39
Step-by-step explanation:
a = small number
b = larger number
a + b = 49
2a = 3b - 97
substitute 49-a into second equation for b
2a = 3(49-a) - 97
2a = 147 - 3a - 97
5a = 50
a = 10
b = 39