A dragon is given 630 ounces of magical potion to sustain her journey from Arlandia to Gargandua. While flying 4/7 of the distance, she drinks 2/9 of the potion. Suppose she continues to drink the magical potion at this rate for the remainder of her journey. How much potion remains when she reaches Gargandua? Can someone help me with this question? I can't even start!
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Step-by-step explanation:

4/7 of distance = 2/9 of potion

=> 7/7 of distance = 2/9 * (7/4) = 7/18 of potion.

The dragon has used 7/18 of the potion for the journey, and only have 11/18 of it left.

Amount left = 630 ounces * 11/18 = 385 ounces.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

that one look

step-by-step explanation: