1). Determinar el valor del parámetro \( k \) de manera que la recta de la familia \( 3 x-k y-7=0 \) que le corresponda sea perpendicular a la recta \( 7 x+4 y-11=0 \).

Suppose \( H(x)=6 \sqrt[3]{x}-3 \). Find two functions \( f \) and \( g \) such that \( (f \circ g)(x)=H(x) \). Neither function can be the identity function. (There may be more than one correct answer.) \( f(x)=\square \)

Solve for \( x \) using the square root property. \( 10(p-4)^{2}-20=470 \) \( p= \) Entry Tip: Do not use a decimal approximation for square roots. To enter a number like \( 5 \sqrt{7} \), type \( 5^{*} \) sqrt( 7 ). Preview your answer before submitting! Furthere Tip: Write your answers as a list, with your answers separated by (a) comma(s). For example, if you get 4 and \( -\frac{2}{3} \) as your answers, then enter \( 4,-2 / 3 \) in the box.

2. In all likelihood, we probably don't care about the order the items are put on the tray. How many options are there to order 5 items from 9 choices? Assume that we connot duplicate any option and that the order is not important.

James visits house 1, house 3 , house 5 , and so on, up to house 99 . He then visits house 2, house 4, house 6, and so on, up to house 100 . How many houses does h visit in total?

8) One of the factors of \( 2 x^{3}-11 x^{2}+17 x-5 \) is \( 2 x-5 \) Find the other factor.