Determine if the relation y=4x−1 is a function by first graphing the relation, then applying the vertical line test. Enter 1 if the relation is a function. Enter 2 if the relation is not a function.(1 point)
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1: 1
2: The function 7x^2+y=5 is a nonlinear function
3: 1
4: B = 10, M = 1.7
5: M = 1/2, B = 21
6: 3, -0.333
7: -20
8: 12
9: 300
10: a linear function
11: y=3x -2
12: y=40x+60
13: 2
14: A (the one that cuts though 2, twos on the line)
15: A function is a relationship or expression involving one or more variables.
The rate of change is m = (y2 - y1) / (x2 - x1) = (25 - 22) / (8 - 2) = 0.5
The initial value is b = y1 - m * x1 = 22 - 0.5 * 2 = 21
Therefore, the rate of change is m = 0.5 and the initial value is b = 21.
To find the initial value and the rate of change of the linear function, we need to determine the slope and y-intercept of the line.
We can choose any two points on the line to calculate the slope using the formula:
slope = (y2 - y1) / (x2 - x1)
Let's choose the points (-3,4) and (0,3):
slope = (3 - 4) / (0 - (-3)) = -1/3
Now, we can use the slope-intercept form of a linear equation to find the y-intercept:
y = mx + b
where m is the slope and b is the y-intercept.
Using the point (-3,4) and the slope -1/3, we can substitute the values into the equation:
4 = (-1/3)(-3) + b
4 = 1 + b
b = 3
Therefore, the initial value is 3 and the rate of change is -1/3.
Rounding to three decimal places gives:
The initial value is 3 and the rate of change is -0.333.
To find the weight of the pan, we need to subtract the weight of the eggs from the total weight of the pan and eggs.
Let x be the weight of the pan.
From the first sentence, we know that 4 eggs weigh 18 - x ounces.
From the second sentence, we know that 8 eggs weigh 24 - x ounces.
Setting these two expressions equal to each other, we get:
18 - x = 24 - x/2
Simplifying and solving for x, we get:
x = 12 ounces
Therefore, the weight of the pan is 12 ounces.
The constant term in the given function represents the hiring bonus.
f(x) = 1500x + 300
Here, 1500x represents the monthly salary and 300 represents the hiring bonus.
Therefore, Manuel received a hiring bonus of $300.
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=
.
The initial value is b=10 inches, and the rate of change is m=1.7 inches per day.
We can use the two given points (0,0) and (5, -100) to calculate the rate of change in the diver's elevation using the formula:
rate of change = (change in elevation) / (change in time)
Using (0,0) and (5,-100), we get:
change in elevation = -100 - 0 = -100 feet
change in time = 5 - 0 = 5 minutes
Substituting these values into the formula, we get:
rate of change = (-100 feet) / (5 minutes)
Simplifying, we get:
rate of change = -20 feet per minute
Therefore, the rate of change in the diver's elevation is -20 feet per minute.
The answer is incorrect.
The correct answer is:
We can use the two given points (0,0) and (5, -100) to calculate the rate of change in the diver's elevation using the formula:
rate of change = (change in elevation) / (change in time)
Using (0,0) and (5,-100), we get:
change in elevation = -100 - 0 = -100 feet
change in time = 5 - 0 = 5 minutes
Substituting these values into the formula, we get:
rate of change = (-100 feet) / (5 minutes)
Simplifying, we get:
rate of change = -20 feet per minute
Therefore, the rate of change in the diver's elevation is -20 feet per minute.