equations, formulas, and the problem-solving process
DESCRIPTION
2.1. Equations, Formulas, and the Problem-Solving Process. 1.Verify solutions to equations. 2.Use formulas to solve problems. What’s the difference?. Expression. Equation. Simplified. Solved. Equation: Two expressions set equal. False. True. - PowerPoint PPT PresentationTRANSCRIPT
Equations, Formulas, and the Problem-Solving Process2.12.1
1. Verify solutions to equations.2. Use formulas to solve problems.
Equation: Two expressions set equal.
Solution: A number that makes an equation true when it replaces the variable in the equation.
3x
537
What’s the difference?
Expression Equation
Simplified Solved
532
True False
53 x
solution. the is 2x
To Check a Possible SolutionReplace the variable in the equation with the value.If the resulting equation is true, the value is a solution.
SolutionsSolutions
Is a = 12 a solution?
5174 a
5174
517124
51748
5155
NO
Use parentheses!
SolutionsSolutions
Is a solution?56x 15238 xx
1556
2356
8
155
123
548
575
512
515
548
563
563
Yes
Determine which of the following is a solution for the equation.
a) –5
b) – 1
c) 2
d) 4
6 4 2 4 3 6 x x
2.1
Determine which of the following is a solution for the equation.
a) –5
b) – 1
c) 2
d) 4
6 4 2 4 3 6 x x
2.1
Formula:
The distance across a circle through its center.
An equation that describes a mathematical relationship.
Perimeter: The distance around a figure.
Area: The total number of square units that fill a figure.
Volume: The total number of cubic units that fill a space.
Circumference: The distance around a circle.
Radius: The distance from the center of a circle to any point on the circle.
Diameter:
FormulasFormulas See page 95!!!!
Area:
Perimeter:
lwA
wlP 22
Area: bhA21
Area:
Circumference:
2rA
rC 2dC
l
w
h
b
r
FormulasFormulas
Perimeter, Area or Volume?
Filling a pool with water? Volume
Cover for a pool? Area
Tile around a pool? Perimeter
Fencing? Perimeter
Laying carpet? Area
Putting up a wallpaper border?
Perimeter
FormulasFormulas
Suppose you have a rectangular pool that is 12 feet wide and 20 feet long. The pool has a constant depth of 4 feet. Find the perimeter, the area and the volume.
Perimeter: wlP 22
122202 P
2440 P
64P feet
FormulasFormulas
Suppose you have a rectangular pool that is 12 feet wide and 20 feet long. The pool has a constant depth of 4 feet. Find the perimeter, the area and the volume.
Area: lwA
1220A
240A square feet or ft2
FormulasFormulas
Suppose you have a rectangular pool that is 12 feet wide and 20 feet long. The pool has a constant depth of 4 feet. Find the perimeter, the area and the volume.
Volume:
cubic feet or ft3
lwhV
41220V
960V
A thermometer reads 30° C: what is this temperature in degrees Fahrenheit?
a) 34F
b) 49F
c) 86F
d) 112F
932
5 F C
2.1
A thermometer reads 30° C: what is this temperature in degrees Fahrenheit?
a) 34F
b) 49F
c) 86F
d) 112F
932
5 F C
2.1