warm-up 1)the sum of three consecutive odd integers is 111. what is the smallest number? 2) write an...

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Warm-Up 1) The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus 5

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Page 1: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

Warm-Up1) The sum of three consecutive odd

integers is 111. What is the smallest number?

2) Write an expression for: Nine more than the quantity x plus 5

3) Solve & graph : 21 – 5r < 3r + 45

Page 2: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

HW Check – Equation Word Problems

Page 3: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

FORMULAS

Pythagorean Theorem & Distance

Page 4: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

The Pythagorean Theorem

Page 5: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

Remember right triangles?

Page 6: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

Special Names for Right Triangles

Hypotenuse!

Legs!

Page 7: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

The Pythagorean Theorem

In any right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse.

a

b

c

Page 8: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

a2

ac

b

+ b2 = c2

+ =a2b2 c2

Page 9: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

1) Find the length of the unknown side of the triangle:

8m

15 m

Page 10: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

2) Find the length of the unknown side of the triangle:

5 y12 y

Page 11: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

Pythagorean Triples

Three side lengths that would form a right triangle.

Ex) 3) Are the following side lengths Pythagorean triples?

a) 8, 4, 10 b) 3, 4, 5

Page 12: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

4) How far does the catcher have to home plate?

Page 13: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

Literal Equations

A literal equation is an equation with more than one variable. Formulas are literal equations.

Sometimes we need to solve a formula for a specific variable

Ex 5) Solve for b.

Page 14: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

6) Which 3 of the following side lengths could be used to create a right triangle?

11, 5, 12, 9, 13

Page 15: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

Word Problems

7) John leaves school to go home. He walks 6 blocks North and then 8 blocks west. How far is John from the school?

Page 16: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

8) A 13 foot ladder is placed 5 feet away from a wall. The distance from the ground straight up to the top of the wall is 13 feet Will the ladder reach the top of the wall?

Page 17: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

. (4, 6)

.(-3, -2)

9) How can we find the distance between the two points?

How long is this leg?

What about this leg?

We can use the Pythagorean Theorem!

Page 18: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

. (4, 6)

.(-3, -2)

The Distance FormulaThe distance formula uses the Pythagorean Theorem to find the distance between two points.

It has the coordinates for each point built in, so it finds the length of each “leg” for you!

Page 19: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

. (4, 6)

.(-3, -2)

The Distance Formula

Use the distance formula to find the distance between the two points.

Page 20: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

. (3, -4)

.(-5, 5)

10)

Use the distance formula to find the distance between the two points.

Page 21: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

Word Problem

11) On a map’s coordinate grid, Walt City is located at (-1, -3) and Smithville is located at (4, 9). How long is a train’s route as the train travels along a straight line from Walt City to Smithville? (One map unit equals one mile.)

Page 22: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

CW:Pythagorean Theorem

& Distance Formula

Page 23: Warm-Up 1)The sum of three consecutive odd integers is 111. What is the smallest number? 2) Write an expression for: Nine more than the quantity x plus

Coming up…

HW tonight – 1.6

QUIZ Thursday!

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