Write the ratio 12:9 as an equivalent ratio of 4:x. Write your answer as a complete ratio.
4:3
Which of the following, Option 1 or Option 2, is a proportion?
Option 1: 5/6=15/18
Option 2: 5/6=20/18
Option 1 is a proportion because when you cross multiply, you get 5 * 18 = 6 * 15, which is 90 = 90. This shows the equality of both sides.
Option 2 is not a proportion as when you cross multiply, you get 5 * 18 = 6 * 20, which is 90 = 120, and this does not hold true.
Therefore, Option 1 (5/6 = 15/18) is the proportion.
Use the table to answer the question.
Cost of Ground Beef
Pounds Cost
($)
10 37.50
8 30.00
6 22.50
4 15.00
What is the cost for 1 pound of ground beef?
To find the cost for 1 pound of ground beef, we can look at the table and see the relationship between the pounds and the cost.
From the table:
- When 10 pounds costs $37.50, the cost for 1 pound of ground beef is 37.50 / 10 = $3.75.
Therefore, the cost for 1 pound of ground beef is $3.75.
There are 48 inches in 4 feet, which is represented by the equation 4y=48x. Determine the number of inches per foot.
The equation given is 4y = 48x.
To determine the number of inches per foot, we need to isolate y, which represents the number of inches per foot.
Dividing both sides of the equation by 4 to solve for y, we get:
y = 48x / 4
y = 12x
Therefore, the number of inches per foot is 12 inches.
Use the image to answer the question.
An illustration shows a coordinate plane with 4 quadrants. The x-axis ranges from negative 9 to 9 in one unit increments, and the y-axis ranges from negative 11 to 11 in one unit increments. A line is graphed on the plane. An upward slanting line passes through points plotted at left parenthesis 1 comma 5 right parenthesis and left parenthesis 2 comma 10 right parenthesis.
The graph shows the proportional relationship. Derive the equation of the line y=mx through the origin.
To find the equation of the line through the points (1,5) and (2,10) that passes through the origin, we first determine the slope of the line using the two points.
The slope (m) of the line passing through two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
Substitute the values (1,5) and (2,10) into the equation to calculate the slope:
m = (10 - 5) / (2 - 1)
m = 5 / 1
m = 5
Since the line passes through the origin, it means it intersects the y-axis at (0,0), indicating the y-intercept is 0.
Therefore, the equation of the line passing through the origin with the slope of 5 is:
y = 5x
Graph the proportional relationship y=2x by plotting points.
A. A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 3 right parenthesis, and left parenthesis 2 comma 6 right parenthesis.
B. A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 2 right parenthesis, and left parenthesis 2 comma 4 right parenthesis.
C. A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 2 comma 1 right parenthesis.
D. A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 1 comma 4 right parenthesis.