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Let's let A=2Z and B=3Z Suppose their is a ring isomorphism from A to B so f:A->B is a ring isomorphism. Then f(2)=3n for some in integer n (1) Now use the ring isomomorphism property that f(a+b)=f(a)+f(b) so f(4)=f(2+2)=f(2)+f(2)=3n+3n using (1) above. Also f(4)=f(2)f(2)=3nx3n=9n^2 But then comparing the two expressions we have for f(4), we obtain 3n+3n=9n^2 but this implies n=0 and we have f(2)=0 (since f(2)=3n for some n as we said above), however, we have f(0)=0 so this is not possible and we must conclude that 2Z is NOT isomorphic to 3Z.
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What is 9y2 - 25yz - 6z2?
9y**2-25yz-6z**2Multiply first and last terms9*-6=-54Find factors of -542,-27 = 2+-27=-25-2,27 = -2+27=25Rewrite9y**2-27zy+2zy-6z**2Factor pairs of terms9y**2-27zy = 9y(y-3z)2zy-6z**2= 2z(y-3z)9y**2-27zy+2zy-6z**2= 9y(y-3z)+2z(y-3z)Factor:9y(y-3z)+2z(y-3z) = (y-3z)(9y+2z)
What is simplified form for 4(2z-1)-5z?
Expand: 8z-4-5z Collect like terms: 3z-4
-3 X -2Z - 7 equals?
(-3) x (-2z - 7) = 6z + 21 = 3 (2z + 7)
What is th ordered triple of these equations x - 2y plus 3z equals -3 2x - 3y - z equals 7 3x plus y - 2z equals 6?
The ordered triple is (x, y, z) = (1, -1, -2)
How do you solve the inequality 3z-5 is less than or equal to 3z-13?
wrong quesion
What does 3z plus 8 plus 2z plus 6 equal?
3z + 8 + 2z + 6 = 5z + 14
How can you find the sum of 2z-20 and 3z plus 5?
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.
What is 9y2 - 25yz - 6z2?
9y**2-25yz-6z**2Multiply first and last terms9*-6=-54Find factors of -542,-27 = 2+-27=-25-2,27 = -2+27=25Rewrite9y**2-27zy+2zy-6z**2Factor pairs of terms9y**2-27zy = 9y(y-3z)2zy-6z**2= 2z(y-3z)9y**2-27zy+2zy-6z**2= 9y(y-3z)+2z(y-3z)Factor:9y(y-3z)+2z(y-3z) = (y-3z)(9y+2z)
What is the general form of the perpendicular bisector equation of the line segment of z 2z and 3z 8z?
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
Simplify 2y plus y plus 3z-z?
3y+2z
What is 9y squared minus 25yz minus 6z squared?
(9y+2z)(y-3z)
What is 2(3z-7) plus 5(2z plus 5)?
It is an algebraic expression that can be simplified to: 16z+11
What is 5y plus 2z plus 2 plus 8y plus z plus 6 equals?
13y+3z+8
How do you solve 9z plus 10-6z equals 7 plus 2z-3?
9z + 10 - 6z = 7 + 2z - 3 gather together z terms on the left 3z + 10 = 7 + 2z - 3 gather integers on the right 3z + 10 = 2z + 4 subtract 2z from each side z + 10 = 4 subtract 10 from each side z = - 6 ----------------check in original equation 9(- 6) + 10 - 6(- 6) = 7 + 2(- 6) - 3 - 54 + 10 + 36 = 7 - 12 - 3 - 8 = - 8 --------------checks
Solve this system of equations 5x plus 3y plus z equals -29 x-3y plus 2z equals 23 14x-2y plus 3z equals -18?
Solve this system of equations. 5x+3y+z=-29 x-3y+2z=23 14x-2y+3z=-18 Write the solution as an ordered triple.
What is the answer for adding polynomials 2z plus 3z plus 5z plus 4 plus 6x-2x?
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.
What is simplified form for 4(2z-1)-5z?
Expand: 8z-4-5z Collect like terms: 3z-4
