* A quantity is a an exact amount or measurement. * A quantity can be exact or approximate depending on the level of accuracy required. * Examples: 1 -Convert 5 miles to feet. 2 -Convert 60 miles per hour to feet per minute.
* 1 mile = 5280 feet * 5 miles = 5 *5280 feet (does this need to be exact?)
There are situations when the units in an answer tell us if the answer is wrong. For example, if the question called for weight and the answer is given in cubic feet, we know the answer cannot be correct.
* The formula for density d is d = m/v where m is mass and v is volume. If mass is measured in kilograms and volume is measured in cubic meters, what is the unit rate for density?
* Arithmetic expressions are comprised of numbers and operation signs. * Algebraic expressions contain one or more variables. * The parts of expressions that are separated by addition or subtraction signs are called terms. * The numerical * factor is called the coefficient.
* It has three terms: 4x 2, 7xy, and 3. * For 4x 2, the coefficient is 4 and the variable factor is x. * For 7xy, the coefficient is 7 and the variable factors are x and y. * The third term, 3, has no variables and is called a constant.
* How should we approach the solution to this equation?
* Understanding solving equations * Solve equations and inequalities in one variable * Solve systems of equations * Represent and solve equations and inequalities graphically.
* Know the properties of operations * Be familiar with the properties of equality and inequality. (Watch out for the negative multiplier.) * Eliminate denominators (multiply by denominators to eliminate them)
* Solve the equation 6(x + 4) = 2(y + 5) for y.
* Karla wants to save up for a prom dress. She figures she can save $9 each week from the money she earns babysitting. If she plans to spend up to $150 for the dress, how many weeks will it take her to save enough money?
* This equation can be used to find h, the number of hours it takes Flo and Bryan to mow their lawn. * How many hours will it take them?
A manager is comparing the cost of buying ball caps with the company emblem from two different companies. * Company X charges a $50 fee plus $7 per cap. * Company Y charges a $30 fee plus $9 per cap. For what number of ball caps will the manager’s cost be the same for both companies? * A. 10 caps * B. 20 caps * C. 40 caps * D. 100 caps
Which graph would represent a system of linear equations that has multiple common coordinate pairs? * A B * C D
Which equation corresponds to the graph shown? * A. y = x + 1 * B. y = 2x + 1 * C. y = x – 2 * D. y = 3x