Equations - Amazon S3€¦ · Equations ( Day 4 ) Date: Think about the process of solving equations. A. Under what circumstances will an equation in which the variable appears on

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Pump Name: Equations (Day 1) Date:

Solve each equation for the unknown variable.

1. x + 5 = 8 2. 9 − a = 2

3. m − 6 = 9 4. 04w = 2

5. j 05 = 3 6. q − 82 = 1

Meeta buys a ticket for the movie and a popcorn, which costs $6. She spends $16.50 in all. How much was the movie ticket?

© Clark Creative Education

Pump Name:

Equations (Day 2) Date:


1. m2 + 1 = 9

2. n 63 + 2 = 2

3. r7 − 1 = 2

4. 14w + 1 = 2

5. j 35 + 3 = 3

6. q − 52 − 7 = 2

The 156 students on the field trip are evenly split among n buses. If there are 39 students on each bus, then how many buses are there?


Pump Name:



1. j j 52 + 3 + 5 = 1

2. w (w ) 53 + 4 + 1 = 2

3. r (r ) 64 − 2 + 5 = 2

4. (m ) (m ) − 33 + 1 + 2 + 2 = 1

5. q (q ) 25 + 2 + 7 + 3 = 5

6. (a ) (a ) 33 + 2 − 2 − 1 = 1

Janey bought 3 granola bars. Later, she bought 4 more. If her total payments were $17.50, how much is a granola bar?


Pump Name:



1. (x ) (x )2 + 4 = 4 + 2

2. w 0 (w ) 12 + 1 = 3 + 1 + 1

3. (a ) 1− 2 − 5 + 3 = a − 1

4. (b ) b4 − 7 = 2 − 8

5. (x ) (x ) 05 − 1 + 4 = 6 + 2 − 2

6. (x ) x2 + 1 = 2 + 3

Henry buys three notebooks and several other items that total $6. Maria buys two notebooks and $9.95 worth of other goods. If Henry and Maria spent the same amount, how much does a notebook cost?


Pump Name:



1. (2x ) x23 + 4 = 4

2. (r (r )) 62 + 2 + 2 = 2

3. (a (3 )) 06 + 2 + 4 + a = 8

4. (x ) 2x4 + 3 = 1 − 4

5. − x )− x − x = ( − 1

6. 43r + 3 = r + 1

Name a value of a for which the equation has an infinite number of (x ) (x ) 3 + 5 + 2 = 3 − 4 + a solutions. Then name a value for which is has no solutions.


Flex Name:


Think about the process of solving equations.

A.

B.

Describe how to write an equation that models the following situation: Norah added a handful of nuts to the bag so that it weighed exactly one pound. If there were 14 ounces in the bag before her addition, what was the weight of her handful? Now describe how to solve that equation:


Flex Name:



A. How is the process of solving the equation for t is different from solving the equation t4 = 6

for w?8w = 2


Flex Name:



A. What is the first step in solving an equation such as ? Why?a (a ) 14 + 3 + 7 = 9


Flex Name:



A. Under what circumstances will an equation in which the variable appears on both sides NOT have a solution? Under what circumstances will the equation have an infinite number of solutions?


Flex Name:



A. Describe how you can use a graphing calculator or other technology to find the value of x that “works” to solve the equation .x − x 65 + 4 = 6 + 2


Equations Name:

Notes Date:

Djamil works as a physicist for a crash test group. His job is to calculate variables from the crashes to include in the safety report. With each crash he is missing a variable in his formula. His supervisor wants the data to be completed, ranked by category for each vehicle tested and a recommendation of the vehicle with the least force on impact. To do so, Djamil needs to solve equations.

Write the definition to the term and include an image or example that represents it.

Term Definition Example

Equation

Solution

Term

Inverse operations

Isolate the variable

Variable

SADMEP

What is the difference between expressions and equations? Write examples of each.

Expression Equation

What is a Solution to an Equation? The Conceptualizer!

A value that makes a variable expression true.

x + 3 = 5 Is x = 1 a solution?

