Brad makes his own snack mix using whole grain cereal and mixed nuts. one batch of his recipe makes 6 cups of snack mix. brad uses 3 times as much cereal as mixed nuts. the system below can be used to find the number of cups of cereal and number of cups of mixed nuts brad uses to make one batch of snack mix.

  of  mixed nut and   of cereal nut.  

Step-by-step explanation:

Let the mixed nut be x

and since, Brad is using 3 times as much cereal as mixed nuts.

So, the cereal nut will be 3x.

Brad is using 6 cups of snack mix for one batch.

So, the equation becomes:

x +3x=6.

4x=6.

x =6/4

x=3/2.

So, Brad is using of  mixed nut

And cereal is 3 times of mixed nut

Therefore,

And

of cereal nut.  

-7

step-by-step explanation:

x^2 + 18x + 74 = (x + 9)^2 - 81 + 74

= (x + 9)^2 - 7.

so q = -7.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.