4th Quarter

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Problems 1-6

Sequences might not be geometric or arithmetic. However they still have a sequence. Remember negative then positive, then negative is never an arithmetic sequence.

Problems 7-15. There will be a lot of problems on the benchmark from this section.

7 more than a number is 12 --- X + 7 = 12

5 more than 3 times a number--3X + 5“there is no (is) so there is no = sign

12 less than 9 times a number is 69X -12 = 6Notice where the less than number goes

You are 20 years less than the age of your momx– 20 = 13

The quotient of a number and -2 X /-2 quotient means division

9 is at least 5 more than a number 9 5+xAt least means it is equal or more than. You have atleast $20. You could have $21 or $50, or 7 mill dollars and this statement is true. You couldn’t have $19.50.

7 more than a number is less than 12 7 + X < 12

2 is at least 7 more than twice a number 2 7+2xAt least means it is equal or more than.

Problems 16-21

5g +9 = 29 Opposite operation solves all equations. Opposite order is also used to solve this problem

-9 = -9 First subtract 9 from both sides.

5g = 20

/5 = /5 divide by 5

g = 4 Now check your answer. 4 times 5 = 20. 20+ 9 = 29. The problem checks out.

Number 19. First add 19 to both sides. The new problem should read -9n = -18. Divide both sides by -9. Remember a negative divided by a negative is a positive. So -18 divided by positive -9 = 2. Now check your work. --9X2 = -18. Negative 18 – 19 = -37.

Problems 22-26 Remember to set problems up in an equation. Then use opposite operation.

#22.10.50 + x(0.75) = 13.50 You know she only ordered one pizza, and a load of breadsticks. You don’t know how many breadsticks were ordered. Knowing 10.50 for the pizza and 75 cents and the total cost is all you need to know. First subtract the 10.50 from both sides. X(0.75) = 3.00. Then divide by 0.75. The answer is 4.

#25 You and two friends = 3 people. Each ticket cost 7.50. so 7.50 X 3 = 22.50. This is the total cost of the tickets. The rest of the cost is popcorn. If all people paid $9.05, then how much total did they pay. $9.05 X 3 equals $27.15. Now subtract the ticket costs from the total, and that will give you cost of the popcorn is $5.65

Problems 27-32 Opposite operation solves all equations and inequalities.

#27 r + 10 . 3 subtract 10 from both sides. Now the problem reads r > -7. Now to graph. means greater than or equal to. The way that we graph this is with a solid circle and a line. When the > doesn’t have a line underneath it, it means not equal, so it is an open circle at the point with a line going in the more than or less than direction.

Problems 33-38. Plug in the number. F(5) if f(p) = -6p +3 Becomes y=-6(5)+ 3 -6 times 5 is -30. -30 +3 is -27. Your answer is -27. Hint. When multiplying numbers with different signs. -6(5) the answer is negative. When adding numbers with opposite signs, subtract them and take the sign of the larger.

Problems 39-41 Find the Y intercept. This is the y value when you have 0 for xThen find the slope by using the slope formula. Y2-Y1 over X2-X1 . Then put this number in front of X to make the correct for Y=mx+b

#39. The Y-intercept is 4 Find the slope by 6-5 over 2-1. So the slope is 1 over 1 or 1. Y=1x + 4, or Y=x+4.

#41 The Y-intercept is 7. Find the slope by 3-5 over 2-1. It should be -2 over 1. Y=-2x+7.

Problems 42-44. Positive relationship is by the X numbers going up as the Y is also going up. For negative relationships as the X goes up, the Y goes down. Think of a ski slope on Negative relationships. If the scatter plot is scattered all over without a pattern of up or down, then it has no relationship.

Problems 45-50. The dependent variable, is the variable that depends on the other.

#45 D is dependent because it depends on the value of C. #47 N is dependent on the value of the value of M.

Problems 51-56. Quadratics are kind of tricky. Linear graphs for a line, quadratics form a U, or an upside down U. Anytime you see a number like 3x2=y, the graph will look like a U or a smiley face. This is called a Parabala. If the problem is -3X2=Y, then it is still a Parabala, but now it looks like a frowny face. First find out if there is a Y-intercept. You do this by using 0 for the value of x. In 3x2 =Y, if you plugged 0 for X, then the value of Y is 0. In the problem 3x2+5 = Y. If you plugged in 0 for x, then the value of Y is 5. Then make a T-chart, and pick values for x. Pick values and their opposites. Example: 1 and -1. 2 and -2.3 and -3. Then graph the x ‘s and y’s.

Problems 57-62 Inequalities in story problem form. Pick out the words you know.

More than 9=x9

Less than 12=x12

At least10=x10 Means greater than or equal to.

Under 15=x15

Maximum load of 2000=x2000If it was 2000 it would be okay. If it was less it would be okay.

Problems 63-65 are scatter plots. Pick your X axis, and your Y axis. ON #63 your X axis is the number of laps, and your Y axis is the heart rate. You then plot all of the results, and look for a pattern. It would make sense that as the number of laps increase so would the heart rate.