I’m sorry but Where is the graph
Direction vector of line of intersection of two planes is the cross product of the normal vectors of the planes, namely
p1: x+y+z=2
p2: x+7y+7z=2
and the corresponding normal vectors are: (equiv. to coeff. of the plane)
n1:<1,1,1>
n2:<1,7,7>
The cross product n1 x n2
vl=
i j l
1 1 1
1 7 7
=<7-7, 1-7, 7-1>
=<0,-6,6>
Simplify by reducing length by a factor of 6
vl=<0,-1,1>
By observing the equations of the two planes, we see that (2,0,0) is a point on the intersection, because this points satisfies both plane equations.
Thus the parametric equation of the line is
L: (2,0,0)+t(0,-1,1)
or
L: x=2, y=-t, z=t
Slope intercept form: y = mx + b
m = slope and b = y-intercept
The equation is: y = -3x + 6
The m value for this is -3, so the line has a slope of -3. If y = 1/3x - 8 was parallel to y = -3x + 6 then they would have the same slope, which they do not. So they aren't parallel.
The find the slope of a perpendicular line, take the negative reciprocal of the slope of y = -3x + 6. The negative reciprocal of -3 is 1/3. y = 1/3x - 8 has a slope of 1/3, so they are perpendicular to each other.
Answer:the number of adult tickets that the movie theatre sold is 63.
the number of child's tickets that the movie theatre sold is 61
Step-by-step explanation:
Let x represent the number of adult tickets that the movie theatre sold.
Let y represent the number of child's tickets that the movie theatre sold.
The total number of tickets sold is 124. It means that
x + y = 124
Movie theater charges $11.00 for an adult ticket and $8.00 for a child's ticket. The total cost of the tickets sold is 1181. It means that
11x + 8y = 1181 - - - - - - - - - - - -1
Substituting x = 124 - y into equation 1, it becomes
11(124 - y) + 8y = 1181
1364 - 11y + 8y = 1181
- 11y + 8y = 1181 - 1364
- 3y = - 183
y = - 183/ - 3
y = 61
x = 124 - y = 124 - 61
x = 63
Answer:
- B. Y = 32x + 35
- E. Y = 35x + 30
- F. Y = 40x + 40
Step-by-step explanation:
First find out how much Mary was charging per hour:
= 500 / 20
= $25 per hour
She charges $60 for plants.
In a linear equation of the form: y = mx + c, the m represents the variable cost which in this case is the $25 per hour and the c is the fixed cost which is the $60.
Her rate as a linear equation would be:
y = 25x + 60
Looking a the value of the m of other gardeners will tell you who is charging higher hourly rates with anything above $25 doing so.
The gardeners with higher values of m than Mary are:
B. Y = 32x + 35
E. Y = 35x + 30
F. Y = 40x + 40
