Systems of Equations
How many solutions does this system have?
y = 2x + 1
y = 2x + 8
no solution
The lines are parallel
50 = ___
1
Anything to the power of 0 will be 1
Write the following value in scientific notation:
57,124,933
5.7124933 x 107
Which set of ordered pairs is a function?
a) (3, 2) (2, -1) (4, -5) (3, -8)
b) (½, 4) (⅔, 6) (-2, 9) (-2, 0)
c) (5, -2) (6, 1) (0,3) (-5, 2)
d) (4, -2) (4, 4) (5, 1) (-3, 8)
C
Each x value has exactly one y value
Solve:
4x + 1 = x - 8
x = -3
Explain what types of lines you will see if there is no solution to a specific system.
Explain what types of lines you will see if there are infinitely many solutions to a specific system.
infinitely many = same line = same slope and same y intercept
no solution = parallel lines = same slope different y intercepts
True or false?
3-2 = -9
False!
negative exponents mean reciprocal!
3-2 = 1/9
Write the following value in scientific notation:
0.00004982
4.982 x 10-5
Which of the following are linear functions?
a) y = 5x - 1
b) 12x + 4y = 8
c) y = 3x² - 4
d) y = 5/x
A and B
must be able to write in y = mx + b format
Solve. ½(4x + 12) = 18
x = 6
Solve the System:
3x + 4y = 14
x + 4y = 10
(2, 2)
Solve for x: x3 = -27
a) x = 3
b) x = -3
c) x = 3 and -3
b) x = -3
Put the following in order from least to greatest:
3.13 x 10-4 0.0313 3.03 x 10-4 0.00303
3.03 x 10-4 < 3.13 x 10-4 < 0.00303 < 0.0313
Find the slope of the line that passes through (-2, 1) and (4, 5)
2/3
change in y over change in x
Solve. -3(2x + 4) = 2x + 4
x = -2
Solve the system:
y = 7 - 3x
6x + 2y = 14
all real numbers (infinitely many solutions)
Simplify (write answer in exponential form)
8-5 x (89)2
813
(8.3 x 106) (5.2 x 104)
4.316 x 1011
Which has the greater rate of change:
Which of the two functions below has the greater rate of change? Show any necessary work and explain your reasoning.
Function I: y = 0.2x + 2
OR
Function II: a line with y-intercept (0,2) which passes through the point (2,6)
Function 2 - has a greater rate of change with a slope of 2 while the first function has a slope of 0.2 or 1/5
**GEOMETRY**
The ramp outside of a building is a right triangle. The hypotenuse measures 25 and one leg measures 15. What is the length of the other leg?
20 feet
Solve the system:
-8x + 3y = -6
9x - 3y = 6
(0,-2)
Simplify:
(912)3 divided by 97
929
(2.8 x 1010) divided by (2 x 1020)
1.4 x 10-10
The cost of renting a car from the Frugal Car Rental Company includes a $20 non-refundable deposit and a travel cost of 40¢ per mile. Write an equation that represents the cost for any number of miles.
y = 20 + 0.4x
y = total cost
x = # of miles
Solve: 3(1 + 2f) - 5 = 6f - 2
All real numbers - infinite solutions