3. mrs. galicia bought 3 tacos and 2 sodas and paid $9.75. the next day she went back and bought 5 tacos and 1 soda and paid $12.75. (a) write and solve a system of equations that model the problem. show all your work. (b) how much was one soda? (c) how much was one taco?

(a) System of equations: and

(b) One soda costs

(c) One taco costs

SOLUTION:

Given, Mrs. Galicia bought 3 tacos and 2 sodas and paid .  

The next day she went back and bought 5 tacos and 1 soda and paid .  

Let the cost of 1 tacos be m, and cost of 1 soda be n.

Now, We have to find  

(a) System of equations:  

3 tacos and 2 sodas cost

5 tacos and 1 soda cost

System of equations are  

Now,

So, substitute n in (1)

(b) cost of one soda

(c) cost of one taco

answer: 8

step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.