3x 4y 2. 3y 4. Math 65 Weekly Activity 1 (50 points) Name: Simplify the following expressions. Make sure to use the = symbol appropriately.

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1 Math 65 Weekl Activit 1 (50 points) Name: Simplif the following epressions. Make sure to use the = smbol appropriatel. Due (1) (a) - 4 (b) ( - ) 4 () () Evaluate the epressions when = - and = : (4) 4 (5) 5 4 Solve for : (6) - 8 = ( + 7 ) (7) (8) =.5 16 (9) Show how to check our answer for problem (8).

2 (10) Solve the inequalit, and graph the solution on the number line. 4 + < + 1 Find the slopes of the lines between each of the following pairs of points: (reduce fractions, assume that each square stands for one unit.) (11) (1) Recall: slope = rise run (1) Graph = 1 on the graph below. (14) Graph = -4 on the same graph.

3 Math 65 Weekl Activit (50 points) Name: Make sure to use the = smbol appropriatel. No = between equations. Due Neatl solve each equation, lining up the = s down the page... and check our answer in original equation: () (1) 1 ( ) 5 ( 6) () (4) (5) (6)

4 Find each fractions answer, showing our work and appropriate use of the equal sign: (7) (8) For the following: i) fill in the T-table, ii) plot each point, iii) draw the line using a straight edge so that it passes through the entire coordinate sstem given, iv) include arrows on each end of the line, v) identif the -intercept and -intercept using ordered pairs. (9) slope = -intercept:

5 (10) Graph both of the following equations on the included coordinate plane: = + 1 and = 1 slope = slope = -intercept: -intercept: Solve the following sstem of equations using the substitution method or the elimination method: Epress the solution as an ordered pair. = + 1 { = 1 How does the solution to the sstem appear on a graph?

6 (11) Consider the following problem: a) What quantit are ou tring to find? Describe in words and label it : b) Set up an equation that represents the situation given. Solve our equation. What did ou get for? c) Use a sentence to answer the original question:

7 Math 65 Weekl Activit (50 points) Name: Make sure to use the = smbol appropriatel. No = between equations. Due Graphing from the equation: fill in the t-table, plot the points, and then graph the line or curve. Graph the points eactl, and use a ruler to draw all straight lines so that the pass through the entire coordinate sstem given, with arrows. Identif the -intercept and -intercept using ordered pairs. (1) Recall: slope = rise run slope = -intercept: () slope = -intercept:

8 Graph the following on the same coordinate sstem: () 5 (4) slope = -intercept: slope = -intercept: Recall: slope = rise run (5) Graph each of the following equations: (Hint: Solve each of the equations for so ou can graph each equation using the slope-intercept form) 4 = 9 { + = Use the graphs to determine the solution of the sstem as an ordered pair. (Hint: where do the graphs intersect each other?) 4 = 9 { + = Solution:

9 For the following: fill in the table, plot each point and carefull draw the smooth curve that passes through each point so that it passes through the entire coordinate sstem given, with arrows on the ends. Note the shape! It is called a parabola. Parabolas don t have a slope like a line does. Where is the lowest point for (6)? That point is called the verte. (6) (7) verte: -intercept(s): How is the graph in (7) different from (6)? Where do ou think the verte is now? verte: -intercept(s):

10 (8) Simplif: (You might eventuall need 108 as a common denominator) (9) Solve: (10) Simplif (the final epression must not contain an negative eponents): (a) ( - 4 ) (b) (- )(-5-5 ) Write the equation of each line in Slope-Intercept form (11) passing through the point (-,6) (1) a line passing through the with slope m = ½ points (-, 6) and (, 1)

11 Math 65 Weekl Activit 4 (50 points) Name: Make sure to use the = smbol appropriatel. No = between equations. Due Graphing from the equation: build our own T-table, if necessar, then graph the line or curve. Remember to show graph over the entire coordinate sstem and arrows on the end. (1) 1 slope = -intercept: () Graph and 5 on the same graph. Label each with its correct slope. State the intersection of the two lines as an ordered pair:

12 Use the given form of the equations to find the associated value for each of the given s. () ( )( ) (4) 4 verte: -intercept(s): What do the graphs have in common? Wh? verte: -intercept(s):

13 (5) ( 4)( ) verte: -intercept(s): (6) What do the graphs have in common? Wh? verte: -intercept(s):

14 Where appropriate, simplif the epression OR solve the equation: (7) (8) Solve the following sstems, show work: (9) - = 7 + = 5 (10) 4 + = + = Simplif (the final epression must not contain an negative eponents): (11) (a b 4 )(4 - a 5 b - ) (1) (5 (5 )( 4 )(6 4 ) )

15 Math 65 Weekl Activit 5 (50 points) Name: Make sure to use the = smbol appropriatel. No = between equations. Due Graphing from the equation: build our own T-table, if necessar, then graph the line or curve. Remember to show graph over the entire coordinate sstem and arrows on the end. You will have to estimate the -intercepts for the following two graphs. (1) 5 verte: -intercept(s): () 7 verte: -intercept(s):

16 () slope = -intercept: (4) ( 6)( ) verte: -intercept(s): (5) Graph the line = + 5 on the same graph: At what points (as ordered pairs) does the line intersect the parabola?