1 + 3 = 5 True or False?

Thus x = 1 is NOT a solution?

is true! 2 + 3 = 5 Thus x = 2 is a solution?

Is there always just One Solution? The Conceptualizer!

Consider x + 3 = x + 3

Is x = 1 a solution?

is true!1 + 3 = 1 + 3 Is x = 2 a solution?

is true!2 + 3 = 2 + 3 … if we subtract 3 from both sides we get x=x. So it will be true for ANY x. This means there are infinite solutions.


Are there any other possible types of Solutions? The Conceptualizer!

Consider

x + 3 = x + 5 … if we subtract 3 from both sides we get…

x = x + 2 … if we subtract x from both sides we get…

0 = 2

This can never be true! … so it is possible to have no solutions.

The Step of Solving an Equation = Undoing the Order of Operations

Step 1

Step 2

Step 3

Step 4


Performing Inverse Operations to Both Sides The Conceptualizer!

Consider

x + 3 = 4 If you do the inverse operation of add 3 you will isolate the variable. We need to subtract 3.

x + 3 = 4 − 3

so... x = 4

is incorrect

What you do to one side you have to do to the other side. Otherwise, like in the above example, it is not equal any more.

x + 3 = 4

− 3 − 3

x 1 =

The inverse operation has isolated the

variable to give us the solution to the equation . #learningnewlanguages

One-Step Equation Notes

x + 3 = 5


Checking Solutions Details

You don’t ever have to be wrong unless you want to. #fact If you substitute your solution INTO the equation and follow the order of operations, the statement MUST BE TRUE. Pretty much all math is this way.


x 55 = 1

Multi-Step Equation Notes

x 03 − 2 = 1



x23 − 7 = 2

Equations Break Down the Same

Harder equations just mean more new steps at the beginning. You will usually reach a point where it is a two-step equation, and usually a point where it is a one-step equation. This is why a strong foundation is so very important.

Write examples of equations that can be solved in one-step or are multi-steps.

One-Step Multi-Step


Equations with Variables on Both Sides Notes

y y3 + 5 = 2 − 4


1 y − y1 − 6 = 4 + 1


Equations with Parentheses Notes

(w ) (w )2 − 3 + 5 = 3 − 1

Write examples where the first operation in a multi-step equation is either

addition, subtraction, multiplication or division in each box.

Addition Subtraction Multiplication Division


Four friends get the lunch special at a restaurant and leave a $3 tip. The total amount paid was $26.00. How much does the lunch special cost? 326 people were in a tour group. Six buses were completely filled and 8 people chose to walk. How many people did the bus hold? Cara has $600 in her savings account and she deposits $30 every week. Logan has $900 in his savings account and withdraws $10 a week. How many weeks will it take until Cara has more money?


Equations Name:

a 21st Century Math Test Date:

(2 points each)

Match the definition with the correct term.

1. ______ Solution a. Two expressions, equated with an equals sign. A statement of equality.

2. ______ Equation

b. The process of solving an equation by using inverse operations.

3. ______ Term

c. A value that can be substituted into the variable that can satisfy an equation.

4. ______ Isolating the variable d. Either a single number, a variable, or numbers and/or variables multiplied together

Determine if each statement is true or false. If it is false, explain why.

5. True / False The inverse operation of subtraction is division. 6. True / False Isolating the variable should be done by applying inverse operations in

the reverse order of the order of operations used for evaluating expression.

7. True / False For the equation , the constant term 2 should be moved before5

2+x = 4 remove the denominator 5.

___________/14


(4 points each, choose 6)

Solve the following equations.

1. 8 x − 6 = 1

2. 1 y 1 − 3 = 8

3. 7

4w = 6

4. −3p−10 = 2

5. x x 5 − 7 = 3 + 9

6. y32y+1 = 5 − 4

7. (p ) p 2 − 3 = 5 + 3

8. (2w ) 24 − 7 = 34w + 1

___________/24



General Directions

1. The sum of the ages of the Diallo sisters is 57. Their ages can be represented as three consecutive odd integers. What is the age of the middle sister?

