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

HW Check 1. 10

FORMULAS!!!

Pythagorean Theorem & Distance

The Pythagorean Theorem

Remember right triangles?

Special Names for Right Triangles

Hypotenuse!

Legs!

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

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

8m

15 m

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

5 y12 y

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

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

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

11, 5, 12, 9, 13

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.

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?

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?

Remember plotting coordinates? The Coordinate Plane

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

Practice

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

. (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!

. (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!

. (4, 6)

.(-3, -2)

The Distance Formula

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

. (3, -4)

.(-5, 5)

10)

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

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.)

Coming up….

HW tonight – 1.11

Quiz 1.3 Friday!