monday, april 23 rd
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4251 30011 0010 1010 1101 0001 0100 1011
Monday, April 23rd
Please complete Warm up
1. What is k?Y=3/4x
2. What point does a direct Variation equation have to go through?
Warm UP
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0011 0010 1010 1101 0001 0100 1011Last March Madness
Denman Test 10: Measurement & Geometry
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0011 0010 1010 1101 0001 0100 1011FORMULA SHEET
a=Bh Rectangular Prism: l x w
Cylinder Prism: π 𝒓 ²
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0011 0010 1010 1101 0001 0100 1011Direct Variation
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y=kx
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0011 0010 1010 1101 0001 0100 1011What is k?
Give the value shown for k1.Y = 4x 2.Y=1/2x 3.Y=.75x 4.Y=x
41/2
.751
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Recap• A Linear equation makes a LINE
when graphed• Y= kx is a special kind of LINEAR
equation• Y=kx must go through (0,0)• In an equation we always put in a
number for k (y=2x) • K is our slope (how steep the line
is)
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Part I: Determining if a function is a Direct Variation
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Which one is a direct variation?
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Which one is a direct variation?
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0011 0010 1010 1101 0001 0100 1011Direct variation equation
• Equation can not have anything added or subtracted to it.
• Remember that y=x/4 is the same as y = 1/4 x
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Which Equation(s) are examples of direct
variation?1. Y= 3x+22. Y=3. Y= 0.85x4. Y= 5. Y= 443x
2 3
And 5
*Nothing can be added or subtracted!
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Part II: Finding K in a Table
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0011 0010 1010 1101 0001 0100 1011Finding K
K = y ÷ x
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0011 0010 1010 1101 0001 0100 1011Example #1
X 2 4 6Y 8 16 24
Answer: k=4
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0011 0010 1010 1101 0001 0100 1011Example #2
Answer: k=1/4
x y 8 212 320 528
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0011 0010 1010 1101 0001 0100 1011Example #3
Answer: k=5/2 or 2 ½
X 4 12 16Y 10 30 40
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0011 0010 1010 1101 0001 0100 1011EXCITING NEWS!!!
Now that we know how to find k in a table, we can look at a table to see if
it’s truly a direct variation!!! Steps: • For each ordered pair, divide y by x
and make sure it’s the same number!
• If it’s not then it isn’t a direct variation
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Which table shows a Direct Variation?
X 4 12 16Y 3 9 12
X 5 10 15Y 1 3 4
X 1 2 3Y 2 4 8
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Graphing
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Where is the origin?!?!
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0011 0010 1010 1101 0001 0100 1011Do You Remember?
• Which axis is the horizontal axis? _____________
• Which axis is the vertical axis? _____________
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0011 0010 1010 1101 0001 0100 1011K= Slope
When you think of the word SLOPE…what do you think of?!
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Slopes are commonly associated with mountains
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The slope we are studying is associated with the graph of a line
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Different Slopes Po
sitive
Negativezero
Undefined
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POSITIVE SLOPE“Reaching the Goal”
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Negative Slope“The Tumbler”
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Zero Slope“Not Much Happening”
Horizontal Line
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We will only be working with POSTIVE SLOPES
that go through the point (0,0)
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0011 0010 1010 1101 0001 0100 1011K= Rise ÷ Run
Rise= y axis
Run= x axis
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0011 0010 1010 1101 0001 0100 1011What goes first?
You need to rise up
before you run
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I. Finding Slope“The Meat of it”
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Find k (slope)
Slope:
Rise: 3
Run: 2
k: 3/2Y=3/2x
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Find k (slope)
Slope:
Rise: 3
Run: 1
k: 3/1= 3Y=3x
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Find k (slope)
Slope:
Rise: 2
Run: 3
k: 2/3= 2/3Y=2/3x
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Find k (slope)
Slope:
Rise: 1
Run: 5
k: 1/5= 1/5Y=1/5x
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The steeper the line is the larger K will be!
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SO. . . If you graphed each set of equations below, all of the graphs would be straight lines. For each group of equations, the steepest line would be represented by which equation?
A. y = 3x B. y = 9x C y = x D. y = 4x
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The cost of a plane ticket varies directly with the amount of people. The cost for 5 people costs $500. What is the constant of variation? Write an equation that represents
this situationK=500/5
=100Y=100X
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Leigh Parker earns $30 for every 3 chores she does. If x represents the number of chores she does, write an
equation that will tell how many dollars (y) she will earn.
K=30/3=10
Y=10X
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0011 0010 1010 1101 0001 0100 1011The equation: y = 7x can be used to determine how much money you make when babysitting. Where y (the total amount you make) varies directly with x (the number of hours you babysat).
If you babysat 10 hours, how much money would you make?
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0011 0010 1010 1101 0001 0100 1011Answer
Since x = hours substitute 10 in for x in your equation.
Y = 7(10) Y=70
You would make $70
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Murphy earns $40 for every 2 dogs she walks. Write an equation that will tell how many dollars she will
earn.
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0011 0010 1010 1101 0001 0100 1011Answer
1. Make y equal money earned since it is dependent
2. Make x equal to the number of dogs she walked since it’s
independent3. Find the CONSTANT: y/x 40/2 = 20
k=204. Write an equation: y=20x
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Produce a table and graph for
y=4x
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0011 0010 1010 1101 0001 0100 1011Answer: Table
x y0 01 42 83 12
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The cost of a ticket for the hunger games varies directly with how many tickets you buy. The cost for 6 people is $54. What is the constant?
x y0 01 ?2 183 274 365 456 54
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0011 0010 1010 1101 0001 0100 1011Y=1/4x
x y What x values would you want to
use?!?!?!You would want to use multiples of 4, since 4 is the
denominator! That way you have whole numbers for your y values
4 18 2
12 316 4
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Whiteboard Review
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The graph shows the dollar amount of sales made at Art’s Autos from 1993 to 2003. Between which 2 years did sales increase the most?
