6. A Dutch door is a door that is split in half to allow the top and bottom to open separately. The top section of a Dutch door is 3.25 feet tall and the bottom section is \( 3 \frac{3}{4} \) feet tall. Write an inequality that compares the heights of the top and bottom sections of the door.

The postal service of a country charges \( \$ 0.36 \) postage for a letter weighing up to 1 ounce, plus \( \$ 0.26 \) for each additional ounce up to 5 ounces. Letters weighing more than 5 ounces do not qualify for these rates. \( C(x)=\left\{\begin{array}{ll}\$ \square & \text { if } 0<x \leq 1 \\ \text { (a) Write a piecewise-defined function } C \text { for the postage charged for a letter weighing } x \text { ounces. } \\ \$ \square & \text { if } 3<x \leq 4 \\ \$ \square & \text { if } 4<x \leq 5\end{array}\right. \)

Consider the number pattern below: \[ \frac{-3}{5} ; \frac{-6}{9} ; \frac{-9}{13} ; \ldots . \ldots \] Determine the next two terms of the number pattern. Determine the \( n^{\text {th }} \) term of the number pattern.

Vergelyk die volgende getalpatroon met die oorspronklike getalpatroon wat in VRAAG 3.1 hierbo gegee is: \[ 4 ; 28 ; 70 ; 130 ; \ldots \] 3.2.1 Beskryf, in woorde, hoe hierdie nuwe patroon gevorm is. 3.2.2 Bepaal die waarde van die \( 15^{\text {de }} \) term in hierdie patroon.

Diketahui fungsi tujuan meminimumkan \( Z=x+5 y \) dengan pembatas-pembatas sebagai berikut \( x+y \leq 8 \) \( 2 x-3 y \leq 6 \) \( x \leq 5 \) \( y \geq 1 \) a. gambarkan daerah layak b. tentukan Z minimum

Use propenties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1 . Where possible, evaluate logarithmic expressions. \( 7 \ln (x-4) \) - \( 3 \ln x \)