14. Error Analysis A student wrote the following conjecture. Find a counterexample and explain the error. If \( x \) is a positive even number and \( y \) is any integer, then the product \( x y \) will be positive.

Use Gaussian elimination to find the complete solution to the system of equations, or show \( \begin{array}{r}w+2 x+2 y-z=6 \\ 2 x-2 y+z=4 \\ w-4 x+y\end{array} \) Select the correct choice below and fill in any answer boxes within your choice. A. There is ohe solution. The solution set is \( \{0 \). There are infinitely many solutions. The solution set is \( \{0 \). B. (Type expressions using \( z \) as the variable. Use integers or fractions for any numb C. There is no solution. The solution set is \( \varnothing \).

El punto \( (2 .-3) \) es un vértice común de cuatro cuadrados cuyos lados miden 2 unidades y son paralelos a los ejes coordenados del plano cartesiano. ¿Cuál de las siguientes coordenadas podria corresponder a un vértice de alguno de los cuadrados? A) \( (2 .-2) \) B) \( (4 .-5) \) C) \( (-1 .-3) \) D) \( (2.1) \)

D.i Estimate sums vad Assessinent Alialics Estimate the sum by rounding each number to the nearest hundred thousand and then adding. \[ 197,389+311,291 \] The sum is approximately Submit

\( f(x)=2 x^{2}+16 x-10 \) (a) The function's vertex is at the point \( (-4,-42) \) (Type an ordered pair, using integers or fractions.) (b) Determine whether the parabola has a maximum value or a minimum value and find the value. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a fraction.) A. The parabola opens downward and has a maximum value of (c) The range of \( f(x) \) is \( [-42, \infty \) ) (Type your answer in interval notation Use integers or fractions for any numbers in the expression.) (d) The function is increasing on (Type your answer in interval notation. Use integers or fractions for any numbers in the expression )

ind point \( Z \) on \( \overline{R S} \) such that the ratio of \( R Z \) to \( Z S \) is 1:3.