warm up # 4 1.a pine tree grower determines that the cost of planting and caring for each pine tree...

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Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm amount to $600. Assuming that the grower plans to charge $65 per Pine tree, at what point will the grower begin to make a profit? Write and SOLVE an equation for this problem. 2. Solve 3. Solve and GRAPH

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Page 1: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

Warm Up # 4

1. A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm amount to $600. Assuming that the grower plans to charge $65 per Pine tree, at what point will the grower begin to make a profit? Write and SOLVE an equation for this problem.

2. Solve 3. Solve and GRAPH

Page 2: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

HW Check 1. 10

Page 3: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

FORMULAS!!!

Pythagorean Theorem & Distance

Page 4: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

The Pythagorean Theorem

Page 5: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

Remember right triangles?

Page 6: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

Special Names for Right Triangles

Hypotenuse!

Legs!

Page 7: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

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 # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

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

8m

15 m

Page 9: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

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

5 y12 y

Page 10: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

Pythagorean Triples

Three side lengths that would form a right triangle.

The two smaller numbers are always “a” and “b”

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

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

Page 11: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

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

Page 12: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

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

11, 5, 12, 9, 13

Page 13: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

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 6) Solve for b.

Page 14: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

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 15: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

8) A suitcase measures 24 inches long and 18 inches high. What is the diagonal length of the suitcase to the nearest tenth of a foot?

Page 16: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

Remember plotting coordinates? The Coordinate Plane

An Ordered Pair of numbers identifies the location of a point.

Page 17: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

Practice

Plot the following coordinates: 1. (-2, 3) 2. (4, -1)3. (1, 1) 4. (-3, -4)5. (0, 0)

Page 18: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

. (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 19: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

. (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 20: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

. (4, 6)

.(-3, -2)

The Distance Formula

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

Page 21: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

. (3, -4)

.(-5, 5)

10)

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

Page 22: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

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 23: Warm Up # 4 1.A pine tree grower determines that the cost of planting and caring for each Pine tree is $18.53. The fixed costs for managing the tree farm

Coming up….

HW tonight – 1.11

Quiz 1.3 Friday!