Please help me do this someone.

Robert is a high school basketball player. In a particular game, he
made some three point shots and some free throws (worth one
point each). Robert made a total of 9 shots altogether and scored
a total of 23 points. Write a system of equations that could be
used to determine the number of three point shots Robert made
and the number of free throws he made. Define the variables that
you use to write the system.

The system of equations are;

a + b = 9 ———(1)

a + 3b = 23———(2)

Step-by-step Explanation: The variables used here are a and b. Where a represents the number of free throws and b represents the number of three-pointers.

From equation (1), what we have is the total number of shots he has taken altogether which is 9 shots in all. All 9 shots are an addition of free throws and three pointers (that is a + b).

In equation (2), what we have is the points obtainable times the number of shots taken (for each shot). This means if a is a free throw, then 1 times a is equal to number of free throws times 1. Similarly, if b is a three-point throw, then 3 times b is equal to the number of three pointers thrown times 3.

The solution to the equation above gives us,

a = 2 and b = 7

hope this !

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.