In order to solve for parallel, perpendicular, or neither, you have to look at the slope.
If the slope is the same for both equations, it is most likely parallel.
If it's the reciprocal (Where you flip the number and add change the signs. For example, the reciprocal of 1/2 is -2)
If the slope is not the same or the reciprocal, then it is neither.
So for the first equation, your slope is:
3x+2y=6
2y=-3x+6
y=-3/2x+3 The equation y=mx+b can help you here, where m is the slope.
Your slope is -3/2
For the second equation, your slope is -3/2 since y=-3/2x+5 is already in y=mx+b form and m is the slope.
Since both slopes are -3/2, then you have parallel equations!
(Be careful though, sometimes it will have the same slope but there will also be the same y-intercept. If that happens, it's no longer parallel, but it's the same equation. Such as y=-3/2x+1 and y=-3/2x+1. In this case there will be infinite solutions, but parallel equations have no solutions.)
I hope this helps!! Please ask if you have more questions!
Let
x------> amount of pounds of apples
y------> amount of pounds of oranges
z-----> amount of pounds of peaches
we know that
x+y+z=127------> equation 1
x=4z-----> equation 2
y=7+z----> equation 3
substitute equation 2 and equation 3 in equation 1
x+y+z=127----> (4z)+(7+z)+z=127---> 6z=127-7---> 6z=120----> z=20 lb
x=4z---> x=4*20----> x=80 lb
y=7+z----> y=7+20---> y=27 lb
amount of pounds of apples----> 80 lb
amount of pounds of oranges----> 27 lb
amount of pounds of peaches---> 20 lb
= > x² + 7x + 12 = 12
= > x² + ( 4 + 3 )x + 12 = 12
= > x² + 4x + 3x + 12 = 12
= > x( x + 4 ) + 3( x + 4 ) = 12
= > ( x + 4 ) ( x + 3 ) = 12
Percy did correct till this step. But by doing like this, Percy can't get the values of the variable x.
Percy should follow the following steps :
= > x² + 7x + 12 = 12
Add -12 on both sides,
= > x² + 7x + 12 - 12 = 12 - 12
= > x² + 7x = 0
= > x( x + 7 ) = 0
= > ( x = 0 ) or ( x + 7 = 0 )
= > ( x = 0 ) or ( x = - 7 )
Hence, required value(s) of x is 0 or -7
Answer:
one solution
Step-by-step explanation:
2/3(3y+6)=0
Multiply by 3/2
3/2 *2/3(3y+6)=0*3/2
3y+6 = 0
Subtract 6 from each side
3y = -6
Divide by 3
3y/3 = -6/3
y = -2
There is one solution
Answer:
20 square meters
Step-by-step explanation:
To do this continue the line of the top of the rectangle so you split the figure into a triangle and a rectangle. The dimensions of the rectangle would be 8 by 2, so 8 * 2 = 16. Next, the dimensions of the triangle would be (4 - 2) by (8 - 4) = 2 by 4. The area would then be 2 * 4 = 8/2 = 4.
All you have to do now is add those two areas together, 16 + 4 = 20 square meters.
