The graphs defined as \( g(x)=a x^{2}+q \) and \( f(x)=k^{x}-14 \) both pass through \( (-2 ; 0) \) on the \( x \)-axis. The \( y \)-intercept of \( g \) is \( (0 ;-5) \). 4.1.1 Write down the equation of the asymptote of \( f \). 4.1.2 Write down the value of \( q \). 1.3 Write down the coordinates of the other \( x \)-intercept of \( g \). 1.4 Determine the equation of \( g \). 1.5 Determine the equation of \( f \).

3.18. Determine el máximo comun divisor de los enteros \( 15,18,24 \) y escríbalo como una combinación lineal de \( 15,18,24 \). 3.19. Sea \( a \in \mathbb{Z}^{+} \)tal que \( \operatorname{mcd}(240, a)=1 \), probar que \( 240 \mid a^{4}-1 \).

42. Julio paid \( 7 \frac{3}{4} \% \) sales tax on an item he bought. He figured that if he had bought the item in a neighboring state where the sales tax is \( 8 \frac{1}{4} \% \), he would have paid \( \$ 75 \) more. What was the cost of the item before tax? (C) \( \$ 15,000.00 \) (IS) \( \$ 3,750.00 \) (C) \( \$ 1,500.00 \) (D) \( \$ 150.00 \) (F) \( \$ 37.50 \)

3. At a school, \( 40 \% \) of the sikthegrade students said that hip-hop is their favorite kind of music. If 100 sixth-gade students preler hip hop music, how many sixth-grade studer are at the school? Explain or show your reasoning.

(Express \( \frac{6}{7 h}-\frac{3-4 g}{14 h} \) as a single fraction in its simplest form. Ungkapkan \( \frac{6}{7 h}-\frac{3-4 g}{14 h} \) sebagai pecahan tunggal dalam bentuk termudah.

expunencial \( \left.\left(4^{2}\right)\left(2^{3}\right)^{2 x-5}\right)=8 \)