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5x plus 3y-x plus 10-2y?
5x + (3y-x) + (10-2y) = 5x + 3y - x + 10 -2y = 5x - x + 3y - 2y + 10 = 4x + y +10
What are the intercepts of 2x-3y-4z equals -24?
2x-3y-4z=-24 has 3 potential intercepts. The x, y and z interceps. To find the x intercept we set y=z=0 This gives 2x=-24 or x=-12 To find the z intercept we set x=y=0 This gives -4z=-24 or z=6 Lastly to find the y intercept, x=z=0 so -3y=-24 and y=8 The x intercept is (-12,0,0), the y intercept is (0,8,0) and the z intercept is (0,0,6)
3y plus 4z plus 12y equals 3y?
3y + 4z + 12y = 3y -3y -3y ------------------------- 4z + 12y = 0 divide everything by 4 z + 3y = 0 -3y -3y z = -3y
What is the number of a two digit number that is four times the sum of its digits The tens digit is 3 less than the units digit what are you?
Let's break it down: "What is the two digit number ..." x is the 10's place; y is the 1's place; and z is the answer. 10x + y = z "... that is [equal to] 4 times the sum of its digits ..." 4(x + y) = 10x + y "... The tens digit is [equal to] 3 less than the units [1's] digit ..." x = y - 3 Break down the complex equation: 4x + 4y = 10x + y 3y = 6x Substitute the other equation for x, because x = y - 3, and continue: 3y = 6(y - 3) 3y = 6y - 18 -3y = -18 -y = -6 y = 6 So 6 is y, the 1's number. x = y - 3 x = 6 - 3 x = 3 And 3 is x, your 10's number. Almost there! Now find your final answer, z: 10x + y = z 10(3) + 6 = z 30 + 6 = z 36 = z Your answer is 36.
How do you factorize 4xy²(3y-x)-2x²(x-3y)² to get -2x(x-3y)(x-y)(x-2y)?
4xy²(3y-x)-2x²(x-3y)²=4xy²(x-3y)-2x²(x-3y)²=(x-3y)[4xy²-2x²(x-3y)²]=(x-3y)(4xy²-2x³+6x²y)=(x-3y)(-2x³+6x²y+4xy²)=-2x(x-3y)(x²-3xy-2y²)= -2x(x-3y)(x-y)(x-2y)
