How does the saying “You get what you give” relate to Newton’s third law?

Explain how you can find the opposite of the opposite of any number without using a number line.

Rewrite this sentence eliminating the redundancy: Although many people hold the belief and opinion that watching TV is a solitary activity, some researchers have evidence that families use the time in front of the TV as a way of spending time together.

The force of gravity is twice as great on a 2-kg rock as on a 1-kg rock. Why does the 2-kg rock not fall with twice the acceleration?

The bus fare in a city is $1.25. People who use the bus have the option of purchasing a monthly discount pass for$21.00. With the discount pass, the fare is reduced to $0.50. Express the total monthly cost to use the bus with a discount pass, as a function of the number of times in a month the bus is used, x.

What is atmospheric pressure, and how is it measured?

Find the values of x and y for which the sequence 2, x, y, 17,... is arithmetic

An occupant of a car has a chance of surviving a crash if the deceleration during the crash is not more than 30 g. Calculate the force on a 70-kg person decelerating at this rate.

Graph each system of linear inequalities by hand. Verify your results using a graphing utility.

$$\left\{\begin{array}{l}{x-4 y \leq 4} \\ {x-4 y \geq 0}\end{array}\right.$$

A salesperson starts with a full tank of gas, drives her car 363 miles and then refuels. It takes 11 gallons of gas to fill the car’s tank. How many miles per gallon did the car get?

A television with an original pr ice of $850 is on sale at 35% off. a. What is the discount amount? b. What is the television's sale price?

Using the usual generators and relations for the dihedral group

$$D_{2n}$$

show that for $n=2k$ an even integer the conjugacy classes in $D_{2n}$ are the following: $\{1\}, \{r^k\}, \{r^{\pm 1}\}, \ldots \{r^{\pm(k-1)}\}, \{sr^{2b}\ |\ b=1,\ldots,k\}$ and $\{sr^{2b-1}\ |\ b=1,\ldots,k\}$. Give the class equation for $D_{2n}$.

When transforming the right side of a polynomial equation to determine if it is an identity, which would be the first step? $(a+b)^{3}=a^{3}+3 a^{2} b-3 a b^{2}+b^{3}$ A. Subtract $b^{3}$. B. Divide both sides of the equation by (a + b). C. Expand $(a+b)^{3}$ D. Factor $a^{3}+3 a^{2} b$.

Laurie mows lawns to earn extra money. She can mow at most 30 lawns in one week. She profits $15 on each lawn she mows. Identify the reasonable domain and range for this situation and draw a graph.