Answer:
Step-by-step explanation:
A. If children are considered people under the age of 18, then the answer would be
13 < a < 18 where the a represents age, where the inequality signs do not have an equals to because those ages are excluded
B. This inequality can be shown on a number line with open circles denoting the endpoints 13 and 18 as they are not included, and a line connecting these two points which represents the ages encompassed by the range
10. is f 11. is a I dont know for 12 though
The required plane Π contains the line
L: (-1,1,2)+t(7,6,2)
means that Π is perpendicular to the direction vector of the line L, namely
vl=<7,6,2>
It is also required that Π be perpendicular to the plane
Π 1 : 5y-7z+8=0
means that Π is also perpendicular to the normal vector of the given plane, vp=<0,5,-7>.
Thus the normal vector of the required plane, Π can be obtained by the cross product of vl and vp, or vl x vp:
i j k
7 6 2
0 5 -7
=<-42-10, 0+49, 35-0>
=<-52, 49, 35>
which is the normal vector of Π
Since Π has to contain the line, it must pass through the point (-1,1,2), so the equation of the plane is
Π : -52(x-(-1))+49(y-1)+35(z-2)=0
=>
Π : -52x+49y+35z = 171
Check that normal vector of plane is orthogonal to line direction vector
<-52,49,35>.<7,6,2>
=-364+294+70
=0 ok
We have the next number
The expanded form of the number is
Also, we can verify that Alex was incorrect because if we do the sum of the expanded form that Alex calculated we obtain
Finally, the correct answer is
