Answer and Step-by-step explanation: The distance between 2 points is the distance of the straight line that passes through both points. It calculated using the following formula:
d = ![\sqrt{(x_{B} - x_{A} )^{2} + (y_{B} - y_{A} )^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_%7BB%7D%20-%20x_%7BA%7D%20%29%5E%7B2%7D%20%2B%20%28y_%7BB%7D%20-%20y_%7BA%7D%20%20%29%5E%7B2%7D%20%20%7D)
1) For A (2,1) and B(4, -1)
d = ![\sqrt{(4-2)^{2} + (1+1)^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%284-2%29%5E%7B2%7D%20%2B%20%281%2B1%29%5E%7B2%7D%20%7D)
d = ![\sqrt{4+4}](https://tex.z-dn.net/?f=%5Csqrt%7B4%2B4%7D)
d = 2![\sqrt{2}](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D)
2) 5 = ![\sqrt{(0-x)^{2} + (1-2)^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%280-x%29%5E%7B2%7D%20%2B%20%281-2%29%5E%7B2%7D%20%7D)
25 = x² + 1
x² = 24
x = 2![\sqrt{6}](https://tex.z-dn.net/?f=%5Csqrt%7B6%7D)
3) d = ![\sqrt{(-5-2)^{2} + (-2-5)^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%28-5-2%29%5E%7B2%7D%20%2B%20%28-2-5%29%5E%7B2%7D%20%7D)
d = ![\sqrt{(-7)^{2} + (-7)^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%28-7%29%5E%7B2%7D%20%2B%20%28-7%29%5E%7B2%7D%20%7D)
d = 7![\sqrt{2}](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D)
The answer is D. -3
you subtract x2 for x1 over y2 for y1 then you'll get 15/-3 then simplify the fraction
Answer:
6x^2+5x+4
Step-by-step explanation:
hope this helps
Answer: ![9240\ ft^3](https://tex.z-dn.net/?f=9240%5C%20ft%5E3)
Step-by-step explanation:
Given
Dimension of the bathroom is ![12'\times 16'](https://tex.z-dn.net/?f=12%27%5Ctimes%2016%27)
Dimension of the bedroom is ![14'\times 18](https://tex.z-dn.net/?f=14%27%5Ctimes%2018)
Dimension of the great room is ![20'\times 30'](https://tex.z-dn.net/?f=20%27%5Ctimes%2030%27)
Height of the ceiling is ![h=10'](https://tex.z-dn.net/?f=h%3D10%27)
Total area of the cabin
![\Rightarrow A=12\times6+14\times 18+20\times 30\\\Rightarrow A=72+252+600\\\Rightarrow A=924\ ft^2](https://tex.z-dn.net/?f=%5CRightarrow%20A%3D12%5Ctimes6%2B14%5Ctimes%2018%2B20%5Ctimes%2030%5C%5C%5CRightarrow%20A%3D72%2B252%2B600%5C%5C%5CRightarrow%20A%3D924%5C%20ft%5E2)
Volume of the cabin is ![V=A\times h](https://tex.z-dn.net/?f=V%3DA%5Ctimes%20h)
![\Rightarrow V=924\times 10\\\Rightarrow V=9240\ ft^3](https://tex.z-dn.net/?f=%5CRightarrow%20V%3D924%5Ctimes%2010%5C%5C%5CRightarrow%20V%3D9240%5C%20ft%5E3)
an explicit formula for the arithmetic sequence -5,13,31,49 is
.
<u>Step-by-step explanation:</u>
Here we have an arithmetic sequence -5,13,31,49 . We need to find an explicit formula for the arithmetic sequence .Let's find out:
Let
be terms of an A.P , common difference is :
⇒ ![d=a_2-a_1](https://tex.z-dn.net/?f=d%3Da_2-a_1)
⇒ ![d=13-(-5)](https://tex.z-dn.net/?f=d%3D13-%28-5%29)
⇒ ![d=13+5](https://tex.z-dn.net/?f=d%3D13%2B5)
⇒ ![d=18](https://tex.z-dn.net/?f=d%3D18)
We know that general term of an Arithmetic Progression ( A.P) is :
⇒ ![a_n = a+(n-1)d](https://tex.z-dn.net/?f=a_n%20%3D%20a%2B%28n-1%29d)
So , Here we will have ![a_n = -5+(n-1)18](https://tex.z-dn.net/?f=a_n%20%3D%20-5%2B%28n-1%2918)
⇒ ![a_n = -5+(n-1)18](https://tex.z-dn.net/?f=a_n%20%3D%20-5%2B%28n-1%2918)
⇒ ![a_n = -5+18n-18](https://tex.z-dn.net/?f=a_n%20%3D%20-5%2B18n-18)
⇒ ![a_n =18n-23](https://tex.z-dn.net/?f=a_n%20%3D18n-23)
Therefore , an explicit formula for the arithmetic sequence -5,13,31,49 is
.