2. Mr. Shipley is in charge of a school trip. 324 students will go on the trip. The school has seven buses and one van. If the van can haul nine students, how many students will ride on each bus?

3. Callie has $500 in her savings account and she deposits $25 every week. Leah has $750 in his savings account and withdraws $20 a week. How many weeks will it take until Callie has more money?

4. Urijah is starting a catering business. The cost to start the business is $50,000 and the monthly costs are $8,000. He has been earning $10,800 every month in revenue. In how many months will Urijah’s business break-even and earn a profit?

___________/24


(20 points)

General Directions

1. Djamil works as a physicist for a crash test group. His job is to calculate variables from the crashes to include in the report. With each crash he is missing a variable that he needs to solve. His supervisor wants the data to be completed, ranked by category for each vehicle tested and a recommendation of the vehicle with the least force on impact. Djamil uses the formula where F is the average force, t is the time length (v ) F · t = m 1 − v2 of the impact, m is the mass of the car, v1 is the velocity before the crash and v2 is the velocity after the crash on the recoil.

Force (N) Time (s) Mass (kg) Velocity 1 (m/s)

Velocity 2 (m/s)

Century 0.85 1521.35 35.76 -20.12

Elantra 85,342.16 1225.15 36.66 -20.46

Monte Carlo 93,373.16 0.86 36.21 -21.91

Odyssey 118,760.33 0.93 1993.99 -19.86

Tacoma 108,993.84 0.95 1861.97 35.87

___________/20


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Pump Name:



1. x + 5 = 8

x = 3

2. 9 − a = 2

a = 7

3. m − 6 = 9

5m = 1

4. 04w = 2

0w = 8

5. j 05 = 3

j = 6

6. q − 82 = 1 −q = 9

Meeta buys a ticket for the movie and a popcorn, which costs $6. She spends $16.50 in all. How much was the movie ticket?

6.50; m 0.50m + 6 = 1 = 1


Pump Name:



1. m2 + 1 = 9

m = 4

2. n 63 + 2 = 2

n = 8

3. r7 − 1 = 2

1r = 2

4. 14w + 1 = 2

0w = 8

5. j 35 + 3 = 3

j = 6

6. q − 52 − 7 = 2 −q = 9

The 156 students on the field trip are evenly split among n buses. If there are 39 students on each bus, then how many buses are there?

56/n 39 ; n 1 = = 4


Pump Name:



1. j j 52 + 3 + 5 = 1

j 0; j5 = 1 = 2

2. w (w ) 53 + 4 + 1 = 2

w 5;7 + 4 = 2 w = 3

3. r (r ) 64 − 2 + 5 = 2

r 0 6; r 82 − 1 = 2 = 1

4. (m ) (m ) − 33 + 1 + 2 + 2 = 1

m − 3; m −5 + 7 = 1 = 4

5. q (q ) 25 + 2 + 7 + 3 = 5

q 7 2; q7 + 1 = 5 = 5

6. (a ) (a ) 33 + 2 − 2 − 1 = 1

a a 3; a 3; a3 + 6 − 2 + 2 = 1 + 8 = 1 = 5

Janey bought 3 granola bars. Later, she bought 4 more. If her total payments were $17.50, how much is a granola bar? g g 7.50; 7g 7.50; g .50 3 + 4 = 1 = 1 = 2


Pump Name:



1. (x ) (x )2 + 4 = 4 + 2

x x ; 2x x;2 + 8 = 4 + 8 = 4 x = 0

2. w 0 (w ) 12 + 1 = 3 + 1 + 1

w 0 w 4; w −2 + 1 = 3 + 1 = 4

3. (a ) 1− 2 − 5 + 3 = a − 1

a 3 1; 24 a; a− 2 + 1 = a − 1 = 3 = 8

4. (b ) b4 − 7 = 2 − 8

b 8 b ; 2b 0; b 04 − 2 = 2 − 8 = 2 = 1

5. (x ) (x ) 05 − 1 + 4 = 6 + 2 − 2

x x ; x5 − 1 = 6 − 8 = 7

6. (x ) x2 + 1 = 2 + 3

x x ; ; o solution2 + 2 = 2 + 3 0 = 1 n

Henry buys three notebooks and several other items that total $6. Maria buys two notebooks and $9.95 worth of other goods. If Henry and Maria spent the same amount, how much does a notebook cost? n n .95 ; n .95 3 + 6 = 2 + 9 = 3


