Mid-point: (3z+z)/2, (2z+8z)/2 = (2z, 5z) Slope: (8z-2z)/(3z-z) = 6z/2z = 3 Perpendicular slope: -1/3 Equation: y -5z = -1/3(x -2z) => y = -1/3x+2z/3+5z => y = -1/3x+17z/3 General form of the bisector equation: x+3y-17z = 0
3z + 8 + 2z + 6 = 5z + 14
(5a)(2z) - (4a)(2c) + 15xz - 12xc group and factor each group = 2a(5z - 4c) + 3x(5z - 4c) factor again (5z - 4c)(2a + 3x)
2z + 9.75 - 7z = 5.15grouping terms, -5z = 5.15 - 9.75subtracting terms on right side, -5z = -4.6dividing both sides by -5, z = 0.92Verifying:Left Side = (2 x .92) + 9.75 - (7 x .92) = 1.84 + 9.75 - 6.44 = 11.69 - 6.44 = 5.15 = Right Side
We can simplify this expression by combining the like terms. Here the likes terms are the z's and the x's.2z + 3z + 5z = 10z. (If we have 2 of something and add three of the same thing and then 5 of the same thing we will end up with 10 of that thing).Likewise we can combine the x's.6x - 2x = 4x. (You could think of this as 6x + - 2x if this helps with the idea of "combining".)Therefore we are able to simplify this expression as:2z + 3z + 5z + 4 + 6x - 2x = 10z + 4 + 4x.
2z(5z - 1)(25z^2 + 5z + 1)
Mid-point: (3z+z)/2, (2z+8z)/2 = (2z, 5z) Slope: (8z-2z)/(3z-z) = 6z/2z = 3 Perpendicular slope: -1/3 Equation: y -5z = -1/3(x -2z) => y = -1/3x+2z/3+5z => y = -1/3x+17z/3 General form of the bisector equation: x+3y-17z = 0
3z + 8 + 2z + 6 = 5z + 14
Add like terms to like: (2z - 20) + (3z + 5) = (2z + 3z) + (-20 + 5) = 5z - 15 2z is shorthand for z+z, 3z is shorthand for z+z+z, so: 2z + 3z = (z+z) + (z+z+z) = z+z+z+z+z = 5z Or, to put it another way, just add the coefficients: 2z + 3z = (2+3)z = 5z.
Total students in class = C Number of boys = Z Number of girls = C-Z Total stamps distributed = (3xZ) + [(C-Z)x5] = 3Z + 5C - 5Z = 5C - 2Z
(5a)(2z) - (4a)(2c) + 15xz - 12xc group and factor each group = 2a(5z - 4c) + 3x(5z - 4c) factor again (5z - 4c)(2a + 3x)
Expand: 8z-4-5z Collect like terms: 3z-4
2z + 9.75 - 7z = 5.15grouping terms, -5z = 5.15 - 9.75subtracting terms on right side, -5z = -4.6dividing both sides by -5, z = 0.92Verifying:Left Side = (2 x .92) + 9.75 - (7 x .92) = 1.84 + 9.75 - 6.44 = 11.69 - 6.44 = 5.15 = Right Side
We can simplify this expression by combining the like terms. Here the likes terms are the z's and the x's.2z + 3z + 5z = 10z. (If we have 2 of something and add three of the same thing and then 5 of the same thing we will end up with 10 of that thing).Likewise we can combine the x's.6x - 2x = 4x. (You could think of this as 6x + - 2x if this helps with the idea of "combining".)Therefore we are able to simplify this expression as:2z + 3z + 5z + 4 + 6x - 2x = 10z + 4 + 4x.
x+2y-6=z -z -z x+2y-z-6=0 +6 +6 ---------> x+2y-z=6 3y-2z=7 ---------> 0x+3y-2z=7 4+3x=2y-5z -3x -3x ---------> -3x+2y-5z=4 Put them into a matrix, for x,y,z and their answers. Solve for [A]-1[B], and the answer comes to: x= 1.75, y= 1.5, and z= -1.25
2x+5y+2z-3w=3 3x+6y+5z+2w=2 4x+5y+14z+14w=11
I am not sure what the question is, but heres my 2 cents. You know what? Never mind. I don't get the question at all. In order to use substitution, you must totally isolate a variable to 1 side, and only have the variable on 1 side. Then you substitute it. Ex: 2y+4x-5z=45 2z+x-4y=54 Isolate x in the 2nd equation, as it is easier: x=54-2z+4y Now, substitute it: 2y+4(54-2z+4y)-5z=45 Got it? I might have done something wrong.