Answer: 3
Step-by-step explanation:
In theory we know that the equation of a linear function is expressed as
Eq.(1): y = m*x + c,
where m is the slope and c is a constant.
From the table we know the values of x and y, so we can use any of those, but in this case lets use the first and third rows of the table and substituting in Eq.(1) we obtain a 2-equation system as follow:
Point (-2,-2) gives: -2 = (-2)*m + c Eq.(2)
Point (0,4) gives: 4 = (0)*m + c Eq.(3)
Now rearranging Eq.(2) we get: -2 = -2*m + c <=> -2 - c = -2m Eq.(4)
Then rearranging Eq.(3) we get: 4 = 0 + c <=> c = 4
Plugging the value of c in Eq.(4) we get:
-2 = -2m + 4 <=> -2 - 4 = - 2m <=> -6 = -2m <=> m = 3
So finally and from Eq.(1) we obtain
y = 3x + c
Answer:
240
Step-by-step explanation:
Multiply them altogether.
5 x 4 x 4 x 2 x 1.5 = 10 x 24 = 240
Answer:
k=3
Step-by-step explanation:
Move k over to the 2k side and 2 to the five 5-2=3 and 2k-k=k
k+2=5
k=3
Step-by-step explanation:
✧ ![\underline{ \underline{ \large{ \tt{G\: I \: V \: E\: N}}} }:](https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Cunderline%7B%20%5Clarge%7B%20%5Ctt%7BG%5C%3A%20I%20%5C%3A%20V%20%5C%3A%20E%5C%3A%20N%7D%7D%7D%20%7D%3A%20)
Here , Perpendicular ( p ) = 8 & hypotenuse ( h ) = 9
♨ ![\underline{ \underline{ \large{ \tt{ T \: O \: \: F \: I\: N\: D}}}} :](https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Cunderline%7B%20%5Clarge%7B%20%5Ctt%7B%20T%20%5C%3A%20O%20%5C%3A%20%20%5C%3A%20F%20%5C%3A%20I%5C%3A%20N%5C%3A%20D%7D%7D%7D%7D%20%3A%20)
♨ ![\underline{ \underline{ \large{ \tt{S \: O \: L\: U \: T\: I\: O \: N}}}} :](https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Cunderline%7B%20%5Clarge%7B%20%5Ctt%7BS%20%5C%3A%20O%20%5C%3A%20L%5C%3A%20U%20%5C%3A%20T%5C%3A%20I%5C%3A%20O%20%5C%3A%20N%7D%7D%7D%7D%20%3A%20)
- First, Find the base ( b ) using Pythagoras theorem :
☪ ![\boxed{ \bf{ {h}^{2} = {p}^{2} + {b}^{2} }}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Cbf%7B%20%7Bh%7D%5E%7B2%7D%20%3D%20%20%7Bp%7D%5E%7B2%7D%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%20%20%7D%7D)
~Plug all the known values and then simplify!
⇾ ![\large{ \bf{ {9}^{2} = {8}^{2} + {b}^{2} }}](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Cbf%7B%20%7B9%7D%5E%7B2%7D%20%20%3D%20%20%7B8%7D%5E%7B2%7D%20%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%7D%7D)
⇾ ![\large{ \bf{81 = 64 + {b}^{2} }}](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Cbf%7B81%20%3D%2064%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%7D%7D)
⇾ ![\large{ \bf{64 + {b}^{2} = 81}}](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Cbf%7B64%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%20%3D%2081%7D%7D)
⇾ ![\large{ \bf{ {b}^{2} = 81 - 64}}](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Cbf%7B%20%7Bb%7D%5E%7B2%7D%20%20%3D%2081%20-%2064%7D%7D)
⇾ ![\large{ \bf{ {b}^{2} = 17}}](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Cbf%7B%20%7Bb%7D%5E%7B2%7D%20%20%3D%2017%7D%7D)
⇾ ![\large{ \bf{b = \sqrt{17}}}](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Cbf%7Bb%20%3D%20%20%5Csqrt%7B17%7D%7D%7D%20)
- Now , Find the value of cot θ
We know ;
⟿ ![\large{ \bf{cot \theta = \frac{b}{p} = \boxed{ \bf{ \frac{ \sqrt{17} }{8}}}}}](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Cbf%7Bcot%20%5Ctheta%20%3D%20%20%5Cfrac%7Bb%7D%7Bp%7D%20%20%3D%20%20%5Cboxed%7B%20%5Cbf%7B%20%5Cfrac%7B%20%5Csqrt%7B17%7D%20%7D%7B8%7D%7D%7D%7D%7D%20)
⤷ ![\boxed{ \boxed{ \underline{ \large{ \tt{Our \: Final \: Answer : { \tt{ \frac{ \sqrt{17} }{8} }}}}}}}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Cboxed%7B%20%5Cunderline%7B%20%5Clarge%7B%20%5Ctt%7BOur%20%5C%3A%20Final%20%5C%3A%20Answer%20%3A%20%20%7B%20%5Ctt%7B%20%5Cfrac%7B%20%5Csqrt%7B17%7D%20%7D%7B8%7D%20%7D%7D%7D%7D%7D%7D%7D)
( Correct me if I'm wrong )
Hope I helped ! ♡
Have a wonderful day / night ! ツ
☄ Let me know if you have any questions regarding my answer !
!! ✎
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