Determine it 7x^2 + y = 5 is a linear or nonlinear function. (1 point)
• The graph of the function 7x^2 + y = 5 is not a straight line.
• The function 7x^2 + y = 5 is a linear function.
• The function 7x^2 + y = 5 is a nonlinear function
• There is not enough information to determine if 7x^2 + y = 5 is a linear or nonlinear function.
11 answers
The function 7x^2 + y = 5 is a nonlinear function because it contains a quadratic term (7x^2).
Determine the initial value and the rate of change in the following description.
Last year, Joshua's tomato plant reached a maximum height of 2 feet. He is growing another tomato plant this year, and he is tracking its growth. The plant's height today is 10 inches, and it grows 1.7 inches each day.
(1 point)
The initial value is b=? and the rate of change is m = ?
Last year, Joshua's tomato plant reached a maximum height of 2 feet. He is growing another tomato plant this year, and he is tracking its growth. The plant's height today is 10 inches, and it grows 1.7 inches each day.
(1 point)
The initial value is b=? and the rate of change is m = ?
The initial value (b) in this case is the height of the tomato plant when Joshua started tracking its growth, which is 2 feet. We need to convert this to inches for consistency with the other measurements:
2 feet = 24 inches
Therefore, the initial value (b) is 24 inches.
The rate of change (m) is the growth rate of the tomato plant, which is 1.7 inches each day. So, the rate of change (m) is 1.7 inches per day.
2 feet = 24 inches
Therefore, the initial value (b) is 24 inches.
The rate of change (m) is the growth rate of the tomato plant, which is 1.7 inches each day. So, the rate of change (m) is 1.7 inches per day.
Use the table to answer the question.
х У
2 22
8 25
Determine the rate of change and the initial value of the linear function given here as a table of values.
(1 point)
The rate of change is m = ?, and the initial value is b = ?
х У
2 22
8 25
Determine the rate of change and the initial value of the linear function given here as a table of values.
(1 point)
The rate of change is m = ?, and the initial value is b = ?
To find the rate of change (m) of a linear function from a table of values, we need to calculate the change in the y-values divided by the change in the x-values.
For the given table of values:
When x changes from 2 to 8, y changes from 22 to 25.
Change in x: 8 - 2 = 6
Change in y: 25 - 22 = 3
Rate of change (m) = Change in y / Change in x
Rate of change (m) = 3 / 6
Rate of change (m) = 0.5
Therefore, the rate of change (m) of the linear function is 0.5.
Now, to find the initial value (b), we can choose any point from the table. Let's use the point (2, 22) in this case.
So, when x = 2, y = 22.
Putting this point into the linear function equation y = mx + b:
22 = 0.5(2) + b
22 = 1 + b
b = 22 - 1
b = 21
Therefore, the initial value (b) of the linear function is 21.
For the given table of values:
When x changes from 2 to 8, y changes from 22 to 25.
Change in x: 8 - 2 = 6
Change in y: 25 - 22 = 3
Rate of change (m) = Change in y / Change in x
Rate of change (m) = 3 / 6
Rate of change (m) = 0.5
Therefore, the rate of change (m) of the linear function is 0.5.
Now, to find the initial value (b), we can choose any point from the table. Let's use the point (2, 22) in this case.
So, when x = 2, y = 22.
Putting this point into the linear function equation y = mx + b:
22 = 0.5(2) + b
22 = 1 + b
b = 22 - 1
b = 21
Therefore, the initial value (b) of the linear function is 21.
A pan with four eggs weighs 18 ounces. A pan with eight eggs weighs 24 ounces. What is the weight of the pan? (1 point)
? OZ
? OZ
Let's denote the weight of the pan as "p" ounces.
From the given information:
4 eggs + pan = 18 ounces
8 eggs + pan = 24 ounces
Let's subtract the weight of the pan from each total weight to determine the weight of the eggs alone:
18 - p = Weight of 4 eggs
24 - p = Weight of 8 eggs
The difference in weight for the eggs when increasing from 4 to 8 eggs is:
(24 - p) - (18 - p) = 24 - 18 = 6 ounces
This represents the additional weight of adding 4 more eggs.
Since each additional egg weighs the same amount when adding 4 eggs, we can determine the weight of one egg by dividing the additional weight by the number of additional eggs:
6 ounces / 4 eggs = 1.5 ounces per egg
Therefore, each egg weighs 1.5 ounces. To find the weight of the pan, we substitute this back into the initial equations:
4 eggs + (1.5 ounces per egg * 4 eggs) = 18 ounces
4 eggs + 6 ounces = 18 ounces
4 eggs = 12 ounces (weight of the eggs alone)
Therefore, the weight of the pan is the total weight minus the weight of the eggs:
18 - 12 = 6 ounces
The weight of the pan is 6 ounces.
From the given information:
4 eggs + pan = 18 ounces
8 eggs + pan = 24 ounces
Let's subtract the weight of the pan from each total weight to determine the weight of the eggs alone:
18 - p = Weight of 4 eggs
24 - p = Weight of 8 eggs
The difference in weight for the eggs when increasing from 4 to 8 eggs is:
(24 - p) - (18 - p) = 24 - 18 = 6 ounces
This represents the additional weight of adding 4 more eggs.
Since each additional egg weighs the same amount when adding 4 eggs, we can determine the weight of one egg by dividing the additional weight by the number of additional eggs:
6 ounces / 4 eggs = 1.5 ounces per egg
Therefore, each egg weighs 1.5 ounces. To find the weight of the pan, we substitute this back into the initial equations:
4 eggs + (1.5 ounces per egg * 4 eggs) = 18 ounces
4 eggs + 6 ounces = 18 ounces
4 eggs = 12 ounces (weight of the eggs alone)
Therefore, the weight of the pan is the total weight minus the weight of the eggs:
18 - 12 = 6 ounces
The weight of the pan is 6 ounces.
Manuel got a new job and was given a hiring bonus along with his monthly salary. His earnings after x months are modeled by the
function f(x) = 1,500x + 300. How much did he receive as a hiring bonus? (1 point)
function f(x) = 1,500x + 300. How much did he receive as a hiring bonus? (1 point)
In the given function f(x) = 1,500x + 300, the hiring bonus is represented by the constant term 300.
Therefore, Manuel received a hiring bonus of $300.
Therefore, Manuel received a hiring bonus of $300.
The equation y = mx + 6 defines what type of function? (1 point)
• an initial value function
• a nonlinear function
• а linear function
• a slope function
• an initial value function
• a nonlinear function
• а linear function
• a slope function
The equation y = mx + 6 defines a linear function.
1 answer