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How to Use a Math Medic Answer Key
Written by Luke Wilcox published 3 years ago
Answer key might be the wrong term here. Sure, the Math Medic answer keys do provide the correct answers to the questions for a lesson, but they have been carefully designed to do much more than this. They are meant to be the official guide to teaching the lesson, providing specific instructions for what to do and say to make a successful learning experience for your students.
Before we look at the details of the answer key, let's make sure we understand the instructional model first.
Experience First, Formalize Later (EFFL)
A typical Math Medic lesson always has the same four parts: Activity, Debrief Activity, QuickNotes, and Check Your Understanding. Here are the cliff notes:
Activity: Students are in groups of 2 - 4 working collaboratively through the questions in the Activity. The teacher is checking in with groups and using questions, prompts, and cues to get students to refine their communication and understanding. As groups finish the activity, the teacher asks students to go to the whiteboard to write up their answers to the questions.
Debrief Activity: In the whole group setting, the teacher leads a discussion about the student responses to the questions in the activity, often asking students to explain their thinking and reasoning about their answers. The teacher then formalizes the learning by highlighting key concepts and introducing new vocabulary, notation, and formulas.
QuickNotes: The teacher uses direct instruction to summarize the learning from the activity in the QuickNotes box - making direct connections to the learning targets for the lesson.
Check Your Understanding: Students are then asked to apply their learning from the lesson to a new context in the Check Your Understanding (CYU) problem. This can be done individually or in small groups. The CYU is very flexible in it's use, as it can be used as an exit ticket, a homework problem, or a quick review the next day.
How Do I See EFFL in the Answer Key?
You will see EFFL in the answer key like this:
![lesson 12 homework 1.1 answer key Activity (blue) and Debrief Activity (red).png](https://res.cloudinary.com/mathmedic-prod/image/authenticated/s--zcpG4i_G--/v1627473801/Activity_blue_and_Debrief_Activity_red_57b99272b2.png)
Anything written in blue is something we expect our students to produce. This might not be quite what we expect by the end of the lesson, but provides us with a starting point when we move to formalization.
Anything written in red is an idea added by the teacher - the formalization of the learning that happened during the Activity. Students are expected to add these "notes" to their Activity using a red pen or marker.
What Do Students Write Down For Notes?
By the end of the lesson, students will have written down everything you see on the Math Medic Answer Keys. The most important transition is when students finish the Activity and we move to Debrief Activity. "Students, now is the time for you to put down your pencils and get out your your red Paper Mate flair pens" We give each student a Paper Mate flair pen at the beginning of the school year and tell them they must cherish and protect it with their life. They all think we should be sponsored by Paper Mate (anyone have any leads on this?)
The lessons you see on Math Medic are all of the notes we use with our students. We do not have some secret collection of guided notes.
Do Students Have Access to Answer Keys?
Yes! Any student can create a free Math Medic account to get access to the answer keys. We often send students to the website when they are absent from a lesson or when we don't quite finish the lesson in class. We are comfortable with students having access to these answer keys because we do not think Math Medic lessons should be used as a summative assessment or be used for a grade (unless it's for completion). Our lessons are meant to be the first steps in the formative process of learning new concepts.
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2.1 The Rectangular Coordinate Systems and Graphs
x -intercept is ( 4 , 0 ) ; ( 4 , 0 ) ; y- intercept is ( 0 , 3 ) . ( 0 , 3 ) .
125 = 5 5 125 = 5 5
( − 5 , 5 2 ) ( − 5 , 5 2 )
2.2 Linear Equations in One Variable
x = −5 x = −5
x = −3 x = −3
x = 10 3 x = 10 3
x = 1 x = 1
x = − 7 17 . x = − 7 17 . Excluded values are x = − 1 2 x = − 1 2 and x = − 1 3 . x = − 1 3 .
x = 1 3 x = 1 3
m = − 2 3 m = − 2 3
y = 4 x −3 y = 4 x −3
x + 3 y = 2 x + 3 y = 2
Horizontal line: y = 2 y = 2
Parallel lines: equations are written in slope-intercept form.
y = 5 x + 3 y = 5 x + 3
2.3 Models and Applications
C = 2.5 x + 3 , 650 C = 2.5 x + 3 , 650
L = 37 L = 37 cm, W = 18 W = 18 cm
2.4 Complex Numbers
−24 = 0 + 2 i 6 −24 = 0 + 2 i 6
( 3 −4 i ) − ( 2 + 5 i ) = 1 −9 i ( 3 −4 i ) − ( 2 + 5 i ) = 1 −9 i
5 2 − i 5 2 − i
18 + i 18 + i
−3 −4 i −3 −4 i
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2.5 Quadratic Equations
( x − 6 ) ( x + 1 ) = 0 ; x = 6 , x = − 1 ( x − 6 ) ( x + 1 ) = 0 ; x = 6 , x = − 1
( x −7 ) ( x + 3 ) = 0 , ( x −7 ) ( x + 3 ) = 0 , x = 7 , x = 7 , x = −3. x = −3.
