1. Find one pair $(x, y)$ of real numbers such that $x + y = 4$ and $x^3 + y^3 = 100.$ 2.For what real values of $k$ does the quadratic $12x^2 + kx + 27 = 0$ have nonreal roots? Enter your answer as an interval.
3.Find all pairs $(x, y)$ of real numbers such that $x + y = 10$ and $x^2 + y^2 = 56$.
4.Simplify $\displaystyle\frac{1-i}{2+3i}$, where $i^2 = -1.$
5.What is the smallest value of $x$ that satisfies the equation $8x^2 - 38x + 35 = 0$? Express your answer as a decimal.

answer: i think it is (1,-2)

3 is greater then both of those numbers

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

b

step-by-step explanation: