Write the ratio 12: 9 as an equivalent ratio of 4 : x.
To find the equivalent ratio of 12:9 as 4 : x, we need to find the value of x.
First, we can simplify the ratio 12:9 by dividing both numbers by their greatest common divisor, which is 3.
Dividing 12 by 3 gives us 4, and dividing 9 by 3 gives us 3.
So, the simplified ratio is 4:3.
To make an equivalent ratio of 4 : x, we need to find the value of x when the ratio is in the same proportion as the simplified ratio.
Since the simplified ratio is 4:3, we can set up the proportion 4/3 = 4/x and solve for x.
Cross-multiplying, we have 4x = 4*3.
Simplifying the right side of the equation, we get 4x = 12.
Finally, dividing both sides of the equation by 4, we find that x = 3.
Therefore, the equivalent ratio of 12:9 as 4 : x is 4 : 3.
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?
We can calculate the cost per pound of ground beef by dividing the cost by the number of pounds.
For 10 pounds at a cost of $37.50, the cost per pound is $37.50 / 10 = $3.75.
For 8 pounds at a cost of $30.00, the cost per pound is $30.00 / 8 = $3.75.
For 6 pounds at a cost of $22.50, the cost per pound is $22.50 / 6 = $3.75.
For 4 pounds at a cost of $15.00, the cost per pound is $15.00 / 4 = $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.
To determine the number of inches per foot, we need to find the value of y in the equation 4y = 48x.
Dividing both sides of the equation by 4, we get y = 12x.
This equation tells us that y represents the number of inches, and x represents the number of feet.
Therefore, the value of y (number of inches) per foot is 12.
Hence, there are 12 inches per foot.
Graph the proportional
relationship y = 22 by plotting
points.
Graph 1
(2,4) (1,2) (0,0)
Graph 2
(2,6) (1,3) (0,0)
Graph 3
(1,4) (0,0)
Graph 4
(2,1) (0,0)
Graph 1: (2,4), (1,2), (0,0)
To plot the points, we will use the coordinates given:
(2,4): This means that when x = 2, y = 4. So, plot a point at (2,4).
(1,2): When x = 1, y = 2. Plot a point at (1,2).
(0,0): When x = 0, y = 0. Plot a point at (0,0).
After plotting these three points, connect them with a straight line. The graph will look like a diagonal line that goes through the origin (0,0) and passes through the points (1,2) and (2,4).
Graph 2: (2,6), (1,3), (0,0)
Similarly, we plot the given points:
(2,6): When x = 2, y = 6. Plot a point at (2,6).
(1,3): When x = 1, y = 3. Plot a point at (1,3).
(0,0): When x = 0, y = 0. Plot a point at (0,0).
Connect these three points with a straight line. The graph will look like a diagonal line going through the origin (0,0) and passing through the points (1,3) and (2,6).
Graph 3: (1,4), (0,0)
Plotting the given points:
(1,4): When x = 1, y = 4. Plot a point at (1,4).
(0,0): When x = 0, y = 0. Plot a point at (0,0).
Connect these two points with a straight line. The graph will look like a line that passes through the origin (0,0) and the point (1,4).
Graph 4: (2,1), (0,0)
Plotting the given points:
(2,1): When x = 2, y = 1. Plot a point at (2,1).
(0,0): When x = 0, y = 0. Plot a point at (0,0).
Connect these two points with a straight line. The graph will look like a line that goes through the origin (0,0) and the point (2,1).
Note: Graphs 1, 2, and 4 represent proportional relationships. Graph 3, however, is not a proportional relationship since it does not form a straight line passing through the origin.
Which one is Graphing the proportional
relationship y = 2x by plotting
points.
The graph representing the proportional relationship y = 2x by plotting points would look like a straight line passing through the origin (0,0) with a slope of 2.
To plot the points, we can choose different values for x and calculate the corresponding y-values based on the equation y = 2x.
For example, we can take the following points:
(0,0): When x = 0, y = 2(0) = 0. So, plot a point at (0,0).
(1,2): When x = 1, y = 2(1) = 2. Plot a point at (1,2).
(2,4): When x = 2, y = 2(2) = 4. Plot a point at (2,4).