( x + 5 ) ( x −5 ) = 0 , ( x + 5 ) ( x −5 ) = 0 , x = −5 , x = −5 , x = 5. x = 5.
( 3 x + 2 ) ( 4 x + 1 ) = 0 , ( 3 x + 2 ) ( 4 x + 1 ) = 0 , x = − 2 3 , x = − 2 3 , x = − 1 4 x = − 1 4
x = 0 , x = −10 , x = −1 x = 0 , x = −10 , x = −1
x = 4 ± 5 x = 4 ± 5
x = 3 ± 22 x = 3 ± 22
x = − 2 3 , x = − 2 3 , x = 1 3 x = 1 3
2.6 Other Types of Equations
{ −1 } { −1 }
0 , 0 , 1 2 , 1 2 , − 1 2 − 1 2
1 ; 1 ; extraneous solution − 2 9 − 2 9
−2 ; −2 ; extraneous solution −1 −1
−1 , −1 , 3 2 3 2
−3 , 3 , − i , i −3 , 3 , − i , i
2 , 12 2 , 12
−1 , −1 , 0 0 is not a solution.
2.7 Linear Inequalities and Absolute Value Inequalities
[ −3 , 5 ] [ −3 , 5 ]
( − ∞ , −2 ) ∪ [ 3 , ∞ ) ( − ∞ , −2 ) ∪ [ 3 , ∞ )
x < 1 x < 1
x ≥ −5 x ≥ −5
( 2 , ∞ ) ( 2 , ∞ )
[ − 3 14 , ∞ ) [ − 3 14 , ∞ )
6 < x ≤ 9 or ( 6 , 9 ] 6 < x ≤ 9 or ( 6 , 9 ]
( − 1 8 , 1 2 ) ( − 1 8 , 1 2 )
| x −2 | ≤ 3 | x −2 | ≤ 3
k ≤ 1 k ≤ 1 or k ≥ 7 ; k ≥ 7 ; in interval notation, this would be ( − ∞ , 1 ] ∪ [ 7 , ∞ ) . ( − ∞ , 1 ] ∪ [ 7 , ∞ ) .
2.1 Section Exercises
Answers may vary. Yes. It is possible for a point to be on the x -axis or on the y -axis and therefore is considered to NOT be in one of the quadrants.
The y -intercept is the point where the graph crosses the y -axis.
The x- intercept is ( 2 , 0 ) ( 2 , 0 ) and the y -intercept is ( 0 , 6 ) . ( 0 , 6 ) .
The x- intercept is ( 2 , 0 ) ( 2 , 0 ) and the y -intercept is ( 0 , −3 ) . ( 0 , −3 ) .
The x- intercept is ( 3 , 0 ) ( 3 , 0 ) and the y -intercept is ( 0 , 9 8 ) . ( 0 , 9 8 ) .
y = 4 − 2 x y = 4 − 2 x
y = 5 − 2 x 3 y = 5 − 2 x 3
y = 2 x − 4 5 y = 2 x − 4 5
d = 74 d = 74
d = 36 = 6 d = 36 = 6
d ≈ 62.97 d ≈ 62.97
( 3 , − 3 2 ) ( 3 , − 3 2 )
( 2 , −1 ) ( 2 , −1 )
( 0 , 0 ) ( 0 , 0 )
y = 0 y = 0
not collinear
A: ( −3 , 2 ) , B: ( 1 , 3 ) , C: ( 4 , 0 ) A: ( −3 , 2 ) , B: ( 1 , 3 ) , C: ( 4 , 0 )
1 | |
0 | 2 |
3 | 3 |
6 | 4 |
–3 | 0 |
0 | 1.5 |
3 | 3 |
d = 8.246 d = 8.246
d = 5 d = 5
( −3 , 4 ) ( −3 , 4 )
x = 0 y = −2 x = 0 y = −2
x = 0.75 y = 0 x = 0.75 y = 0
x = − 1.667 y = 0 x = − 1.667 y = 0
15 − 11.2 = 3.8 mi 15 − 11.2 = 3.8 mi shorter
6 .0 42 6 .0 42
Midpoint of each diagonal is the same point ( 2 , –2 ) ( 2 , –2 ) . Note this is a characteristic of rectangles, but not other quadrilaterals.