Pump Name:



1. (2x ) x23 + 4 = 4

(2x ) x; x 2 x;3 + 4 = 8 6 + 1 = 8 x = 6

2. (r (r )) 62 + 2 + 2 = 2

(r r ) 6; 3r 3;2 + 2 + 4 = 2 + 4 = 1 r = 3

3. (a (3 )) 06 + 2 + 4 + a = 8

(a 2 a) 0; 5a 2 76 + 2 + 1 + 4 = 8 + 1 = 3 a = 5

4. (x ) 2x4 + 3 = 1 − 4

x 2 2x ; 16 x;4 + 1 = 1 − 4 = 8 x = 2

5. − x )− x − x = ( − 1

x − ; x −− 2 = x + 1 = 1

6. 43r + 3 = r + 1

; rr

4 = 2 = 8

Name a value of a for which the equation has an infinite number of (x ) (x ) 3 + 5 + 2 = 3 − 4 + a solutions. Then name a value for which is has no solutions. x 5 x 2 ; 17 − 2 ; 29 3 + 1 + 2 = 3 − 1 + a = 1 + a = a

If there is an infinite number of solutions; if there are no solutions.9 a = 2 is not equal to 29 a


Flex Name:



A. Describe how to write an equation that models the following situation: Norah added a handful of nuts to the bag so that it weighed exactly one pound. If there were 14 ounces in the bag before her addition, what was the weight of her handful? Let n by the weight of that handful of nuts. There are 16 ounces in a pound. Then

.4 6n + 1 = 1 Now describe how to solve that equation: Work backwards to “undo” the addition of 14 by subtracting 14 from both sides. Isolate the variable with inverse operations. Then .n = 2


Flex Name:



A. How is the process of solving the equation for t is different from solving the equation t4 = 6

for w?8w = 2 In a sense, there is no difference: in both cases, isolate the variable by applying inverse operations. For the first equation, undo the division by 4 by multiplying both sides by 4, getting . For the second, undo the division by w by multiplying both sides by w, 4t = 2 getting ; then divide both sides by 2 to get . In another sense, though, the w8 = 2 w = 4 equations are different because of where the variable is located, meaning that the second equation is most easily solved by writing its equivalent, and immediately obtaining 2

8 = w .w = 4


Flex Name:



A. What is the first step in solving an equation such as ? Why?a (a ) 14 + 3 + 7 = 9 Nothing can happen to the quantities in parentheses until the parenthese are “broken” i.e. removed. The first step is to get rid of parentheses by applying the distributive rule, obtaining , then and .a a 1 14 + 3 + 2 = 9 a 07 = 7 0a = 1


Flex Name:



A. Under what circumstances will an equation in which the variable appears on both sides NOT have a solution? Under what circumstances will the equation have an infinite number of solutions? There is no solution (for linear equations) when each side represents a line, and the two lines are parallel. Then, there are no points of intersection. For example, (x ) x2 + 1 = 2 + 3 has no solution, because the lines and are parallel; there is no value of xy = 2 + 2 xy = 2 + 3 x for which they intersect. There is an infinite number of solutions when the lines are collinear, as in , (x ) x2 + 1 = 2 + 2 for which every value of x is a solution.


Flex Name:



A. Describe how you can use a graphing calculator or other technology to find the value of x that “works” to solve the equation .x − x 65 + 4 = 6 + 2 Rewrite each side as a line, and , creating a system of two linear xy = 5 + 4 − x 6y = 6 + 2 equations. Because the lines have different slopes, they intersect in exactly one point. The point of intersection, as determined by the graphing calculator, is , meaning is 2, 4)( 1 x = 2 the unique solution to the equation.


