The other day, we made drink mixtures by mixing 4 teaspoons of powdered drink mix for every cup of water. Here are two ways to represent multiple batches of this recipe: How can we tell that 4:1 and 12:3 are equivalent ratios?

How are these representations the same? How are these representations different?

How many teaspoons of drink mix should be used with 3 cups of water?
How many cups of water should be used with 16 teaspoons of drink mix?
What numbers should go in the empty boxes on the double number line diagram? What do these numbers mean?

The question asked, “ How many teaspoons of drink mix should be used with 3 cups of water” You would have to put 12 teaspoons of drink mix.

the final function for the graph becomes x-2=-1. before graphing you solve the equation, where x=1. then graph accordingly.   ( on the x-axis, 1 on the line will possess a vertical line.)

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."