(-1,-2): When x = -1, y = 2(-1) = -2. Plot a point at (-1,-2).
(-2,-4): When x = -2, y = 2(-2) = -4. Plot a point at (-2,-4).
After plotting these points, connect them with a straight line passing through the origin (0,0). The graph will represent the proportional relationship y = 2x.
The proportional relationship between calories and ounces of soda is shown in the graph. How many calories are in 1 ounce?
(1 point)
There are calories in 1
ounce of soda.
(3,36)
To determine the number of calories in 1 ounce of soda, we need to refer to the given graph point (3,36), where 3 represents the number of ounces and 36 represents the number of calories.
As per the graph, for every 3 ounces of soda, there are 36 calories. To find out how many calories are in 1 ounce, we need to divide 36 by 3.
36 calories / 3 ounces = 12 calories.
Therefore, there are 12 calories in 1 ounce of soda.
Use similar triangles to determine the slope of the line.
(2, 6)
(1, 3)
(3, 9)
(0,0)
1
2
3
6
To determine the slope of the line using similar triangles, we can consider the points (2,6) and (1,3) on the line.
The slope represents the ratio of the change in y-coordinates to the change in x-coordinates between two points.
The change in y-coordinates is 6 - 3 = 3, and the change in x-coordinates is 2 - 1 = 1.
So, the ratio of the change in y-coordinates to the change in x-coordinates is 3/1, which simplifies to 3.
Therefore, the slope of the line is 3.
How could you write the equation of a line that would be parallel to
y = -3x - 2 but not share any
points? (1 point)
Y =3x - 2
y =3x + 8
y =-3x + 8
y=-3x-2
Since the given line is in the form y = -3x - 2, any line that has the same slope of -3 will be parallel to it. However, to ensure that the parallel line does not share any points with the given line, the y-intercept must be different.
Therefore, the correct equation of a line that is parallel to y = -3x - 2 but does not share any points is: y = -3x + 8.
Cost of Candy Bar 1
Quantity. ($) Cost
1 1.25
2 2.50
3 3.75
4 5.00
5 6.25
The cost of Candy Bar 1 is displayed in the table. The proportional relationship between the cost and quantity for Candy Bar 2 is represented by the
equation y = X. Which candy bar
is the cheapest cost per bar?
Enter 1 for Candy Bar 1. Enter 2 for Candy Bar 2.
To determine which candy bar has the cheapest cost per bar, we need to compare the cost per bar for both candy bars based on the given information.
For Candy Bar 1:
Quantity: 1
Cost: $1.25
For Candy Bar 2:
Quantity: x
Cost: x (since the equation representing the proportional relationship is y = x)
Since the cost for Candy Bar 2 is directly proportional to the quantity, the cost per bar for Candy Bar 2 is simply x divided by x, which simplifies to 1.
Comparing the cost per bar for both candy bars, we find that the cost per bar for Candy Bar 1 is $1.25, while the cost per bar for Candy Bar 2 is $1.
Therefore, Candy Bar 2 has the cheapest cost per bar. Enter 2 for Candy Bar 2.
Use the graph to derive the equation of the line in slope-intercept form.
(1,3) (0,-2)
To derive the equation of the line in slope-intercept form, we need to find the slope and the y-intercept.
Given the points: (1,3) and (0,-2)
Step 1: Find the slope (m) using the formula: (change in y) / (change in x)
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates into the formula:
m = (-2 - 3) / (0 - 1)
m = -5 / -1
m = 5
So, the slope (m) is 5.
Step 2: Find the y-intercept (b) by substituting one of the points into the slope-intercept form (y = mx + b) and solving for b.
Using the point (1,3):
3 = 5(1) + b
3 = 5 + b
b = 3 - 5
b = -2
So, the y-intercept (b) is -2.
Therefore, the equation of the line in slope-intercept form is: y = 5x - 2.
Write y - 6x = 5 in slope-
intercept form
To write the equation y - 6x = 5 in slope-intercept form (y = mx + b), we need to isolate the y-term.
Rearranging the given equation:
y = 6x + 5
Now the equation is in slope-intercept form, where the slope (m) is 6 and the y-intercept (b) is 5.
Therefore, y - 6x = 5 can be written in slope-intercept form as y = 6x + 5.