Equations Name:

Notes Date:

Djamil works as a physicist for a crash test group. His job is to calculate variables from the crashes to include in the safety report. With each crash he is missing a variable in his formula. His supervisor wants the data to be completed, ranked by category for each vehicle tested and a recommendation of the vehicle with the least force on impact. To do so, Djamil needs to solve equations.

Write the definition to the term and include an image or example that represents it.

Term Definition Example

Equation Two expressions, equated with an equals sign. A statement of equality.

x 55 = 1

Solution A value that can be substituted into the variable that can satisfy an equation.

Term Either a single number, a variable, or numbers and/or variables multiplied together

10, 12x, xyz, 12ab

Inverse operations

Operations that undo each other. Add & Sub Mul & Div

Exponent & Roots

Isolate the variable

When the variable is by itself on one side of the equals sign. 0 3x = 1 +

Variable A symbol for an unknown value. Usually a letter, such as a, x or y. x 55 = 1

The x is the variable.

SADMEP The reverse of PEMDAS. A reminder that isolating the variable should be done by applying inverse operations in the reverse order of the order of operations used for evaluating expressions: add and subtract first, then multiply and divide, then exponents.

SA DM E P

What is the difference between expressions and equations? Write examples of each.

Expression Equation

3 5xy 2 4z1 + rπ 2 x 55 = 1 −52x−9 = 2

wh V = l a2 + b2 = c2

What is a Solution to an Equation? The Conceptualizer!

A value that makes a variable expression true.

x + 3 = 5 Is x = 1 a solution?

1 + 3 = 5 True or False?

Thus x = 1 is NOT a solution?

is true! 2 + 3 = 5 Thus x = 2 is a solution?

Save it for later, but this is true too! Where the left side of an equation and right side of an

equation cross on a graph is this solution too.

Is there always just One Solution? The Conceptualizer!

Consider x + 3 = x + 3

Is x = 1 a solution?

is true!1 + 3 = 1 + 3 Is x = 2 a solution?

is true!2 + 3 = 2 + 3 … if we subtract 3 from both sides we get x=x. So it will be true for ANY x. This means there are infinite solutions.

The left side and the right side are the same line!


Are there any other possible types of Solutions? The Conceptualizer!

Consider

x + 3 = x + 5 … if we subtract 3 from both sides we get…

x = x + 2 … if we subtract x from both sides we get…

0 = 2

This can never be true! … so it is possible to have no solutions.

The left side and the right side lines will never touch! What are these kinds of lines called?

The Steps of Solving an Equation = Undoing the Order of Operations.

Step 1 Additions & Subtractions

Step 2 Multiplications & Divisions

Step 3 Exponents

Step 4 Inside Parenthesis


Performing Inverse Operations to Both Sides The Conceptualizer!

Consider

x + 3 = 4 If you do the inverse operation of add 3 you will isolate the variable. We need to subtract 3.

x + 3 = 4 − 3

so... x = 4

is incorrect

What you do to one side you have to do to the other side. Otherwise, like in the above example, it is not equal any more.

x + 3 = 4

− 3 − 3

x 1 =

The inverse operation has isolated the

variable to give us the solution to the equation . #learningnewlanguages

then

and finally


x + 3 = 5 As variable x is not alone on either side, it needs to be isolated from the constant term +3. The inverse operation of adding 3 is subtracting 3.

x + 3 = 5 − 3 − 3

The inverse operation of adding 3 is subtracting 3.

x = 2 Simplify, x is isolated (Mini-Concept: the coefficient 1 doesn’t have to be written) and the solution is x = 2


Checking Solutions Details

You don’t ever have to be wrong unless you want to. #fact If you substitute your solution INTO the equation and follow the order of operations, the statement MUST BE TRUE. Pretty much all math is this way.

