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1 Chapter 2: EquationsAlgebra I

2 2.2- Solving Equations by Multiplying and Dividing2.3- Solving Two-Step and Multi-Step Equations2.4- Solving Equations with Variables on Both Sides2.5- Solving for a Variable2.6- Solving Absolute-Value Equations2.7- Rates, Ratios, and Proportions2.9- Percents2.10- Applications of Percents

3 **2.1 – Solving Equations by Adding or Subtracting**Algebra I

4 2-1Algebra 1 An equation is a mathematical statement that two expressions are equal.A solution of an equation is a value of the variable that makes the equation true.To find solutions, isolate the variable. A variable is isolated when it appears by itself on one side of an equation, and not at all on the other side.

5 **Solve the equation. Check your answer.**2-1Example 1Solving Equations by Using AdditionSolve the equation. Check your answer.= z 7165y 8 = 24+716y = 32= z34Checky 8 = 24Check= z 716532 345167516

6 **Solve + p = . 2 11 5 6 = k 6 + 6 + 6 + 5 11 0 = k p = 3 11**2-1Solve + p = 21156 = k 6+5110 = kp =311Check6 = k 6 6Check+ p = 2115 625113+211

7 **Solve the equation. Check your answer.**2-1Example 2Solving Equations using SubtractionSolve the equation. Check your answer.m + 17 = 33d = 112 17 17m = 1612d =12Checkm + 17 = 33

8 Math JokeParent: Why do you have that sheet of paper in a bowl of water?Student: Its my homework, Im trying to dissolve an equation

13 2.1HW pg. 802.121-35 , 46, 47, , 66, 80, 83, 86

24 2-3Solve2 2n = 0

57 2.5Solve for VVD = m

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**Vocabulary and Core Concept Check**

Question 1.**COMPLETE THE SENTENCE** A parabola is the set of all points in a plane equidistant from a fixed point called the ______ and a fixed line called the __________ .Answer:

Question 2.**WRITING **Explain how to find the coordinates of the focus of a parabola with vertex and directrix y = 5.Answer:

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**In Exercises 310, use the Distance Formula to write an equation of the parabola.**

Question 3.

Answer:

Question 47.**MODELING WITH MATHEMATICS** Scientists studying dolphin echolocation simulate the projection of a bottlenose dolphins clicking sounds using computer models. The models originate the sounds at the focus of a parabolic reflector. The parabola in the graph shows the cross section of the reflector with focal length of 1.3 inches and aperture width of 8 inches. Write an equation to represent the cross section of the reflector. What is the depth of the reflector?Answer:

Question 48.**MODELING WITH MATHEMATICS** Solar energy can be concentrated using long troughs that have a parabolic cross section as shown in the figure. Write an equation to represent the cross section of the trough. What are the domain and range in this situation? What do they represent?Answer:

Question 49.**ABSTRACT REASONING** As | p | increases, how does the width of the graph of the equation y = \x2 change? Explain your reasoning.Answer:

**Write an equation of the line that passes through the points.**

Question 55.

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