2.2 Section Exercises
It means they have the same slope.
The exponent of the x x variable is 1. It is called a first-degree equation.
If we insert either value into the equation, they make an expression in the equation undefined (zero in the denominator).
x = 2 x = 2
x = 2 7 x = 2 7
x = 6 x = 6
x = 3 x = 3
x = −14 x = −14
x ≠ −4 ; x ≠ −4 ; x = −3 x = −3
x ≠ 1 ; x ≠ 1 ; when we solve this we get x = 1 , x = 1 , which is excluded, therefore NO solution
x ≠ 0 ; x ≠ 0 ; x = − 5 2 x = − 5 2
y = − 4 5 x + 14 5 y = − 4 5 x + 14 5
y = − 3 4 x + 2 y = − 3 4 x + 2
y = 1 2 x + 5 2 y = 1 2 x + 5 2
y = −3 x − 5 y = −3 x − 5
y = 7 y = 7
y = −4 y = −4
8 x + 5 y = 7 8 x + 5 y = 7
Perpendicular
m = − 9 7 m = − 9 7
m = 3 2 m = 3 2
m 1 = − 1 3 , m 2 = 3 ; Perpendicular . m 1 = − 1 3 , m 2 = 3 ; Perpendicular .
y = 0.245 x − 45.662. y = 0.245 x − 45.662. Answers may vary. y min = −50 , y max = −40 y min = −50 , y max = −40
y = − 2.333 x + 6.667. y = − 2.333 x + 6.667. Answers may vary. y min = −10 , y max = 10 y min = −10 , y max = 10
y = − A B x + C B y = − A B x + C B
The slope for ( −1 , 1 ) to ( 0 , 4 ) is 3. The slope for ( −1 , 1 ) to ( 2 , 0 ) is − 1 3 . The slope for ( 2 , 0 ) to ( 3 , 3 ) is 3. The slope for ( 0 , 4 ) to ( 3 , 3 ) is − 1 3 . The slope for ( −1 , 1 ) to ( 0 , 4 ) is 3. The slope for ( −1 , 1 ) to ( 2 , 0 ) is − 1 3 . The slope for ( 2 , 0 ) to ( 3 , 3 ) is 3. The slope for ( 0 , 4 ) to ( 3 , 3 ) is − 1 3 .
Yes they are perpendicular.
2.3 Section Exercises
Answers may vary. Possible answers: We should define in words what our variable is representing. We should declare the variable. A heading.
2 , 000 − x 2 , 000 − x
v + 10 v + 10
Ann: 23 ; 23 ; Beth: 46 46
20 + 0.05 m 20 + 0.05 m
90 + 40 P 90 + 40 P
50 , 000 − x 50 , 000 − x
She traveled for 2 h at 20 mi/h, or 40 miles.
$5,000 at 8% and $15,000 at 12%
B = 100 + .05 x B = 100 + .05 x
R = 9 R = 9
r = 4 5 r = 4 5 or 0.8
W = P − 2 L 2 = 58 − 2 ( 15 ) 2 = 14 W = P − 2 L 2 = 58 − 2 ( 15 ) 2 = 14
f = p q p + q = 8 ( 13 ) 8 + 13 = 104 21 f = p q p + q = 8 ( 13 ) 8 + 13 = 104 21
m = − 5 4 m = − 5 4
h = 2 A b 1 + b 2 h = 2 A b 1 + b 2
length = 360 ft; width = 160 ft
A = 88 in . 2 A = 88 in . 2
h = V π r 2 h = V π r 2
r = V π h r = V π h
C = 12 π C = 12 π
2.4 Section Exercises
Add the real parts together and the imaginary parts together.
Possible answer: i i times i i equals -1, which is not imaginary.