Like in Skill Practice #1 x = 2

The original equation x + 3 = 5

2) ( + 3 = 5 is true!5 = 5

Sleep well, you know you are right!


x 55 = 1 As variable x is not alone, it needs to be isolated from its coefficient 5.

55x = 5

15 The inverse of multiply by 5 is divide by 5. Divide both sides by 5. (Mini-Concept: the coefficient of a term represents the operation of multiplication)

x = 3 Simplify, x is isolated (Mini-Concept: the coefficient 1 doesn’t have to be written) and the solution is x = 3

(3) 55 = 1 Check the solution


x 0 3 − 2 = 1 + 2 + 2

The inverse of subtract 2 is add 2 to both sides.

x 23 = 1 Simplify. Note: Back to one-step!

33x = 3

12 The inverse of multiply by 3 is divide by 3. Divide both sides by 3.

x = 4 Simplify, x is isolated, the solution is x = 4

(4) 0 3 − 2 = 1 Check the solution



x 23 − 7 = 2

+ 7 + 7 The inverse of subtract 7 is add 7 to both sides.

x23 = 9 Simplify

x23 × 2 = 9 × 2 The inverse of divide by 2 is multiplying 2.

x 83 = 1 Simplify. Note: Back to one-step!

33x = 3

18 The inverse of multiplying by 3 is dividing by 3.

x = 6 Simplify, x is isolated, the solution is x = 6

(6)23

− 7 = 2 Check the solution

Equations break down the same way.

Harder equations just mean adding more new steps at the beginning. You will usually reach a point where it is a two-step equation, and usually a point where it is a one-step equation. This is why a strong foundation is so very important.

Write examples of equations that can be solved in one-step or are multi-steps.

One-Step Multi-Step

x 5 = 6

649 + x = 1

x − 0 3 + 4 = 1

38−2x = 7



y y 3 + 5 = 2 − 4 y y − 2 − 2

When variables are on both sides there are a few ways to solve it. I suggest identifying the side with the smaller coefficient in front of the variable. Then moving it (you deal with less negative signs this way). In this case 3y is larger than 2y. So we will subtract 2y from both sides.

− y + 5 = 4 Simplify. Note: Back to one-step!

− y + 5 = 4 − 5 − 5

The inverse operation of add 5 is subtract 5.

− y = 9 Simplify, the y is isolated, and the solution is − y = 9

(− ) (− ) 3 9 + 5 = 2 9 − 4 Check the solution


1 y − y 1 − 6 = 4 + 1 y y+ 6 + 6

Since -4y is larger than -6y, we will add 6y to both sides.

1 y1 = 2 + 1 − 1 − 1

Simplify. Note: Back to two-step! The inverse operation of add 1 is subtract 1.

0 y1 = 2 Simplify.

210 = 2

2y The inverse operation of multiply by 2 is divide by 2.

5 = y Simplify, y is isolated and the solution is y = 5

1 (5) − (5) 1 − 6 = 4 + 1 Check the solution


Equations with Parentheses Notes

(w ) (w ) 2 − 3 + 5 = 3 − 1 You have some options for how to begin. Using distribution may be the simplest.

w w 2 − 6 + 5 = 3 − 3 Simplify. Combine like terms.

w w 2 − 1 = 3 − 3 w w − 2 − 2

2w is less than 3w so subtract 2w from both sides.

− 1 = w − 3 Simplify.

− 1 = w − 3 + 3 + 3

The inverse operation of subtract 3 is add 3.

2 = w Simplify both sides, the w is isolated, the solution is w = 2

((2) ) ((2) ) 2 − 3 + 5 = 3 − 1 Check the solution

Write examples where the first operation in a multi-step equation is either

addition, subtraction, multiplication or division in each box.

