Answer:
2x + 6 = -18
x + 1 = -11
3x = -36
Step-by-step explanation:
First find the solution! Then you can create your own equations
2x+9=-15
2x=-24
x=-12
Thus u need solutions with:
x = -12
Knowing the equation of a line as:
y = mx + b
we can can start by making y = -12 (our solution)
mx + b = -12
Now we can pick a value for m and b by adding and miltiplying on both sides
We do this to keep both sides equal.
if we make m = 2 and b = 3:
2x + mb = -12*m + 2b
2x + 6 = -24 + 6
2x + 6 = -18
Solving this we also get x = -12, as we expect.
An alternative way to think about it is to imagine that we start with a simple equation and make it more complex. We have our solution:
x = -12 => lets add a b value!
x + b = -12 + b => Lets add a slope (m)
xm + bm = -12m + bm
Giving values for this can give you multiple equation of the same solution.
General Formula:
m(x+b) = m(y+b)
mx + bm = my + bm
Answer:
24 cars
Step-by-step explanation:
1 hour = 3 * 20 minutes
which means he can service 3 cars in an hour
for 8 hours:
8 hours * 3 cars = 24 cars
: he can service 24 cars in an 8 hour work day.
If u= (u1,u2,u3) andv= (v1,v2,v3), then the dot product of u and v is u·v=u1v1+u2v2+u3v3. For instance, the dot product of u=i−2j−3kandv= 2j−kisu·v= 1·0 + (−2)·2 + (−3)(−1) =−1.
Properties of the Dot Product.
Let u,v, and w be three vectors and let c be a real number. Then u·v=v·u,(u+v)·w=u·w+v·w,(cu)·v=c(u·v).
Further, u·u=|u|2.
Thus, if u=0is the zerovector, then u·u= 0, and otherwise u·u>0.1
Orthogonality Two vectors u and v are said to be orthogonal(perpendicular), if the angle between them is 90◦.Theorem. Two vectors u and v are orthogonal if and only if u·v= 0.
