In case you meant 64x^3 - 27y^3, that factors to (4x - 3y)(16x^2 + 12xy + 9y^2)
Since 27y is a factor of 54y3, it is automatically the GCF.
It is: 3y and y
9(x - 3y)
(y + 27)(y^2 - 27y + 729)
Since 54y3 is a multiple of 27y, it is automatically the LCM.
Reorder the terms: -5 + 42y + 27y2 Factor a trinomial. (-5 + -3y)(1 + -9y)
It depends on where there are parentheses, if there are any. y + 33 + 2/4 = y + 27.5 (y+3)3 + 2/4 = y3 + 9y2 + 27y + 27.5
2(7y + 14y - 27y)or you could just total them-1 x 2 x 2 x 3 x y = -12y
~(3)-27y=(36)/(1000)Reduce the expression (36)/(1000) by removing a factor of 4 from the numerator and denominator.~(3)-27y=(9)/(250)Since ~(3) does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting ~(3) from both sides.-27y=-~(3)+(9)/(250)Divide each term in the equation by -27.-(27y)/(-27)=(-~(3)+(9)/(250))/(-27)Simplify the left-hand side of the equation by canceling the common terms.y=(-~(3)+(9)/(250))/(-27)Simplify the right-hand side of the equation by simplifying each term.y=(250~(3)-9)/(6750) y=0.06
tammy fey from mesquite,texas. 27y/o
Factorising 15x-27xy gives 3x (5 - 9y).Factorising is to express a number or expression as a product of factors.When factorising always look for common factors. To factorise (15x-27xy) look for the highest factor between the two terms (3x). 15x - 27y = 3x (5 - 9y)
5*3y+1+12y-1 = 15y+1+12y-1 = 27y.
This can be interpreted as a line in 2d space. There are an infinite number of solutions. More than likely your real question is: "How can 27y + 18x = 21 be written in standard slope-intercept form?"Same as 9y + 6x = 7 (divide both sides by 3).Solve for y:9y = 7 - 6xy = (7 - 6x) / 9, ory = (-2/3)x + 7/9We now have an eaquation of a line: slope = -2/3, y-intercept = 7/9Paste -2/3x + 7/9 into the calculator at http://www.coolmath.com/graphit/and click "Eval" to visualize it.
n=72 satisfies the relation. 2*72 = 12**2, and 3*72 = 6**3. The only question is whether or not that is the smallest integer that will do so. All perfect squares of which 2n is a factor are of form (2x)**2 = 4x**2, with n= 2x**2. Similarly all perfect cubes of which 3n is a factor are of form (3y)**3 = 27y**3 with n = 9y**3. So, we need integers x and y such that 2x**2 = 9y**3. If the integers x and y are the smallest that satisfy the equation, then we have the smallest n. It doesn't work for y = 1, or any other odd number. If y = 2, n = 72. There is a number x =6 which satisfies the relation. Since y is smallest possible, then n=72 is the smallest positive integer that satisfies the relation.
Multiply first equation by 3 and second equation by 5:30x + 27y = 12, -30x + 20y = -25; add these two:47y = -13, making y = -13/47 and x = -61/94I have checked these values against the original equations and they satisfy both. Weird solution tho'!
There is a trick to this one. cube the first and write it down. write the opposite sign of the middle term. multiply the first constant times the second constant times 2 and write it down. square the first term write it down, square the second term and write it down. cube the last term including its sign and write it down. Example: (a-b)^3= a^3+2a^2b^2-b^3 (2x+3y)^3=8x^3=12x^2y^2+27y^3
Fortunately, one of the three roots of 27y3 - 1 is really obvious, y = 1/3. Therefore we can pull (y - 1/3) out of the expression giving us:(y - 1/3)(27y2 + 9y +3).Using the quadratic formula on the second multiplicative expression gives:[-9 Ã‚Â± Ã¢Ë†Å¡(-243)]/54 = (-9 Ã‚Â± 9iÃ¢Ë†Å¡3)/54.So the complete, factored form of 27y3 - 1 is:(y - 1/3)[y - (9 + 9iÃ¢Ë†Å¡3)/54][y - (9 - 9iÃ¢Ë†Å¡3)/54].
5x - 9y = 43 (A)3x + 8y = 68 (B)(A)*3: 15x - 27y = 129(B)*5: 15x + 40y = 340Subtracting the first from the second gives67y = 211 => y = 211/67 = 3.15 approxSubstituting the [rational] value of y in (B)5x - 9*211/67 = 43 => 5x = 43 + 1899/67 = 4780/67therefore x = 956/67 = 14.27 approx.
y will be multiplied by 27. Remember, whatever you do to one side of an equation, you must do to the other. In this case, the relationship between x and y would be expressed as y = x^3 To triple x would look like y = (3x)^3 ...b/c you're tripling the value x alone, not the entire term x^3 y = 27x^3 ...after distributing the exponent (3^3 = 27) In order to set both sides of the equation equal, y must be multiplied by 27... 27y = 27x^3 TADA!
5x - 2y = 4  x + 5y = 0  Substituting x into 1st equasion, by re-arranging 2nd: x + 5y = 0 x = -5y 5(-5y) - 2y = 4 -25y - 2y = 4 -27y = 4 y = -4/27 x = -5y x = -5(-4/27) x = 139/27 note: in most cases you will need to simplify the fraction. not in this case, this is an unlikely sum, usually given by an out of school tutor or there is an error with your reading of the question, usually the answers are better fractions.
3x = 7y - 2 (subtract 3x and 7y to both sides of the first equation)9y = 4x + 1-7y = -3x - 2 (multiply by 4 each term of both sides of the first equation)9y = 4x + 1 (multiply by 3 each term of both sides of the second equation)-28y = -12x - 827y = 12x + 3 (add both equations)-y = -5 (multiply by -1 both sides)y = 53x = 7y - 2 (substitute 5 for y)3x = 7(5) - 23x = 33 (divide both sides by 3)x = 11Thus, the solution of the given system of the equations is x = 11 and y = 5.