Algebra-2 Section 1-3 And Section 1-4

Quiz Simplify using “step-by-step” (provide a reason or justification for each step). -4y – x + 10x + y 2. Is x = -2 a solution to following equation? 3. Solve using “step-by-step” (provide a reason or justification for each step).

Section 1-4 Rewrite Formulas and Equations. Section 1-4 Rewrite Formulas and Equations.

Worksheet Problems 1 - 4

Your turn: 1. What does it mean to find the “solution” to an equation?

Vocabulary Solve the single variable equation: Use properties of equality to rewrite the equation as an equivalent equation with the variable on one side of the equal sign and a number on the other side.

Vocabulary Solve for a variable (more then one variable in the equation): Use properties of equality to rewrite the equation as an equivalent equation with the specified variable on one side of the equal sign and all other terms on the other side.

Solve for ‘x’ 4 + 2x + y = 6 ÷ 2 ÷ x + y = 2 2x + y = 2 - y - y 2x = 2 – y 2x = 2 – y Solve for the variable: Use properties of equality to rewrite the equation as an equivalent equation with the specified variable on one side of the equal sign and all other terms on the other side.

Solve for “x” yx – 2 = Solve for the variable: Use properties of equality to rewrite the equation as an equivalent equation with the specified variable on one side of the equal sign and all other terms on the other side. ÷ y ÷ y yx = 6 yx = 6

Worksheet Problems 5 - 7

What do you think? Can these be numbers? length, width, temperature, pressure, weight, mass, etc. What is the length of a football field? Do either of these by themselves answer the question?

Worksheet Problems

Your turn: 2. Solve for ‘k’ 3. Solve for ‘k’ 4. Solve for ‘k’

Vocabulary Unit of measure: (“unit” for short) the type of measure used to describe quantities. Quantity: A measure of a real world physical property (length, width, temperature, pressure, weight, mass, etc.). Quality: An attribute or a property. (miniscule, small, medium, large, gigantic)

Unit of measure cold cool hot warm Temperature QualityQuantity Degrees: Fahrenheit, Centigrade, Kelvin When we combine numbers with units of measure, we can quantify physical attributes.

Vocabulary 5. If the area of a rectangle is 100 square inches, and its length is 25 inches, how long is it? 6. If the perimeter of a rectangle is 140 feet and its width is 20 feet, how long is it?

Your turn: for the area of a triangle formula: (‘A’ is a function of ‘b’ and ‘h’.) 7. Solve for “b” 8. Solve for “h”. We call this new version of the formula “b” is a function of “h” and “A” “b” is a function of “h” and “A” 9. What do you call this new version of the formula? (similar to: ‘A’ is a function of ‘b’ and ‘h’.)

Your turn: 10. The width of a rectangle is 2 feet. The length is twice the width. What is the perimeter of the rectangle? 11. The width of a rectangle is 3 feet. The length is four times the width. What is the area of the rectangle?

Formulas are used extensively in science. Science and math come together when mathematical equations are used to describe the physical world. Once a formula is known then scientists can use the equation to predict the value of unknown variables in the formula.

Solve for radius We will now solve for “r” In this form, we say that ‘c’ is a function of ‘r’. ‘c’ is a function of ‘r’. ÷ 2π ÷ 2π In this form, we say that ‘r’ is a function of ‘c’. ‘r’ is a function of ‘c’.

Your Turn: 12. Solve for ‘h’. 13. Solve for (Area of a trapezoid: where the length of the parallel bases are of the parallel bases are and the distance between them is ‘h’.) and the distance between them is ‘h’.)

What if two terms have the variable you’re trying to solve for? Solve the equation for “y”. Use “reverse distributive property 9y + 6xy = 30 ÷(9 + 6x) ÷ (9 + 6x) What is “common” to both of the left side terms? the left side terms? “Factor out” the common term “same thing left/right”

Example Solve for ‘x’. ‘x’ is common to both terms  factor it out (reverse distributive property). factor it out (reverse distributive property). How do you turn (3y – 2) into a “one” so that it disappears a “one” so that it disappears on the left side of the equation? on the left side of the equation? ÷(3y – 2) ÷(3y – 2)

14. Solve for ‘x’. Your turn: Your turn: 15. Solve for ‘y’.

Solving formula Problems The perimeter of a rectangular back yard is 41 feet. Its length is 12 feet. What is its width? Draw the picture Write the formula Replace known variables in the formula with constants ÷2 ÷2 Solve for the variable

Solving formula Problems 1. Draw the picture (it helps to see it) 2. Write the formula 3. Replace known variables in the formula with constants 4. Solve for the variable

16. If the base of a triangle is 4 inches and its area is 15 square inches, what is its height? 18. The perimeter of a rectangle is 100 miles. It is 22 miles long. How wide is the rectangle? Your turn: Your turn: 17. The area of a trapezoid is 40 square feet. The length of one base is 8 feet and its height is 3 feet, what is the length of the other base?