−8 + 2 i −8 + 2 i
14 + 7 i 14 + 7 i
− 23 29 + 15 29 i − 23 29 + 15 29 i
8 − i 8 − i
−11 + 4 i −11 + 4 i
2 −5 i 2 −5 i
6 + 15 i 6 + 15 i
−16 + 32 i −16 + 32 i
−4 −7 i −4 −7 i
2 − 2 3 i 2 − 2 3 i
4 − 6 i 4 − 6 i
2 5 + 11 5 i 2 5 + 11 5 i
1 + i 3 1 + i 3
( 3 2 + 1 2 i ) 6 = −1 ( 3 2 + 1 2 i ) 6 = −1
5 −5 i 5 −5 i
9 2 − 9 2 i 9 2 − 9 2 i
2.5 Section Exercises
It is a second-degree equation (the highest variable exponent is 2).
We want to take advantage of the zero property of multiplication in the fact that if a ⋅ b = 0 a ⋅ b = 0 then it must follow that each factor separately offers a solution to the product being zero: a = 0 o r b = 0. a = 0 o r b = 0.
One, when no linear term is present (no x term), such as x 2 = 16. x 2 = 16. Two, when the equation is already in the form ( a x + b ) 2 = d . ( a x + b ) 2 = d .
x = 6 , x = 6 , x = 3 x = 3
x = − 5 2 , x = − 5 2 , x = − 1 3 x = − 1 3
x = 5 , x = 5 , x = −5 x = −5
x = − 3 2 , x = − 3 2 , x = 3 2 x = 3 2
x = −2 , 3 x = −2 , 3
x = 0 , x = 0 , x = − 3 7 x = − 3 7
x = −6 , x = −6 , x = 6 x = 6
x = 6 , x = 6 , x = −4 x = −4
x = 1 , x = 1 , x = −2 x = −2
x = −2 , x = −2 , x = 11 x = 11
z = 2 3 , z = 2 3 , z = − 1 2 z = − 1 2
x = 3 ± 17 4 x = 3 ± 17 4
One rational
Two real; rational
x = − 1 ± 17 2 x = − 1 ± 17 2
x = 5 ± 13 6 x = 5 ± 13 6
x = − 1 ± 17 8 x = − 1 ± 17 8
x ≈ 0.131 x ≈ 0.131 and x ≈ 2.535 x ≈ 2.535
x ≈ − 6.7 x ≈ − 6.7 and x ≈ 1.7 x ≈ 1.7
a x 2 + b x + c = 0 x 2 + b a x = − c a x 2 + b a x + b 2 4 a 2 = − c a + b 4 a 2 ( x + b 2 a ) 2 = b 2 − 4 a c 4 a 2 x + b 2 a = ± b 2 − 4 a c 4 a 2 x = − b ± b 2 − 4 a c 2 a a x 2 + b x + c = 0 x 2 + b a x = − c a x 2 + b a x + b 2 4 a 2 = − c a + b 4 a 2 ( x + b 2 a ) 2 = b 2 − 4 a c 4 a 2 x + b 2 a = ± b 2 − 4 a c 4 a 2 x = − b ± b 2 − 4 a c 2 a
x ( x + 10 ) = 119 ; x ( x + 10 ) = 119 ; 7 ft. and 17 ft.
maximum at x = 70 x = 70
The quadratic equation would be ( 100 x −0.5 x 2 ) − ( 60 x + 300 ) = 300. ( 100 x −0.5 x 2 ) − ( 60 x + 300 ) = 300. The two values of x x are 20 and 60.
2.6 Section Exercises
This is not a solution to the radical equation, it is a value obtained from squaring both sides and thus changing the signs of an equation which has caused it not to be a solution in the original equation.
He or she is probably trying to enter negative 9, but taking the square root of −9 −9 is not a real number. The negative sign is in front of this, so your friend should be taking the square root of 9, cubing it, and then putting the negative sign in front, resulting in −27. −27.
A rational exponent is a fraction: the denominator of the fraction is the root or index number and the numerator is the power to which it is raised.
x = 81 x = 81
x = 17 x = 17
x = 8 , x = 27 x = 8 , x = 27
x = −2 , 1 , −1 x = −2 , 1 , −1
y = 0 , 3 2 , − 3 2 y = 0 , 3 2 , − 3 2
m = 1 , −1 m = 1 , −1
x = 2 5 , ±3 i x = 2 5 , ±3 i
x = 32 x = 32
t = 44 3 t = 44 3
x = −2 x = −2
x = 4 , −4 3 x = 4 , −4 3
x = − 5 4 , 7 4 x = − 5 4 , 7 4
x = 3 , −2 x = 3 , −2
x = 1 , −1 , 3 , -3 x = 1 , −1 , 3 , -3
x = 2 , −2 x = 2 , −2
x = 1 , 5 x = 1 , 5
x ≥ 0 x ≥ 0
x = 4 , 6 , −6 , −8 x = 4 , 6 , −6 , −8
2.7 Section Exercises
When we divide both sides by a negative it changes the sign of both sides so the sense of the inequality sign changes.
