To determine if (1, -4) is a solution to the equation y = -2x, substitute the x and y values from the point (1, -4) into the equation and check if it is true.
Substituting, we get:
-4 = -2(1)
Simplifying, we have:
-4 = -2
Since -4 is not equal to -2, the equation is not true. Therefore, (1, -4) is not a solution to the equation y = -2x.
Is (1, −4) a solution to the equation y = −2x?
11 answers
(4, 0), (3, −1), (6, 3), (2, −4)
Which are solutions to y = x − 4? Choose all correct answers.
Which are solutions to y = x − 4? Choose all correct answers.
To determine which points are solutions to the equation y = x - 4, substitute the x and y values from each point into the equation and check if it is true.
Substituting for each point:
1. For (4, 0):
0 = 4 - 4
0 = 0
The equation is true, so (4, 0) is a solution.
2. For (3, -1):
-1 = 3 - 4
-1 = -1
The equation is true, so (3, -1) is a solution.
3. For (6, 3):
3 = 6 - 4
3 = 2
The equation is not true, so (6, 3) is not a solution.
4. For (2, -4):
-4 = 2 - 4
-4 = -2
The equation is not true, so (2, -4) is not a solution.
Therefore, the correct answers are:
- (4, 0)
- (3, -1)
Substituting for each point:
1. For (4, 0):
0 = 4 - 4
0 = 0
The equation is true, so (4, 0) is a solution.
2. For (3, -1):
-1 = 3 - 4
-1 = -1
The equation is true, so (3, -1) is a solution.
3. For (6, 3):
3 = 6 - 4
3 = 2
The equation is not true, so (6, 3) is not a solution.
4. For (2, -4):
-4 = 2 - 4
-4 = -2
The equation is not true, so (2, -4) is not a solution.
Therefore, the correct answers are:
- (4, 0)
- (3, -1)
There are 8 crackers in 1 serving, 16 crackers in 2 servings, 24 crackers in 3 servings, and so on. How many crackers are in a box of 12 servings?
To find the total number of crackers in a box of 12 servings, we can use the information given about the number of servings and the number of crackers per serving.
We can observe that the number of crackers increases by 8 for each additional serving. So, for each serving, we can calculate the number of crackers by multiplying the number of servings by 8.
To find the number of crackers in a box of 12 servings, we can multiply 12 by 8:
12 servings * 8 crackers per serving = 96 crackers
Therefore, there are 96 crackers in a box of 12 servings.
We can observe that the number of crackers increases by 8 for each additional serving. So, for each serving, we can calculate the number of crackers by multiplying the number of servings by 8.
To find the number of crackers in a box of 12 servings, we can multiply 12 by 8:
12 servings * 8 crackers per serving = 96 crackers
Therefore, there are 96 crackers in a box of 12 servings.
Give an example of an open equation.
An example of an open equation is:
2x + 3 = y
In this equation, the variables x and y are not assigned specific values, so the equation is open and can have multiple solutions depending on the values assigned to x and y.
2x + 3 = y
In this equation, the variables x and y are not assigned specific values, so the equation is open and can have multiple solutions depending on the values assigned to x and y.
How can you use an equation to make a prediction from a pattern?
To use an equation to make a prediction from a pattern, you need to identify the relationship between the pattern's variables and formulate an equation that describes that relationship. Once you have the equation, you can use it to make predictions about future values or missing values in the pattern.
Here are the steps to use an equation for prediction from a pattern:
1. Identify the variables: Determine which variables are involved in the pattern you are analyzing. For example, if you are studying a sequence of numbers, your variables may be the term number (n) and the corresponding value (a).
2. Analyze the pattern: Observe the relationship between the variables and examine how they change throughout the pattern. Look for any repeating patterns or trends.
3. Formulate an equation: Based on your analysis, create an equation that represents the relationship between the variables. This equation should capture the pattern and allow you to calculate missing or future values.
4. Test the equation: Verify the equation's accuracy by checking if it correctly predicts values that you already know. Substitute known values into the equation and see if it gives the expected result. If it does, you can have confidence in the equation's predictive power.
5. Make predictions: Once you have validated the equation, you can use it to predict future values or fill in missing values in the pattern. By plugging in appropriate values into the equation, you can calculate the predicted outcome.
Using an equation to make predictions from a pattern allows you to extend the pattern beyond the observed data and make informed guesses about what may occur next based on the underlying relationship.
Here are the steps to use an equation for prediction from a pattern:
1. Identify the variables: Determine which variables are involved in the pattern you are analyzing. For example, if you are studying a sequence of numbers, your variables may be the term number (n) and the corresponding value (a).
2. Analyze the pattern: Observe the relationship between the variables and examine how they change throughout the pattern. Look for any repeating patterns or trends.
3. Formulate an equation: Based on your analysis, create an equation that represents the relationship between the variables. This equation should capture the pattern and allow you to calculate missing or future values.
4. Test the equation: Verify the equation's accuracy by checking if it correctly predicts values that you already know. Substitute known values into the equation and see if it gives the expected result. If it does, you can have confidence in the equation's predictive power.
5. Make predictions: Once you have validated the equation, you can use it to predict future values or fill in missing values in the pattern. By plugging in appropriate values into the equation, you can calculate the predicted outcome.
Using an equation to make predictions from a pattern allows you to extend the pattern beyond the observed data and make informed guesses about what may occur next based on the underlying relationship.
Pizza costs $1.50 per slice. Use a table and an equation to represent the relationship between the number of slices of pizza bought and the total cost.
To represent the relationship between the number of slices of pizza bought and the total cost, we can create a table and an equation.
Table:
Number of Slices | Total Cost
--------------------------------
1 | $1.50
2 | $3.00
3 | $4.50
...
Equation:
Let x represent the number of slices of pizza bought, and let y represent the total cost.
The equation that represents the relationship between the number of slices and the total cost is:
y = 1.50x
In this equation, y represents the dependent variable (total cost), and x represents the independent variable (number of slices). The coefficient 1.50 represents the cost per slice.
Using this equation, you can easily calculate the total cost (y) by multiplying the number of slices (x) by the cost per slice (1.50). For example, if you buy 5 slices of pizza, the total cost would be:
y = 1.50 * 5
y = $7.50
Thus, the equation allows you to calculate the total cost based on the number of slices purchased.
Table:
Number of Slices | Total Cost
--------------------------------
1 | $1.50
2 | $3.00
3 | $4.50
...
Equation:
Let x represent the number of slices of pizza bought, and let y represent the total cost.
The equation that represents the relationship between the number of slices and the total cost is:
y = 1.50x
In this equation, y represents the dependent variable (total cost), and x represents the independent variable (number of slices). The coefficient 1.50 represents the cost per slice.
Using this equation, you can easily calculate the total cost (y) by multiplying the number of slices (x) by the cost per slice (1.50). For example, if you buy 5 slices of pizza, the total cost would be:
y = 1.50 * 5
y = $7.50
Thus, the equation allows you to calculate the total cost based on the number of slices purchased.