Proportional VS Non Proportional
Which of the following tables represents a non-proportional relationship between x and y?
A) x: 1, 2, 3 y: 5, 10, 15
B) x: 2, 4, 6 y: 7, 11, 15
C) x: 0, 5, 10 y: 0, 10, 20
D) x: 3, 6, 9 y: 1, 2, 3
B) x: 2, 4, 6 y: 7, 11, 15.
NonProportional - y/x is not constant, and cannot pass through origin.
Which is the smallest value?
A) 4.5 X 10^(- 3)
B) 6.1 X 10^(- 4)
C) 2.9 X 10^(- 3)
D) 8.7 X 10(- 5)
D) 8.7 X 10(- 5)
A water tank holds 500 gallons but is leaking at a rate of 5 gallons per hour. Which equation represents the relationship between the total gallons in the tank (y) and the number of hours (x)?
A) y = 500x - 5
B) y = 500 + 5x
C) y = 500 - 5x
D) y = - 500x + 5
C) y = 500 - 5x
A right triangle has legs with lengths of 9cm and 12cm. What is the length of the hypotenuse in centimeters.
15 cm
What are the slope and y-intercept of the equation y = - 3x + 8?.
slope: -3
y-intercept: 8
A linear function is graphed on a coordinate plane. If the graph is a straight line that passes through the points (2, 10) and (4, 20), which statement is true?
A) The relationship is non-proportional because the line does not pass through the origin.
B) The relationship is proportional because the ratio of y to x is constant at 5:1.
C) The relationship is non-proportional because the y-intercept is 5.
D) The relationship is proportional because the line has a positive slope.
B) The relationship is proportional because the ratio of y to x is constant at 5:1.
Which number is not written in proper scientific notation?
A) 6.7 X 10^(2)
B) 5.5 X 10^(- 4)
C) 3 X 10^(10)
D) 15.5 X 10^(4)
D) 15.5 X 10^(4)
A linear relationship has a slope of 3 and a y-intercept of - 4. If x = 10, what is the value of y?
A) 26
B) 34
C) 14
D) - 14
A) 26
Triangle ABC has vertices A(1, 2), B(3, 1), and C(2,4). If the triangle is dilated by a scale factor of 2.5 with the origin as the center of dilation, what are the new coordinates of vertex C'?
C'(5, 10)
If $1,500 is invested at a simple interest rate of 4% for 3 years, how much interest is earned?
$180
Which situation describes a proportional relationship?
A) gym membership costs $25 per month plus a $50 sign-up fee.
B) A taxi driver charges a flat fee of $3 and then $.50 per mile.
C) A water tank contains 100 gallons and leaks at a rate of 2 gallons per hour.
D) An apple juice recipe requires 3 cups of water for every 1 cup of concentrate.
D) An apple juice recipe requires 3 cups of water for every 1 cup of concentrate.
The population of a city is about 4,500,000. How is this number written in scientific notation?
4.5 X 10^(6)
Using the vertical line test, which of the following shapes cannot be a function?
A) A diagonal line
B) A horizontal line
C) A vertical line
D) A V-shaped line
C (A vertical line fails the vertical line test because one x-value has infinite y-values).
A trapezoid is rotated 90 degrees clockwise about the origin. If a vertex was originally at (x, y), what quadrant is its new location at (x', y')?
Quadrant 4
A cylinder has a radius of 3 and a height of 10. What is its volume in terms of pi?
90 pi
Look at the four equations below. Which equation represents a non-proportional linear relationship?
A) y = 2/3 x
B) y = - 4x
C) y = x + 1.5
D) y = 0.5x
C) y = x + 1.5.
A proportional linear relationship is a specific type of function that passes through the origin (0,0).
The density of a substance is 0.00000084 How is this number written in scientific notation?
8.4 X 10^(- 7)
A gym charges a one-time membership fee of $50 and $15 per month. What does the "slope" represent in this scenario?
A) The total cost after 1 year.
B) The initiation fee.
C) The monthly cost of $15
D) The total number of members
C (Rate of change = slope)
Triangle XYZ is rotated 180 degrees and then translated 3 units down. Which statement is true?
A) The new triangle is similar but not congruent.
B) The new triangle is congruent to the original.
C) The angles of the new triangle are larger.
D) The side lengths have changed.
B (Rotations and translations are rigid transformations; they preserve size and shape.)
A rectangular prism has a length of 10, width of 4, and height of 5. What is the total surface area?
220
A technician charges a flat service fee of $45 plus $30 per hour for repairs.
Part A: Write an equation in y = mx + b form to represent the total cost (y) for (x) hours of work.
Part B: Is this relationship proportional or non-proportional? Explain why.
Part A: y = 30x + 45
Part B: Non-proportional because of the 45 flat fee (the y-intercept is not 0).
A scientist estimated the distance between two stars to be 3.2 X 10^(5) light-years. What is this distance in standard form?
320,000 (Move decimal 5 places right)
A graph shows a line passing through (0, 3) and (2,7). What is the equation of this line in y = mx + b format?
y = 2x + 3
A cone-shaped paper cup has a diameter of 6cm and a height of 8cm. What is the volume of the cone in cubic centimeters?
75.40 cm^3
Solve for x: 3(x - 2) = 2x + 10.
x = 16