( − ∞ , ∞ ) ( − ∞ , ∞ )
We start by finding the x -intercept, or where the function = 0. Once we have that point, which is ( 3 , 0 ) , ( 3 , 0 ) , we graph to the right the straight line graph y = x −3 , y = x −3 , and then when we draw it to the left we plot positive y values, taking the absolute value of them.
( − ∞ , 3 4 ] ( − ∞ , 3 4 ]
[ − 13 2 , ∞ ) [ − 13 2 , ∞ )
( − ∞ , 3 ) ( − ∞ , 3 )
( − ∞ , − 37 3 ] ( − ∞ , − 37 3 ]
All real numbers ( − ∞ , ∞ ) ( − ∞ , ∞ )
( − ∞ , − 10 3 ) ∪ ( 4 , ∞ ) ( − ∞ , − 10 3 ) ∪ ( 4 , ∞ )
( − ∞ , −4 ] ∪ [ 8 , + ∞ ) ( − ∞ , −4 ] ∪ [ 8 , + ∞ )
No solution
( −5 , 11 ) ( −5 , 11 )
[ 6 , 12 ] [ 6 , 12 ]
[ −10 , 12 ] [ −10 , 12 ]
x > − 6 and x > − 2 Take the intersection of two sets . x > − 2 , ( − 2 , + ∞ ) x > − 6 and x > − 2 Take the intersection of two sets . x > − 2 , ( − 2 , + ∞ )
x < − 3 or x ≥ 1 Take the union of the two sets . ( − ∞ , − 3 ) ∪ [ 1 , ∞ ) x < − 3 or x ≥ 1 Take the union of the two sets . ( − ∞ , − 3 ) ∪ [ 1 , ∞ )
( − ∞ , −1 ) ∪ ( 3 , ∞ ) ( − ∞ , −1 ) ∪ ( 3 , ∞ )
[ −11 , −3 ] [ −11 , −3 ]
It is never less than zero. No solution.
Where the blue line is above the orange line; point of intersection is x = − 3. x = − 3.
( − ∞ , −3 ) ( − ∞ , −3 )
Where the blue line is above the orange line; always. All real numbers.
( − ∞ , − ∞ ) ( − ∞ , − ∞ )
( −1 , 3 ) ( −1 , 3 )
( − ∞ , 4 ) ( − ∞ , 4 )
{ x | x < 6 } { x | x < 6 }
{ x | −3 ≤ x < 5 } { x | −3 ≤ x < 5 }
( −2 , 1 ] ( −2 , 1 ]
( − ∞ , 4 ] ( − ∞ , 4 ]
Where the blue is below the orange; always. All real numbers. ( − ∞ , + ∞ ) . ( − ∞ , + ∞ ) .
Where the blue is below the orange; ( 1 , 7 ) . ( 1 , 7 ) .
x = 2 , − 4 5 x = 2 , − 4 5
( −7 , 5 ] ( −7 , 5 ]
80 ≤ T ≤ 120 1 , 600 ≤ 20 T ≤ 2 , 400 80 ≤ T ≤ 120 1 , 600 ≤ 20 T ≤ 2 , 400
[ 1 , 600 , 2 , 400 ] [ 1 , 600 , 2 , 400 ]
Review Exercises
x -intercept: ( 3 , 0 ) ; ( 3 , 0 ) ; y -intercept: ( 0 , −4 ) ( 0 , −4 )
y = 5 3 x + 4 y = 5 3 x + 4
72 = 6 2 72 = 6 2
620.097 620.097
midpoint is ( 2 , 23 2 ) ( 2 , 23 2 )
0 | −2 |
3 | 2 |
6 | 6 |
x = 4 x = 4
x = 12 7 x = 12 7
y = 1 6 x + 4 3 y = 1 6 x + 4 3
y = 2 3 x + 6 y = 2 3 x + 6
females 17, males 56
x = − 3 4 ± i 47 4 x = − 3 4 ± i 47 4
horizontal component −2 ; −2 ; vertical component −1 −1
7 + 11 i 7 + 11 i
−16 − 30 i −16 − 30 i
−4 − i 10 −4 − i 10
x = 7 − 3 i x = 7 − 3 i
x = −1 , −5 x = −1 , −5
x = 0 , 9 7 x = 0 , 9 7
x = 10 , −2 x = 10 , −2
x = − 1 ± 5 4 x = − 1 ± 5 4
x = 2 5 , − 1 3 x = 2 5 , − 1 3
x = 5 ± 2 7 x = 5 ± 2 7
x = 0 , 256 x = 0 , 256
x = 0 , ± 2 x = 0 , ± 2
x = 11 2 , −17 2 x = 11 2 , −17 2
[ − 10 3 , 2 ] [ − 10 3 , 2 ]
( − 4 3 , 1 5 ) ( − 4 3 , 1 5 )
Where the blue is below the orange line; point of intersection is x = 3.5. x = 3.5.
