Answer:
56
Step-by-step explanation:
A∆ = BH/2
Area of a parm is BH (base x height) so we multiply area of triangle by 2.
28 x 2 = 56. There you go
<u>Answer-</u>
The equations of the locus of a point that moves so that its distance from the line 12x-5y-1=0 is always 1 unit are
![12x-5y+14=0 \\ 12x-5y-14=0](https://tex.z-dn.net/?f=12x-5y%2B14%3D0%20%5C%5C%2012x-5y-14%3D0)
<u>Solution-</u>
Let a point which is 1 unit away from the line 12x-5y-1=0 is (h, k)
The applying the distance formula,
![\Rightarrow \left | \frac{12h-5k-1}{\sqrt{12^2+5^2}} \right |=1](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cleft%20%7C%20%5Cfrac%7B12h-5k-1%7D%7B%5Csqrt%7B12%5E2%2B5%5E2%7D%7D%20%5Cright%20%7C%3D1)
![\Rightarrow \left | \frac{12h-5k-1}{\sqrt{169}} \right |=1](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cleft%20%7C%20%5Cfrac%7B12h-5k-1%7D%7B%5Csqrt%7B169%7D%7D%20%5Cright%20%7C%3D1)
![\Rightarrow \left | \frac{12h-5k-1}{13} \right |=1](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cleft%20%7C%20%5Cfrac%7B12h-5k-1%7D%7B13%7D%20%5Cright%20%7C%3D1)
![\Rightarrow 12h-5k-1=\pm 13](https://tex.z-dn.net/?f=%5CRightarrow%2012h-5k-1%3D%5Cpm%2013)
![\Rightarrow 12h-5k=\pm 14](https://tex.z-dn.net/?f=%5CRightarrow%2012h-5k%3D%5Cpm%2014)
![\Rightarrow 12h-5k=14,\ 12h-5k=-14](https://tex.z-dn.net/?f=%5CRightarrow%2012h-5k%3D14%2C%5C%2012h-5k%3D-14)
![\Rightarrow 12h-5k-14=0,\ 12h-5k+14=0](https://tex.z-dn.net/?f=%5CRightarrow%2012h-5k-14%3D0%2C%5C%2012h-5k%2B14%3D0)
![\Rightarrow 12x-5y-14=0,\ 12x-5y+14=0](https://tex.z-dn.net/?f=%5CRightarrow%2012x-5y-14%3D0%2C%5C%2012x-5y%2B14%3D0)
Two equations are formed because one will be upper from the the given line and other will be below it.
Answer:
c?
Step-by-step explanation:
Answer:
The area of triangle for the given coordinates is 1.5![\sqrt{4.6}](https://tex.z-dn.net/?f=%5Csqrt%7B4.6%7D)
Step-by-step explanation:
Given coordinates of triangles as
A = (0,0)
B = (3,4)
C = (3,2)
So, The measure of length AB = a = ![\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_2-x_1%29%5E%7B2%7D%2B%28y_2-y_1%29%5E%7B2%7D%7D)
Or, a = ![\sqrt{(3-0)^{2}+(4-0)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%283-0%29%5E%7B2%7D%2B%284-0%29%5E%7B2%7D%7D)
Or, a = ![\sqrt{9+16}](https://tex.z-dn.net/?f=%5Csqrt%7B9%2B16%7D)
Or, a = ![\sqrt{25}](https://tex.z-dn.net/?f=%5Csqrt%7B25%7D)
∴ a = 5 unit
Similarly
The measure of length BC = b = ![\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_2-x_1%29%5E%7B2%7D%2B%28y_2-y_1%29%5E%7B2%7D%7D)
