Answer:
Error of Andrew: Made incorrect factors from the roots
Step-by-step explanation:
Roots of the polynomial are: 3, 2 + 2i, 2 - 2i. According to the factor theorem, if a is a root of the polynomial P(x), then (x - a) is a factor of P(x). According to this definition:
(x - 3) , (x - (2 + 2i)) , (x - (2 - 2i)) are factors of the required polynomial.
Simplifying the brackets, we get:
(x - 3), (x - 2 - 2i), (x - 2 + 2i) are factors of the required polynomial.
This is the step where Andrew made the error. The factors will always be of the form (x - a) , not (x + a). Andrew wrote the complex factors in form of (x + a) which resulted in the wrong answer.
So, the polynomial would be:
<u>Answer:</u>
Cost of package of paper = 4$
Cost of stapler = 7$
<u>Explanation:</u>
Consider the cost of package of paper = x and that of stapler = y.
Now, we are given that cost of 3 paper packages and 4 staplers = 40$
Hence we get, 3x + 4y = 40 as 1st equation.
we are also given, cost of 5 paper packages and 6 staplers = 62$
Hence, the second equation is 5x + 6y = 62
Now, solving the two equations by method of elimination, we first equate coefficients of any one variable say x by multiplying 1st equation by 5 and second by 3 we get ->
15x + 20y = 200
15x + 18y= 186
Subtracting the two we get y = 7 and substituting this value of y in first equation we get x = 4
which gives the required cost of one paper package = x = 4$
and one stapler = y = 7$
Answer:
{-4.6, -4.2, -3.8, -3.4}
Step-by-step explanation:
The length of the space Karlie is dividing is -3-(-5) = 2 units. Then the length of each of those equal 5 spaces will be 2/5 units = 0.4 units.
Each mark on the number line is 0.4 units to the right of the previous one. The first (left-most) mark is 0.4 units to the right of -5, so is at -5+0.4 = -4.6.
The marks have to be placed at -4.6, -4.2, -3.8, and -3.4.
