Answer:
He have 43 bills of 10 and 13 bills of 5
Step-by-step explanation:
5x + 10y = 495
x + y = 56
Isolate x:
x = 56 - y
Substitute in the first equation:
5(56 - y) +10y = 495
280 -5y +10 y = 495
5y = 495 -280
5y = 215
y = 215/5
y= 43
Now substitute the value of y to find x:
x = 56 - y
x = 56 - 43
x = 13
Answer:
2 and 3.
Step-by-step explanation:
1 + 1
Factor out.
2(1)
Multiply.
= 2
1 + 2
Add the terms.
= 3
A . y = 2(18 + x)
b. y = (8 + x)(10 + x)
or y = x^2 + 80 + 18x
For y= -2x + 8 i think y is -2x + 8 and x is 4 - y/2
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