Or, b = ![\sqrt{(3-3)^{2}+(2-4)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%283-3%29%5E%7B2%7D%2B%282-4%29%5E%7B2%7D%7D)
Or, a = ![\sqrt{0+4}](https://tex.z-dn.net/?f=%5Csqrt%7B0%2B4%7D)
Or, b = ![\sqrt{4}](https://tex.z-dn.net/?f=%5Csqrt%7B4%7D)
∴ b = 2 unit
And
So, The measure of length CA = c = ![\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_2-x_1%29%5E%7B2%7D%2B%28y_2-y_1%29%5E%7B2%7D%7D)
Or, c = ![\sqrt{(3-0)^{2}+(2-0)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%283-0%29%5E%7B2%7D%2B%282-0%29%5E%7B2%7D%7D)
Or, c = ![\sqrt{9+4}](https://tex.z-dn.net/?f=%5Csqrt%7B9%2B4%7D)
Or, c = ![\sqrt{13}](https://tex.z-dn.net/?f=%5Csqrt%7B13%7D)
∴ c =
unit
Now, area of Triangle written as , from Heron's formula
A = ![\sqrt{s\times (s-a)\times (s-b)\times (s-c)}](https://tex.z-dn.net/?f=%5Csqrt%7Bs%5Ctimes%20%28s-a%29%5Ctimes%20%28s-b%29%5Ctimes%20%28s-c%29%7D)
and s = ![\frac{a+b+c}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D)
I.e s = ![\frac{5+2+\sqrt{13}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B5%2B2%2B%5Csqrt%7B13%7D%7D%7B2%7D)
Or. s = ![\frac{7+\sqrt{13}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B7%2B%5Csqrt%7B13%7D%7D%7B2%7D)
So, A = ![\sqrt{(\frac{(7+\sqrt{13})}{2})\times ((\frac{(7+\sqrt{13})}{2})-5)\times (\frac{7+\sqrt{13}}{2}-2)\times (\frac{7+\sqrt{13}}{2}-\sqrt{13})}](https://tex.z-dn.net/?f=%5Csqrt%7B%28%5Cfrac%7B%287%2B%5Csqrt%7B13%7D%29%7D%7B2%7D%29%5Ctimes%20%28%28%5Cfrac%7B%287%2B%5Csqrt%7B13%7D%29%7D%7B2%7D%29-5%29%5Ctimes%20%28%5Cfrac%7B7%2B%5Csqrt%7B13%7D%7D%7B2%7D-2%29%5Ctimes%20%28%5Cfrac%7B7%2B%5Csqrt%7B13%7D%7D%7B2%7D-%5Csqrt%7B13%7D%29%7D)
Or, A = ![\sqrt{(\frac{(7+\sqrt{13})}{2})\times (\frac{(\sqrt{13}-3)}{2})\times (\frac{4+\sqrt{13}}{2})\times (\frac{7-\sqrt{13}}{2})}](https://tex.z-dn.net/?f=%5Csqrt%7B%28%5Cfrac%7B%287%2B%5Csqrt%7B13%7D%29%7D%7B2%7D%29%5Ctimes%20%28%5Cfrac%7B%28%5Csqrt%7B13%7D-3%29%7D%7B2%7D%29%5Ctimes%20%28%5Cfrac%7B4%2B%5Csqrt%7B13%7D%7D%7B2%7D%29%5Ctimes%20%28%5Cfrac%7B7-%5Csqrt%7B13%7D%7D%7B2%7D%29%7D)
Or, A =
× ![\sqrt{1+\sqrt{13} }](https://tex.z-dn.net/?f=%5Csqrt%7B1%2B%5Csqrt%7B13%7D%20%7D)
∴ Area of triangle = 1.5![\sqrt{4.6}](https://tex.z-dn.net/?f=%5Csqrt%7B4.6%7D)
Hence The area of triangle for the given coordinates is 1.5
Answer
Answer:
91 short stories
Step-by-step explanation:
You just add 1 + 2 + 3 + 4 + 5 + 6... all the way to 13, and then at the end of 16 months, Troy still only wrote 91 stories since he only wrote them up until 13 months, and then stopped afterwards.