so the points are, from P1 to P2, namely P1P2, and from P2 to P3, namely P2P3, and from P3 back to P1, namely P3P1.
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P1(\stackrel{x_1}{5}~,~\stackrel{y_1}{-4})\qquad P2(\stackrel{x_2}{8}~,~\stackrel{y_2}{-3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ P1P2=\sqrt{[8-5]^2+[-3-(-4)]^2}\implies P1P2=\sqrt{(8-5)^2+(-3+4)^2} \\\\\\ P1P2=\sqrt{3^2+1^2}\implies \boxed{P1P2=\sqrt{10}}\\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%20%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%20%5C%5C%5C%5C%20P1%28%5Cstackrel%7Bx_1%7D%7B5%7D~%2C~%5Cstackrel%7By_1%7D%7B-4%7D%29%5Cqquad%20%20P2%28%5Cstackrel%7Bx_2%7D%7B8%7D~%2C~%5Cstackrel%7By_2%7D%7B-3%7D%29%5Cqquad%20%5Cqquad%20%20d%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20P1P2%3D%5Csqrt%7B%5B8-5%5D%5E2%2B%5B-3-%28-4%29%5D%5E2%7D%5Cimplies%20P1P2%3D%5Csqrt%7B%288-5%29%5E2%2B%28-3%2B4%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20P1P2%3D%5Csqrt%7B3%5E2%2B1%5E2%7D%5Cimplies%20%5Cboxed%7BP1P2%3D%5Csqrt%7B10%7D%7D%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%20)
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P2(\stackrel{x_2}{8}~,~\stackrel{y_2}{-3})\qquad P3(\stackrel{x_2}{7}~,~\stackrel{y_2}{-10}) \\\\\\ P2P3=\sqrt{[7-8]^2+[-10-(-3)]^2}\implies P2P3=\sqrt{(7-8)^2+(-10+3)^2} \\\\\\ P2P3=\sqrt{(-1)^2+(-7)^2}\implies P2P3=\sqrt{50}\implies \boxed{P2P3=5\sqrt{2}}\\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%20%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%20%5C%5C%5C%5C%20P2%28%5Cstackrel%7Bx_2%7D%7B8%7D~%2C~%5Cstackrel%7By_2%7D%7B-3%7D%29%5Cqquad%20%20P3%28%5Cstackrel%7Bx_2%7D%7B7%7D~%2C~%5Cstackrel%7By_2%7D%7B-10%7D%29%20%5C%5C%5C%5C%5C%5C%20P2P3%3D%5Csqrt%7B%5B7-8%5D%5E2%2B%5B-10-%28-3%29%5D%5E2%7D%5Cimplies%20P2P3%3D%5Csqrt%7B%287-8%29%5E2%2B%28-10%2B3%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20P2P3%3D%5Csqrt%7B%28-1%29%5E2%2B%28-7%29%5E2%7D%5Cimplies%20P2P3%3D%5Csqrt%7B50%7D%5Cimplies%20%5Cboxed%7BP2P3%3D5%5Csqrt%7B2%7D%7D%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%20)
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P3(\stackrel{x_2}{7}~,~\stackrel{y_2}{-10})\qquad P1(\stackrel{x_1}{5}~,~\stackrel{y_1}{-4}) \\\\\\ P3P1=\sqrt{[5-7]^2+[-4-(-10)]^2}\implies P3P1=\sqrt{(5-7)^2+(-4+10)^2} \\\\\\ P3P1=\sqrt{(-2)^2+6^2}\implies P3P1=\sqrt{40}\implies \boxed{P3P1=2\sqrt{10}}](https://tex.z-dn.net/?f=%20%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%20%5C%5C%5C%5C%20P3%28%5Cstackrel%7Bx_2%7D%7B7%7D~%2C~%5Cstackrel%7By_2%7D%7B-10%7D%29%5Cqquad%20%20P1%28%5Cstackrel%7Bx_1%7D%7B5%7D~%2C~%5Cstackrel%7By_1%7D%7B-4%7D%29%20%5C%5C%5C%5C%5C%5C%20P3P1%3D%5Csqrt%7B%5B5-7%5D%5E2%2B%5B-4-%28-10%29%5D%5E2%7D%5Cimplies%20P3P1%3D%5Csqrt%7B%285-7%29%5E2%2B%28-4%2B10%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20P3P1%3D%5Csqrt%7B%28-2%29%5E2%2B6%5E2%7D%5Cimplies%20P3P1%3D%5Csqrt%7B40%7D%5Cimplies%20%5Cboxed%7BP3P1%3D2%5Csqrt%7B10%7D%7D%20)
The total monthly cost of the two companies will be the same for 30 texts.
<u>Step-by-step explanation:</u>
It is given that,
- The variables used here are x and y.
- y represent the total monthly cost.
we know that, x must represent the number of texts in a month.
The monthly texting plan of All Star Cell is $11 per month and $0.25 per text.
⇒ y = 11 + 0.25x --------(1)
The monthly texting plan of Top Line Cell is $14 per month and $0.15 per text.
⇒ y = 14 + 0.15x --------(2)
<u>To find the no.of texts for which the total monthly cost of the two companies be the same :</u>
⇒ Total cost of All Star Cell = Total cost of Top Line Cell
⇒ 11 + 0.25x = 14 + 0.15x
⇒ 0.25x - 0.15x = 14 - 11
⇒ 0.1x = 3
⇒ x = 3 / 0.1
⇒ x = 30 texts.
The total monthly cost of the two companies will be the same for 30 texts.
Answer:
33 minutes
Step-by-step explanation:
Answer:
y = -2x - 9
Step-by-step explanation:
so we have our two points, (-4,-1) and (-8,7) What we need to do to find our slope is y2 - y1 over x2 - x1. Once plugging in the numbers and subtracting it should give you 8/-4. 8 divided by -4 is -2. m = -2. Now to find our "b" we plug in our slope, and plug in one of the two points into the format of y = mx + b.
-1 = -2(-4) + b
multiply -2 and -4
-1 = 8 + b
we subtract 8 from itself and -1
-9 = b
Our equation is y = -2x - 9