A. 1993 - 1995
B. 1995 - 1997
C. 1997 - 1999
D. 2001 - 2003
Art's Auto Sales
0
2
4
6
8
10
12
1 2 3 4 5 6
Year
Sale
s
(in m
illio
ns o
f dol
lars
)
1993 1995 1997 1999 2001 2003
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What is the next term in the following pattern?
13.7, 12.8, 11.9, 11.0,
A. 10.1
B. 10.9
C. 11.1
D. 12.9
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Which of the following statements is TRUE about the equation ?3y xA. As the value of x increases by one, the value of y increases by two.
B. As the value of x increases by one, the value of y doubles.
C. As the value of x increases by one, the value of y increases by three.
D. As the value of x increases by one, the value of y triples.
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Using the table, which is the order of insects from shortest to longest?
A. ant, bumblebee, cockroach, midgeB. bumblebee, ant, cockroach, midgeC. midge, cockroach, ant, bumblebeeD. midge, ant, cockroach, bumblebee
Insect Length (in.)
ant
bumblebee
cockroach 0.625
midge
51678
14
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James has a toy box shaped like a cube. Theheight of the toy box is 3 m. What is the volumeof the toy box?
a. 9 m2
b. 9 m3
c. 27 m2
d. 27 m3
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0011 0010 1010 1101 0001 0100 1011Which of the nets below could be used to form a pyramid like the one below?
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0011 0010 1010 1101 0001 0100 1011There are 60 students in the band. According to the graph, how many students play clarinet?
A. 32 students C. 25 students
B. 27 students D. 15 students
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Macy’s is having a sale on the end-of-season clothing. Marika found a skirt that is on sale for 30% off its original price. The original price of a skirt is $75.50. What is the sale price of the skirt?
A. $22.65
B. $38.50
C. $45.50
D. $52.85
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Ernie’s cell phone company charges a monthly fee of $15 and $0.20 per minute used. Ernie talked for 60 minutes this month. How much will his phone bill be, not including taxes?
A. $27
B. $45
C. $85
D. $135
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In a scale drawing of a house,1 inch: 15 ft. If one side of the house is 37.5 feet, what is the length of that side in the drawing?
A. 2.5 in.
B. 0.4 ft.
C. 2.5 ft.
D. 562.5 in.
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Which list is ordered from LEAST to GREATEST?
A. , , 3.025, 32.5%
B. 32.5%, , , 3.025
C. 3.025, 32.5%, ,
D. 32.5%, 3.025, ,
165
134
165
134
134
165
165
134
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The line plot below shows the ages of teachers in your school. Which of the following statements are true according to the data?
A. The oldest teacher is 28 years older than the youngest teacher.
B. Most of the teachers are older than 45.
C. The most common age is 48.
D. All three of the above statements are true.
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Justin is organizing his trophy case. He has 30 baseball trophies and 45 soccer trophies. He wants to arrange the trophies so that each row has the same number of trophies from only one sport. What is the greatest number of trophies that can be in each row?
A. 3 C. 15
B. 5 D. 30
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For her birthday, Jenna received 5 stuffed animals, 3 DVDs, 2 books, 1 game, 8 CDs, 1 shirt, and two pairs of jeans. What is the ratio of DVDs to her total number of gifts?
A. 1:3
B. 3:8
C. 3:19
D. 3:22
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The table shows Maria’s results on a 50-question social studies test. Of the questions she answered correctly, what percent were true-false questions?
Multiple Choice
QuestionsTrue/False Questions
Essay Questions
# of Questions Answered Correctly 27 15 3# of Questions Answered Incorrectly 3 1 1
A. 30% C. 40%
B. 33⅓ % D. 67⅔%
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You are sending a blanket to your friend’s brother in Iraq. To determine the cost for mailing the package, the post office needs to know the dimensions of the package. Which units would be most appropriate for measuring the dimensions of the package?
A. inches
B. cubic inches
C. feet
D. square feet
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A soft drink can holds 350 ml of cola. If the machine at the canning company contains 700 L of cola, how many cans can be filled before the machine is empty?
A. 2
B. 20
C. 200
D. 2000
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What is the measurement of the unmarked side on these similar figures?
x16
54
20
36
36
2424
A. 18 C. 42B. 30 D. 48
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Which expression represents 15 less than a number x?
A. 15 – x
B. x – 15
C. 15 ÷ x
D. x ÷ 15
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A spider crawled 25 centimeters in six seconds. How long will it take the spider to crawl 15 meters if it continues to crawl at the same rate?
A. 36 seconds
B. 1 min. and 30 seconds
C. 3 min. and 15 seconds
D. 6 minutes
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Bianca works at a flower shop. In a recent delivery of roses, Bianca had to throw out 7 roses that had wilted. She divided the remaining roses into bunches of 12. Which expression represents this situation?
A. 12(w – 7)
B. 12w + 7
C. (w – 7) ÷ 12
D. 12(w ÷ 7)
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It takes your teacher 10 minutes to grade 3 of your class papers. Which pair of ratios could be used to determine how long it will take her to grade all 117 of her students’ papers?
A. C.
B. D.
3 11710 p
11710 3
p
3117 10
p
117 103p
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