How would one simplify this equation: -9^n= 3^-⁴?
sol'nwe have-9 ^n = 3^-4here, the result obtain in right side is positive which give us clear that n must be even...so,We knew, both 3^2 =9 =-3^2For this expression to hold true, we should replace 9 to -3^2, we get{-(-3^2)}^n = 3^-4Or, 3^2n =3^-4Equating , we get2n = -4n=-2.Alternatively,-9^n =3^-4Or, (-1 ×9)^n = 3^-4Or, -1^n × 9^n = 3^-4As we already discuss n is even. So, -1^n =1Then, 9^n =3^-4Or, 3^2n = 3^-4Solving we get, n =-2….
How do I simplify the equation (a/x-x/a) /(a+x)?
NOTE: expression is the word you want. An equation requires an equal sign or comparison signHow do I simplify the expression: [math]\frac{\frac{a}{x} - \frac{x}{a}}{a+x}[/math] ?Start by multiplying the entire expression by the value one, by the fraction [math]\frac{xa}{xa}[/math] which is equal to 1.[math]\frac{xa}{xa} · \frac{\frac{a}{x} - \frac{x}{a}}{a+x}[/math]Of course, the one (xa) goes into the numerator, the other into the denominator.[math]\frac{xa (\frac{a}{x} - \frac{x}{a})}{xa (a+x)}[/math]Now, use the distribution property on the numerator[math]xa (\frac{a}{x} - \frac{x}{a})[/math] = a² - x²Factor the numerator:= (a+x)(a-x)Cancel the common factor on both top and bottomCross off the (a+x)What did you end up with?Double-check your answer:Put the original equation and your answer into your graphing calculator(I highly recommend the TI-84 PLUS CE Graphing Calculator)Zoom to a standard viewset A equal to 7Graph the equations and watch to see if the second line covers the firstset A equal to -15Graph it again and watch the second line cover the firstYes, it appears we got the right answer.
How do you simplify this equation?
= 2x^2 + (8x+6x)+24 /(x+4) =2x(x+4)+6(x+4)/(x+4) cancelling (x+4) gives 2x+6 or 2(x+3)
How can I simplify this equation? (a*r) + (a*r^2) =24
(a*r) + (a*r^2) = 24a*r^2 +a*r - 24 = 0Therefore all solutions can be found from the quadratic equation.(-a +/- sqrt(a^2 - 4(a)(-24)))/2a = rOr simplified a bit(-1/2) +/- sqrt(a^2 + 96a)/2a = rFor any given a, except a=0 (divide by 0 issue) and also obvious as -24 is not equal to 0. Real solutions can be found for all a <= -96 and a > 0 while i= sqrt(-1) imaginary solutions can be found for -96
How do I simplify this equation?
I believe you made a mistake in completing the square. This is how I would do it:[math]3x^2 - 2y^2 - 42x - 4y + 133 = 0[/math][math]3x^2 - 42x - 2y^2 - 4y + 133 = 0[/math][math]3 (x^2 - 14x + 49 - 49) - 2 (y^2 + 2y + 1 - 1) + 133 = 0[/math][math]3 (x^2 - 14x + 49) - 3* 49 - 2 (y^2 + 2y + 1) + 2 * 1 + 133 = 0[/math][math]3(x-7)^2-147+2(y-1)^2+2+133=0[/math][math]3(x-7)^2+2(y-1)^2-12=0[/math]Or, you can tell WolframAlpha to do it to you:complete the square 3x^2-2y^2-42x-4y+133=0Evidently, there is a difference, is there not?
Can anyone simplify the following equation?
-7x-12y
Can anyone simplify this boolean equation for me? F(w,x,y,z) = (xy' + w'z)(wx' + yz')?
boolean equation F(w,x,y,z) = (xy' + w'z)(wx' + yz')? (xy' + w'z)(wx' + yz') = (xy')(wx')+(xy')(yz')+(w'z)(wx')+ +(w'z)(yz') = 0 + 0 + 0 + 0 = 0 Thus F(w,x,y,z) = (xy' + w'z)(wx' + yz') = 0