( 3.5 , ∞ ) ( 3.5 , ∞ )
Practice Test
y = 3 2 x + 2 y = 3 2 x + 2
0 | 2 |
2 | 5 |
4 | 8 |
( 0 , −3 ) ( 0 , −3 ) ( 4 , 0 ) ( 4 , 0 )
( − ∞ , 9 ] ( − ∞ , 9 ]
x = −15 x = −15
x ≠ −4 , 2 ; x ≠ −4 , 2 ; x = − 5 2 , 1 x = − 5 2 , 1
x = 3 ± 3 2 x = 3 ± 3 2
( −4 , 1 ) ( −4 , 1 )
y = −5 9 x − 2 9 y = −5 9 x − 2 9
y = 5 2 x − 4 y = 5 2 x − 4
5 13 − 14 13 i 5 13 − 14 13 i
x = 2 , − 4 3 x = 2 , − 4 3
x = 1 2 ± 2 2 x = 1 2 ± 2 2
x = 1 2 , 2 , −2 x = 1 2 , 2 , −2
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Lesson 1.12 COMMON CORE STANDARD CC.5.OA.1 Write and interpret numerical expressions. (10 - 7)] 15 3. 6. 36 - 1. 5 x [(11 - (13 - 3) (13 - 4] 20 9)] 9)] 2. 5. 9)] 5 (12 - 7)] [(11 48 Problem Solving 5]} 5 P25 use the information at the right for 9 and 10. 9. Write an expression to represent the total Joan has a cafe. Each day, she bakes
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1.1 Section Exercises. 1. A relation is a set of ordered pairs. A function is a special kind of relation in which no two ordered pairs have the same first coordinate. 3. When a vertical line intersects the graph of a relation more than once, that indicates that for that input there is more than one output.
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Introduction; 4.1 Solve Systems of Linear Equations with Two Variables; 4.2 Solve Applications with Systems of Equations; 4.3 Solve Mixture Applications with Systems of Equations; 4.4 Solve Systems of Equations with Three Variables; 4.5 Solve Systems of Equations Using Matrices; 4.6 Solve Systems of Equations Using Determinants; 4.7 Graphing Systems of Linear Inequalities
-2 -3 4 3 -1 1 4 9 6 4 3 or -3 9 12 25 30 16 12 144 10 21 60 31 -6 36 Rule: Double x and add 1 Rule: Halve x, and add 1 Rule: Square x. Answer Key 13 3-3. a. x (in) y (out) b. x (in) y (out ... Answer Key 17 Lesson 3.1.5 3-42. a. x-values between $10 and $100 are appropriate. b. The x!
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Aug 267:12 AM. ANSWER KEY 1.1 Points, Lines, and Planes.notebook 2 August 28, 2012 Aug 267:13 AM Aug 267:13 AM ... Lesson 1.1: Points, Lines, and Planes Objective Understand and use the basic undefined terms and defined terms in geometry such as point, line, plane, collinear, coplanar.
Introduction to Systems of Equations and Inequalities; 7.1 Systems of Linear Equations: Two Variables; 7.2 Systems of Linear Equations: Three Variables; 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables; 7.4 Partial Fractions; 7.5 Matrices and Matrix Operations; 7.6 Solving Systems with Gaussian Elimination; 7.7 Solving Systems with Inverses; 7.8 Solving Systems with Cramer's Rule
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Answer Key Lesson 1.1 Practice Level C 1. @BA ... #FE ##$ 9. no 10. yes 11. yes 12. yes 13. point G 14. point G 15. @MN###$ 16. point B 17. Sample answer: 18. Sample answer: 19. Sample answer: 20. Sample answer: ...
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