Find the exact value of the logarithm without using a calculator. \( \log _{9} 81 \) \( \log _{9} 81=\square \) (Type an integer or a simplified fraction.)

Find the value of the determinant. \[ \left|\begin{array}{rrr}9 & 6 & 10 \\ -1 & -1 & 7 \\ -4 & -2 & 1\end{array}\right| \] The determinant value is

Cabinet \( X \) costs \( \$ 30 \), requires 12 sq ft of floor space, and holds 36 cu ft of files. Cabinet \( Y \) costs \( \$ 50 \), requires 6 sq ft of floor space, and holds 30 cu ft . To get maximum storage, how many of each should be purchased with a budget limit of \( \$ 450 \) and floor space of 96 sq ft ? The manager should buy \( \square \) of cabinet \( X \) and \( \square \) of cabinet \( Y \). (If two possibilities provide maximum storage, use the option that involves buying at least one of cabinet \( X \) and at least one of cabinet \( ~ \) .)

Graph the parabola. \( y=x^{2} \) Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.

Aşağıdaki kutuların içine \( 2,4,6,8,70 \) ve 12 sayılarından dört tanesi her kutuya farkıı bir sayı gelecek şekilde yerleştirildiğinde eşitlik sağlanmaktadır. \[ \sqrt{\square}+\sqrt{\square}=\sqrt{\square+\square} \] Buna göre, kutulara yerleştirilmeyen sayılarín toplamı kaçtır? \( \begin{array}{llll}\text { (A) } 12 & \text { B) } 14 & \text { C) } 16 & \text { D) } 18\end{array} \) E) 20

7) Simplify the logarithm so that no argument contains a product, quotient or a powe \( \ln \left(e x^{3}\right)= \) a) \( 1-3 \ln x \) b) \( 01+3 \ln x \) c) \( 03-\ln x \) d) \( 3+\ln x \)