Solving linear equations
How many solutions does n have?
8n+6=3n+21
one solution
8n+6=3n+21
8n-3n=5n
5n+6= 21
21-6=15
5n=15
n=3
Solve the system of equations.
y = −3x + 4
y = 3x − 2
(1,1)
*DOUBLE OR NOTHING* (optional)
Function? (5, 4) (2, 9) (6, 4)
YES, A FUNCTION
Look at the x value.
If x does not repeat, then it is a function.
5, 2, and 6 are the x values.
This is a function.
Right Angle
an angle that measures 90 degrees
A cylindrical water tower is half full of water. How much water is in the tower if it measures 20 feet high and has a radius of 7 feet?
1,538.6
V=πr2h
n=pie
n x 72 x 20 = 3078.76
3078.76/2 = 1538.6
*DOUBLE OR NOTHING* (optional)
Solve the equation for x:
3x+14=8x+4
x=2
3x+14=8x+4
8x-3x=5x
14=5x+4
14-4=10
5x=10
x=2
Solve the system of equations..
y = x + 2
x = −3
(-3,-1)
*DOUBLE OR NOTHING* (optional)
Function? (5, 4) (2, 9) (5, 10)
NOT A FUNCTION
Look at the x values.
If x does not repeat, then it is a function.
The x values are 5, 2, and 5.
This is not a function.
a=3 b=4 c=?
Answer: 5
32 + 42 = c2
9+16 = c2
√25 = √c2
5 = c
*DOUBLE OR NOTHING* (optional)
A cylindrical oil drum is 2.1 meters high and has a radius of 0.9 meter. What is the volume of the oil drum.
5.34
3.14 * 0.92 * 2.1 = 5.34
*DOUBLE OR NOTHING* (optional)
Solve the equation for x:
7+4(x+2)= 3(2x+1)+2
x=5
7+4x+8=6x+3+2
7+8=15 3+2=5
4x+15=6x+5
4x-6x=-2x
-2x+15=5
5-15=-10
-2x=-10
x=5
Solve the system of equations.
x − y = 3
7x − y = −3
(-1,-4)
What is a function called if it has a constant rate of change?
Linear Function
Constant rate of change would mean a straight line on the graph, which makes it a linear function.
*DOUBLE OR NOTHING* (optional)
a=7 b=24 c=?
25
72+ 242=c2
49 + 576 = c2
49 + 576 = 625
72+ 242= 252
A cylindrical glass is 7 inches high and has a diameter of 3 inches. You will fill the glass with water up to 2 inches from the top. What is the volume of the water in the glass?
35.325
7-2 = 5 (5 is the new height due to how much you're filling the cup)
3/2 = 1.5 ( radius)
3.14 * 1.52 * 5 = 35.325
Solve for x:
½(3x-4)=16
x=12
Solve the system of equations.
4x + y = 2
x − y = 3
(1,-2)
What is a Non-linear Function?
An equation where the graph does not form a straight line.
a=6 b=8 c=?
10
62+ 82= c2
36+64=c2
36+64=100
62+82=102
The diameter of a basketball is 28.5 inches. Find the volume of the basketball.
12,114.7
28.5/2=14.25 ( radius)
4/3 * 3.14 * 14.253 = 12,114.7
The product of a number and seven equals the sum of the number and twelve. What is the number?
x=2
*DOUBLE OR NOTHING* (optional)
Solve the system of equations.
7x + 2y = −19
−x + 2y = 21
(-5,8)
*DOUBLE OR NOTHING* (optional)
The number or value that is entered into a function machine is a...
Input
Is this a right triangle: a=4, b=6, c=9
No
42+62 = 92
16 + 36 = 52
92= 81
52 does not equal 81.
What is the volume of the baseball when the diameter is approximately 3 inches.
14.13
3/2=1.5 (radius)
4/3 * 3.14 * 1.53 = 14.3
*DOUBLE OR NOTHING* (optional)