If \(a = 3c − 4\) and \(b = 2(3 − c)\) what is \(3b\) expressed in terms of \(a\)?

Let the function \(f(h,k)\) be defined as \(f (h,k) = (h − k)^2 + hk\).

For every \(x\) and \(y\), what does the function \(f((x^2 + 2y^2),(x^2 − y^2))\) evaluate to?

Let \(x \gt 1\)

What is the value of:

\(\log_x \left(\dfrac{x^4}{x^{10}}\right)\)

If \((a^2 − b^2)^2 = 25\) and \(a^2b^2 = 6\), what is the value of \(a^4 + b^4\)?

A class contains 2 boys for every 1 girl. 75% of the boys have taken Algebra 2, whereas 50% of the girls have taken Algebra 2. What is the ratio of boys who have taken Algebra 2 to girls who have taken it?

At summer camp, Ryan made a circular tablecloth for a circular table that is 3 feet in diameter. The circular tablecloth extended beyond the edge of the table by a fixed amount all the way around. The tablecloth was cut from a single piece of square fabric with sides that were 75 inches long. After the tablecloth was removed, 4104 square inches of the original fabric remained.

How far did the circular tablecloth extend beyond the table’s edge when properly centered?

A company’s profits increased by 12% from 2010 to 2011 and by 18% from 2011 to 2012. By what percent, approximately, did the company’s profits increase from 2010 to 2012?

A certain event has only two possible outcomes. If the probability of one event happening is \(\frac{p}{3}\) and the probability of the other event happening is \(\frac{p}{5}\), then what is the value of \(p\) ?

The figure above consists of rectangle \(ABCD\), rectangle \(CDEF\), and square \(CFGH\). Rectangle \(ABCD\) has an area of \(96 \text{ in}^2.\) In degrees, what is the value of \(x \, (∠FDE)\)? Round to the nearest whole number.

The function \(f(x) = \cos^2(x) * \csc (x)\) can be rewritten as which of the following?