17 Where appropriate, simplif the epression OR solve the equation, showing work and proper use of the equal sign, neatl please. (6) (7) (8) ( ) ( - ) (9) 4 ( 4 ) (10) ( 7 6) ( 5)

18 Solve the following sstems of equations using the substitution or elimination (addition) method: (11) { 1 1 = = 4 (1) { 0 8 = = 0

19 Math 65 Weekl Activit 6 (50 points) Name: Make sure to use the = smbol appropriatel. No = between equations. Due Graphing from the equation: build our own T-table, if necessar, then graph the line or curve. Remember to show graph over the entire coordinate sstem and arrows on the end. You ma have to estimate the -intercepts for some of the following graphs. Factor the right hand side of the following two equations, if possible. (1) 4 1 verte: -intercept(s): Is the graph in (1) a parabola or a line? Wh? How can ou tell from the equation? () verte: -intercept(s): Is the graph in () a parabola or a line? Wh? How can ou tell from the equation?

20 () 1 slope = -intercept: Is the graph in () a parabola or a line? Wh? How can ou tell from the equation? (4) ( )( 4) verte: -intercept(s): Is the graph in (4) a parabola or a line? Wh? How can ou tell from the equation? (5) Graph 4. Label it with its correct slope. (6) Graph 6. Label it with its correct slope.

21 Where appropriate, simplif the epression OR solve the equation: (7) (8)

22 (9) First, make sure each number in the fraction is written in scientific notation (show work b writing this step). Then, perform the indicated operations (without a calculator), and write our answer in scientific notation: (10) Given p( ) 14 Find p ( ) Find p( a 1)

23 Math 65 Weekl Activit 7 (50 points) Name: Make sure to use the = smbol appropriatel. No = between equations. Due Graphing from the equation: build our own T-table, where necessar, then graph the line or curve. Remember to show graph over the entire coordinate sstem and arrows on the end. (1) a) 6 5 verte: -intercept(s): b) Now, solve the equation b factoring: c) How do the solutions to our equation in b) appear on the graph above?

24 () a) 8 Fill in the bo that applies for this graph: verte: -intercept(s): slope = -intercept: b) Now, solve the equation: 8 0 c) How do the solutions to our equation in b) appear on the graph above?

25 () a) b) Now, solve the equation b factoring: 0 c) How do the solutions to our equation in b) appear on the graph above?

26 (4) Rewrite each fraction in its simplest form; use the equal sign appropriatel. If necessar, identif an restrictions for each epression Hint: for the following, factor the numerator and the denominator, use parenthesis correctl: (5) Solve the equation:

27 Math 65 Weekl Activit 8 (50 points) Name: Make sure to use the = smbol appropriatel. No = between equations. Due Graphing from the equation: build our own T-table, if necessar, then graph the line or curve. Remember to show graph over the entire coordinate sstem and arrows on the end. (1) a) 8 verte: -intercept(s): b) Now, solve the equation b factoring: 8 0 c) How do the solutions to our equation in b) appear on the graph above?

28 () a) 9 b) How is this graph different from the previous in (1)? -intercept(s): c) Now, solve the equation b factoring: 9 0 d) How do the solutions to our equation in c) appear on the graph above?

29 Solve each of the following equations b factoring: (1) () () (4) 8 0

30 (5) One positive integer is 6 more than another. Their product is 91. Find the integers. a) Identif our variable: b) Set up and solve an equation that ou can derive from the problem: c) Use a sentence to answer the original question: (6) The height of a triangle is centimeters less than the base. The area of the triangle is 9 square centimeters. Find the length of the base and the height of the triangle. a) Identif our variable, in this case draw and label a picture that represents the situation: b) Set up and solve an equation that ou can derive from the problem: c) Use a sentence to answer the original question:

31 Math 65 Weekl Activit 9 (50 points) Name: Make sure to use the = smbol appropriatel. No = between equations. Due Graphing from the equation: build our own T-table, if necessar, then graph the line or curve. Remember to show graph over the entire coordinate sstem and arrows on the end. Practice graphing lines from the equation: graph the line, using the -intercept and then slope. (1) Graph 5 () Choose one of the points on our graph and check it in the equation. Specif what point ou're checking. It should not be the - intercept. It should be on the line and satisf the equation. slope = -intercept: () Graph 1 4 (4) Choose one of the points on our graph and check it in the equation. Specif what point ou're checking. It should not be the - intercept. It should be on the line and satisf the equation slope = -intercept:

32 (5) Graph (6) Choose one of the points on our graph and check it in the equation. Specif what point ou're checking. It should not be the - intercept. It should be on the line and satisf the equation slope = -intercept: (7) Graph (8) Choose one of the points on our graph and check it in the equation. Specif what point ou're checking. It should not be the - intercept. It should be on the line and satisf the equation slope = -intercept:

33 Graphing from the equation: build our own T-table, if necessar, then graph the line or curve. Remember to show graph over the entire coordinate sstem and arrows on the end. (9) a) 6 11 verte: -intercept(s): b) Now, solve the equation b using the quadratic formula: c) How do the solutions to our equation in b) appear on the graph above? Eplain.

34 (10) Simplif (the final epression must not contain an negative eponents): a) b) 6a b -9a b (11) Given p( ) 6 11 Find p ( ) Find p( a ) (1) Where appropriate, simplif the epression OR solve the equation: a) b) 1

35 Math 65 BONUS (!) Weekl Activit Ch. 7 (50 points) Name: Make sure to use the = smbol appropriatel. Due Simplif the following rational epressions. To get full credit our work must be IN PENCIL, neat, and correct notation. Also, make sure to show all necessar work. To that end, I d recommend ou work some of these out on scratch paper first and cop our work neatl to this paper. 1) ) ) 4) 5) 6)

36 7) 8) 9) 10)

37 11) 1) 1) 14)

38 15) 16) 17) 18)

MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED

FOM 11 T9 GRAPHING LINEAR EQUATIONS REVIEW - 1 MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED 1) -INTERCEPT = the point where the graph touches or crosses the -ais. It occurs when = 0. ) -INTERCEPT = the