Hello :
let A(0,3,2) and (Δ) this line , v vector parallel to (<span>Δ).
M</span>∈ (Δ) : vector (AM) = t v..... t ∈ R
1 ) (Δ) parallel to the plane x + y + z = 5 : let : n an vector <span>perpendicular
to the plane : n </span>⊥ v .... n(1,1,1) so : n.v =0 means : n.vector (AM) = 0
(1)(x)+(1)(y-3)+(1)(z -2) =0 ( vector (AM) = ( x, y -3 , z-2 )
x+y+z - 5=0 ...(1)
2) (Δ) perpendicular to the line (Δ') : x = 1+t , y = 3 - t , z = 2t :
vector (u) ⊥ v .... vector(u) parallel to (Δ') and vector(u) = (1 , -1 ,1)
vector (u) ⊥ vector (AM) means :
(1)(x)+(-1)(y-3)+(2)(z -2) =0
x - y+2z - 1 = 0 ...(2)
so the system :
x+y+z - 5=0 ...(1)
x - y+2z - 1 = 0 ...(2)
(1)+(2) : 2x+3z - 6 =0
x = 3 - (3/2)z
subsct in (1) : 3 - (3/2)z +y +z - 5 =0
y = 1/2z +2
let : z=t
an parametric equations for the line (Δ) is : x = 3 - (3/2)t
y = (1/2)t +2
z=t
verifiy :
1) (Δ) parallel to the plane x + y + z = 5 :
(-3/2 , 1/2 ,1) <span>perpendicular to (1,1,1)
</span>because : (1)(-3/2)+(1)(1/2)+(1)(1) = -1 +1 = 0
2) (Δ) perpendicular to the line (Δ') :
(-3/2 , 1/2 ,1) perpendicular to (1,-1,2)
because : (1)(-3/2)+(-1)(1/2)+(1)(2) = -2 +2 = 0
A(0, 3, 2)∈(Δ) :
0 = 3-(3/2)t
3 = (1/2)t+2
2 =t
same : t = 2
Answer: 4.2 kilograms
Step-by-step explanation:
Let's solve your equation step-by-step.<span><span>
6<span>(<span>x−1</span>)</span></span>=<span>9<span>(<span>x+2</span>)</span></span></span>
Step 1: Simplify both sides of the equation.<span><span>
6<span>(<span>x−1</span>)</span></span>=<span>9<span>(<span>x+2</span>)</span></span></span><span>
Simplify:</span><span><span><span><span>
(6)</span><span>(x)</span></span>+<span><span>(6)</span><span>(<span>−1</span>)</span></span></span>=<span><span><span>(9)</span><span>(x)</span></span>+<span><span>(9)</span><span>(2)</span></span></span></span>(Distribute)<span><span><span><span>
6x</span>+</span>−6</span>=<span><span>9x</span>+18</span></span><span><span><span>
6x</span>−6</span>=<span><span>9x</span>+18</span></span>
Step 2: Subtract 9x from both sides.<span><span><span><span>
6x</span>−6</span>−<span>9x</span></span>=<span><span><span>9x</span>+18</span>−<span>9x</span></span></span><span><span><span>
−<span>3x</span></span>−6</span>=18</span>
Step 3: Add 6 to both sides.<span><span><span><span>
−<span>3x</span></span>−6</span>+6</span>=<span>18+6</span></span><span><span>
−<span>3x</span></span>=24</span>
Step 4: Divide both sides by -3.<span><span><span>
−<span>3x</span></span><span>−3</span></span>=<span>24<span>−3</span></span></span><span>
x=<span>−8</span></span><span>
Answer: x= -8
-Hope I helped.</span>
Your answer is option C. Hope I answered it on time