Addition Subtraction Multiplication Division

3 x − 6 = 1 3x 000 2 − 1 = 1

7 + x = 3 x 8 + 9 = 6

x3 = 6

−52x−9 = 2

x 5 5 = 3 * (x ) 2 − 3 = 4

* could distribute first


Four friends get the lunch special at a restaurant and leave a $3 tip. The total amount paid was $26.00. How much does the lunch special cost? 4x + 3 = 26 4x=23 x=$5.75; The lunch special costs $5.75. 326 people were in a tour group. Six buses were completely filled and 8 people chose to walk. How many people did the bus hold? 6x+8=326 6x=318 x=53; The bus can hold 53 people. Cara has $600 in her savings account and she deposits $30 every week. Logan has $900 in his savings account and withdraws $10 a week. How many weeks will it take until Cara has more money? 600 +30x = 900 - 10x 40x = 300 x = 7.5; Cara will have more money in 8 weeks.


Equations Name:

a 21st Century Math Test Date:

(2 points each)

Match the definition with the correct term.

1. __c____ Solution a. Two expressions, equated with an equals sign. A statement of equality.

2. __a___ Equation

b. The process of solving an equation by using inverse operations.

3. __d___ Term

c. A value that can be substituted into the variable that can satisfy an equation.

4. __b____ Isolating the variable d. Either a single number, a variable, or numbers and/or variables multiplied together

Determine if each statement is true or false. If it is false, explain why.

5. True / False The inverse operation of subtraction is division. 6. True / False Isolating the variable should be done by applying inverse operations in

the reverse order of the order of operations used for evaluating expression.

7. True / False For the equation , the constant term 2 should be moved before5

2+x = 4 remove the denominator 5.

___________/14



Solve the following equations.

1. 8 x − 6 = 1 x=24

2. 1 y 1 − 3 = 8 y=1

3. 7

4w = 6 w=10.5

4. −3p−10 = 2

p=4

5. x x 5 − 7 = 3 + 9 x=8

6. y32y+1 = 5 − 4

y=1

7. (p ) p 2 − 3 = 5 + 3 p=-3

8. (2w ) 24 − 7 = 34w + 1

w=6

___________/24



General Directions

1. The sum of the ages of the Diallo sisters is 57. Their ages can be represented as three consecutive odd integers. What is the age of the middle sister? The middle sister is 19 years old.

2. Mr. Shipley is in charge of a school trip. 324 students will go on the trip. The school has seven buses and one van. If the van can haul nine students, how many students will ride on each bus? x=45; Each bus will hold 45 students.

3. Callie has $500 in her savings account and she deposits $25 every week. Leah has $750 in his savings account and withdraws $20 a week. How many weeks will it take until Callie has more money? w=5.556 Callie will have more money in 6 weeks.

4. Urijah is starting a catering business. The cost to start the business is $50,000 and the monthly costs are $8,000. He has been earning $10,800 every month in revenue. In how many months will Urijah’s business break-even and earn a profit? x=17.86; Urijah would break-even in 18 months.

___________/24


(20 points)

General Directions

1. Djamil works as a physicist for a crash test group. His job is to calculate variables from the crashes to include in the report. With each crash he is missing a variable that he needs to solve. His supervisor wants the data to be completed, ranked by category for each vehicle tested and a recommendation of the vehicle with the least force on impact. Djamil uses the formula where F is the average force, t is the time length (v ) F · t = m 1 − v2 of the impact, m is the mass of the car, v1 is the velocity before the crash and v2 is the velocity after the crash on the recoil.

Force (N) Time (s) Mass (kg) Velocity 1 (m/s)

Velocity 2 (m/s)

Century 100,015.3 0.85 1521.35 35.76 -20.12

Elantra 85,342.16 0.82 1225.15 36.66 -20.46

Monte Carlo 93,373.16 0.86 1381.64 36.21 -21.91

Odyssey 118,760.33 0.93 1993.99 35.53 -19.86

Tacoma 108,993.84 0.95 1861.97 35.87 -19.74

The Elantra has the least force on impact, students can rank the cars in order on each standard.

___________/20


Documents

Equations - Amazon S3€¦ · Equations ( Day 4 ) Date: Think about the process of solving equations. A. Under what circumstances will an equation in which the variable appears on