3 Types of Solutions
(If one solution: solve for the variable)
(If one solution: solve for the variable)
Infinite, one, or no solution
3x + 5 = 3x - 5
No solution (If you got this wrong then you are sad)
What is the equation for the Pythagorean Theorem?
a2 + b2 = c2
Solve for y and x:
y = 5x
y - 3x + 24 = 30
x = 3
y = 15
Convert to scientific notation: 937,200,000
9.372 x 108
If a graph doesn't have a straight lines, what kind of function is it?
Non-linear
If the variables are different on each side of the equation, how many solutions does it have? Infinite, one, or no solution?
One solution
Solve for "b": 62 + b2 = 102
b = 8
Solve for y:
y = x + 3
3y + 2x - 7 = 12
y = 5
Convert to standard notation: 3.26 x 104
32,600
If a function has a constant rate of change, what kind of function is it?
Linear
Infinite, one, or no solution
7x + 6 = 3x - 2
x = -2
Solve for "a": a2 + 122 = 132
a = 5
Solve for x:
x = -4y + 13
2x + 4y - 4 = 18
x = 9
Answer in both Scientific and Standard Notation:
(7 x 105) x (6 x 108)
Scientific Notation: 4.2 x 1014
Standard Notation: 420,000,000,000,000
If a function can be written in Slope-Intercept Form, what type of function is it?
Linear
Infinite, one, or no solution
5x + 4x - x + 7 - 2 = 3x - 2x + 7x - 2x + 4x - 5x + 3x + 4 + 1
Infinite solutions
What is the line across from the right angle of a right triangle called? (In the equation the line is always labeled as "c")
The hypotenuse
Solve for x and y:
2x = 3y - 2
3y + 3x - 4 = 8
x = 2
y = 2
Answer in scientific notation: (57 x 10-3) / (8 x 10-5)
7.125 x 102
What type of function needs to have a constant rate of change to be considered linear?
A table
Infinite, one, or no solution:
7(3x - 5) + 8 = 9x + 3(3x + 2) - 8
One solution: x = 8 1/3
Solve for "c": 842 + 132 = c2
c = 85
Solve for y:
-y = x - 1
3x - y + 4 = 11
(Tip: Get rid of the "-y" from the 1st equation first)
y = -1
(Remember to divide by -1 on both sides to get rid of the "-y")
Answer in standard notation:
(8.06 x 104) + (5.8 x 105)
660600
What 2 things can make an equation non-linear? (Answer both of them)
The "x" is the denominator of a fraction or it has an exponent. (Or it has both)