Solving equations
Solve the Equation:
x/2 - 3 = 2
x = 10
What is the name of the LONGEST side of a right triangle?
BONUS points for your team if you can SPELL the answer correctly!
The Hypotenuse
What two characteristics does the graph of a proportional relationship have?
Straight line
passes through the origin (0,0)
is this relation a function?
(2,4), (3, 4), (4, 4), (5, 4)
Yes, the y-values are OK to repeat. It would create a horizontal line, which passes the vertical line test.
When solving an equation, you get an answer that looks like this:
6 = 6
What does that tell you about the number of solutions?
Many solutions
What is the solution to the equation:
-2x + 10 = 26
-8
A triangle has side lengths 6, 8, 10.
Is this a RIGHT triangle?
YES!
6^2 + 8^2 = 10^2
36 + 64 = 100
100 = 100
What is the difference between the graph of a PROPORTIONAL RELATIONSHIP, and the graph of a FUNCTION?
FUNCTIONS - doesn't have to be straight, must pass the VERTICAL LINE TEST
m = slope
b = y-intercept
What two integers does the square root of 37 fall between?
6, 7
The volume of a cube is 27 cubic inches. What is the length of one side of the cube?
3 inches
In a RIGHT triangle, if the legs each 3 inches long, what is the approximate length of the hypotenuse?
4.2 inches
What is the distance between the points:
(9,2) and (4,8)
7.8
slope = 2/5 y-Intercept = 3
y = 2/5x + 3
What is the CUBE ROOT of 125?
5
Solve the Equation:
10 = -3(x - 3) - 5
x = -2
**Look at the FIRST picture on the reference page**
What is the missing leg of the Triangle on the board? If necessary, round to the nearest tenth.
x =7.9
The point (2,18) is an ordered pair in a proportional relationship. What is the equation that represent this relationship?
y = 9x
**Refer to the 2nd image on the reference page*
Write the slope-intercept equation for the graph?
y = (1/2)x + 2
Write in slope-intercept form (y = mx + b)
y = 3 + 2(x - 1)
y = 2x +1
Solve the equation. Include all answers.
x^2 +15 = 51
x = +/- 6
Marcy took a taxi to the airport. The taxi charged a flat rate of $5, plus $0.50 per mile. The trip cost Marcy a total of $110. How many miles was it to the airport?
210 miles
Do the following points form a proportional relationship? How do you know?
(0,1), (1, 3), (2, 5)
Not proportional. Graph starts at (0,1)
With graph paper...
(included on reference page, image #4)
Graph the equation of the line:
y = 3/4x - 5
Graph should pass through (0,-5) and (8,1)
**Refer to image #3 on your reference page**
1. Does this relationship form a function? How do you know?
2. During which time interval was he going the FASTEST?
3. What do you think happened between 12 and 15 seconds?
**MUST ANSWER ALL PARTS**
1. Yes, passes the vertical line test
2. Between 8 and 12 seconds
3. He STOPPED moving/ biking