In the \(xy\)-coordinate plane, a circle with center \((−4, 0)\) is tangent to the line \(y = −x\). What is the circumference of the circle?

The quadratic equation \(x^2-bx+20=c\), where \(b\) and \(c\) are constants, has only one solution \(x=6\).

What is the value of \(bc\)?

A delivery cart went from Candleford to Lark Rise and back at an average speed of \(\frac{2}{3}\) miles per hour. If the distance from Candleford to Lark Rise is 1 mile, and the trip back took half as much time as the trip there, what was the average speed of the delivery cart on the way to Lark Rise?

Farmer Hank is buying cows and goats. Cows cost $150 per month to feed. Goats cost $50 per month to feed. The land required for the animals is 1 acre for each cow and 1 acre for every 4 goats. The most he can spend on feeding these animals is $2500 per month. The maximum amount of land he can provide to the cows and goats is 14 acres. Hank wants the ratio of goats to cows to exceed 2 to 1.

Which set of inequalities best represents the set of conditions described if c is the number of cows and g is the number of goats?

The midpoints of the sides of a square are connected to form a new inscribed square. How many times greater than the area of the inscribed square is the area of the original square?

Shauna is throwing a bachelorette party for her best friend with \(x\) guests total. All of the guests plan to split the cost of renting a limo for \(y\) dollars. The day before, \(z\) guests cancel. Which of the following represents the percent increase in the amount each guest must pay towards the limo rental?

In the figure, the radius of circle B is three-fourths the radius of circle A. The distance from center A to the circumference of circle B is 3, and the distance from center B to the circumference of circle A is 2. What is the area of the smaller circle?

Note: Figure not drawn to scale.

The function \(f(t) = A(0.5)^t\) represents the amount of a radioactive substance remaining, \(t\) hours after initial measurement, where A was the initial amount of the substance. If there were 40 grams of the substance remaining 4 hours after the initial measurement, how many grams would remain 7 hours after the initial measurement?

The average of several exam scores is 80. One make-up exam was given. Included with the other scores, the new average was 84. If the score on the make-up exam was 92, how many total exams were given?

Consider two parallel lines \(F\) and \(G\) shown below. Line \(F\) forms an angle of \(60°\) with the \(x\)-axis. Line \(G\) has a \(y\)-intercept of \(−3\). What is the shortest distance between the two parallel lines?