Answer:its the one of had possesion
Step-by-step explanation:
Answer:
y =-5/4x +11/2
Step-by-step explanation:
First we need to find the slope of the line
4x-5y = 10
Solve for y
Subtract 4x from each side
4x-4x-5y =-4x-10
-5y = -4x-10
Divide by -5
-5y/-5 = -4x/-5 -10/-5
y = 4/5x +2
The slope is 4/5
The slope of a line that is perpendicular is the negative reciprocal
m perpendicular = - (5/4)
We know have a slope = -5/4 and a point (2,3)
We can use the point slope form of a line
y-y1 = m(x-x1)
y-3 = -5/4 (x-2)
Distribute
y-3 =-5/4x +10/4
Add 3 to each side
y-3+3 = -5/4 x +5/2 +3
Get a common denominator
y = -5/4x +5/2 +6/2
y =-5/4x +11/2
Answer: n=8
Step-by-step explanation:
-8(n-6)=-16
-8n+48=-16
-8n=-64
n=8
ANSWERx = 5/4
EXPLANATION ![2^x \cdot 2^{x-2} = \sqrt{2}](https://tex.z-dn.net/?f=2%5Ex%20%5Ccdot%202%5E%7Bx-2%7D%20%3D%20%5Csqrt%7B2%7D)
Note that
![\sqrt{a} = a^{\frac{1}{2}}](https://tex.z-dn.net/?f=%5Csqrt%7Ba%7D%20%3D%20a%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)
so
![\sqrt{2} = 2^{\frac{1}{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D%20%3D%202%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%7D)
Note that on the left-hand side, we can use exponent properties for multiplying two powers of the same base together:
![\begin{aligned} 2^x \cdot 2^{x-2} &= \sqrt{2} \\ 2^{x + (x-2)} &= 2^{\frac{1}{2}} \\ 2^{2x - 2} &= 2^{\frac{1}{2}} \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%0A2%5Ex%20%5Ccdot%202%5E%7Bx-2%7D%20%26%3D%20%5Csqrt%7B2%7D%20%5C%5C%0A2%5E%7Bx%20%2B%20%28x-2%29%7D%20%26%3D%202%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%20%5C%5C%0A2%5E%7B2x%20-%202%7D%20%26%3D%202%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%0A%5Cend%7Baligned%7D)
We can now equate the exponents because both sides of the equation are of the same base with no other terms.
![\begin{aligned} 2^{2x - 2} &= 2^{\frac{1}{2}} \\ 2x - 2 &= \tfrac{1}{2} \\ 2x &= \tfrac{1}{2} + 2 \\ 2x &= \tfrac{5}{2} \\ x &= \tfrac{5}{4} \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%0A2%5E%7B2x%20-%202%7D%20%26%3D%202%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%20%5C%5C%0A2x%20-%202%20%26%3D%20%5Ctfrac%7B1%7D%7B2%7D%20%5C%5C%0A2x%20%26%3D%20%5Ctfrac%7B1%7D%7B2%7D%20%2B%202%20%5C%5C%20%0A2x%20%26%3D%20%5Ctfrac%7B5%7D%7B2%7D%20%5C%5C%0Ax%20%26%3D%20%5Ctfrac%7B5%7D%7B4%7D%0A%5Cend%7Baligned%7D)
The answer is x = 5/4. We can confirm this by using this value in the original equation to get a true statement.
A) 4a - 3b + 2c
4(2, -1, 5) - 3(4, 3 , -2) + 2(5, 4, 0) = (8, -4, 20) - (12, 9, - 6) + (10, 8, 0) =
= (8 - 12 + 10 , -4 - 9 + 8 , 20 + 6 + 0) = (6, - 5, 26)
Answer: (6, - 5, 26)
b) magnitude of vector b
![\sqrt{4^2+3^2+(-2)^2} = \sqrt{16+9+4} = \sqrt{29} ~ 5.4](https://tex.z-dn.net/?f=%20%5Csqrt%7B4%5E2%2B3%5E2%2B%28-2%29%5E2%7D%20%3D%20%5Csqrt%7B16%2B9%2B4%7D%20%3D%20%5Csqrt%7B29%7D%20~%205.4)
c) vector of length 7 parallel to vector c
=> m(5,4,0) = (5m,4m,0)
=>
![\sqrt{(5m)^2+(4m)^2+0}= \sqrt{25m^2+16m^2}= \sqrt{41m^2}=m \sqrt{41}=7](https://tex.z-dn.net/?f=%20%5Csqrt%7B%285m%29%5E2%2B%284m%29%5E2%2B0%7D%3D%20%5Csqrt%7B25m%5E2%2B16m%5E2%7D%3D%20%5Csqrt%7B41m%5E2%7D%3Dm%20%5Csqrt%7B41%7D%3D7%20%20%20%20)
=> m = 7 / √41 ≈ 1.093
=> 1.093 (5, 4, 0) = (5.465 , 4.372, 0)
Answer: (5.465 , 4.372 , 0)