4. Is point \( (90,68) \) on line \( J \) ? Explain how you know.

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.

Exercice 2: (1) Montrer les implications suivantes: a \( (\forall \mathrm{x}, \mathrm{y} \in \mathbb{R}) ; \quad \mathrm{Si} \quad(|\mathrm{x}| \leq 1 \) et \( |\mathrm{y}| \leq 1) \quad \) alors \( \sqrt{1-\mathrm{x}^{2}}+\sqrt{1-\mathrm{y}^{2}} \leq 2 \sqrt{1-\left(\frac{\mathrm{x}+\mathrm{y}}{2}\right)^{2}} \) b \( \left(\forall \mathrm{x}, \mathrm{y} \in \mathbb{R}^{*}\right) ; \quad 2 \mathrm{x}+4 \mathrm{y}=1 \Rightarrow \frac{1}{\mathrm{x}^{2}+\mathrm{y}^{2}} \leq 20 \) (2) En utilisant "Le raisonnement par les équivalences successives", montrer que: a \( \left(\forall \mathrm{x}, \mathrm{y} \in \mathbb{R}^{+}\right) ; \quad \mathrm{x} \sqrt{\mathrm{x}^{2}+1}=\mathrm{y} \sqrt{\mathrm{y}^{2}+1} \Longleftrightarrow \mathrm{x}=\mathrm{y} \) b \( \left(\forall \mathrm{x}, \mathrm{y} \in \mathbb{R}_{+}^{*}\right) ; \quad \mathrm{x} \prec \mathrm{y} \Longleftrightarrow \frac{\mathrm{x}}{\mathrm{y}} \prec \frac{2 \mathrm{x}+5 \mathrm{y}}{5 \mathrm{x}+2 \mathrm{y}} \prec \frac{\mathrm{y}}{\mathrm{x}} \)

Which was not a location of the first civilizations Mesopotamia Europe Egypt China India

4 Resolver: \( 2 x+3 y=8,3 x-5 y=-7 \), a través del método de reducción * \( x=2, y=1 \) \( x=2, y=2 \) \( x=1, y=2 \) \( x=-1, y=2 \)

28. World History The Chinese kwan note was used in the 1300 , It was about 93 centimeters long. The United States dollar bill is almost 16 centimeters long. About how many times longer was the kwan note?