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.
1
Determine if 7x2+y=5 is a linear or nonlinear function.(1 point)
Responses
There is not enough information to determine if 7x2+y=5 is a linear or nonlinear function.
There is not enough information to determine if , 7 x squared plus y equals 5, is a linear or nonlinear function.
The graph of the function 7x2+y=5 is not a straight line.
The graph of the function , 7 x squared plus y equals 5, is not a straight line.
The function 7x2+y=5 is a linear function.
The function , 7 x squared plus y equals 5, is a linear function.
The function 7x2+y=5 is a nonlinear function.
The function 7x2+y=5 is a nonlinear function.
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=.
Use the table to answer the question.
x y
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=
.
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. A downward slanting line is plotted on the coordinate plane. The downward slanting line with arrows on both ends passes through the following closed points: left parenthesis negative 3 comma 4 right parenthesis, left parenthesis 0 comma 3 right parenthesis, left parenthesis 3 comma 2 right parenthesis, and left parenthesis 6 comma 1 right parenthesis.
Determine the initial value and the rate of change of the linear function as given in the graph. Round the answer to three decimal places as needed.
(1 point)
The initial value is
, and the rate of change is
.
Use the image to answer the question.
A coordinate plane shows quadrant 4 with the x-axis, labeled as minutes, ranging from 0 to 6 in increments of 1 and y-axis, labeled as elevation in feet, ranging from 0 to negative 110 in decrements of 10. A ray with arrow at the bottom end points downward from the origin. The coordinates that it passes through are left parenthesis 0 comma 0 right parenthesis, left parenthesis 3 comma negative 60 right parenthesis, and left parenthesis 5 comma negative 100 right parenthesis.
The graph shows the elevation of a deep-sea diver in relation to minutes passed. Using any two points on the graph, what is the rate of change in the diver’s elevation?
(1 point)
feet per minute
Use the image to answer the question.
A coordinate plane shows quadrant 4 with the x-axis, labeled as minutes, ranging from 0 to 6 in increments of 1 and y-axis, labeled as elevation in feet, ranging from 0 to negative 110 in decrements of 10. A ray with arrow at the bottom end points downward from the origin. The coordinates that it passes through are left parenthesis 0 comma 0 right parenthesis, left parenthesis 3 comma negative 60 right parenthesis, and left parenthesis 5 comma negative 100 right parenthesis.
The graph shows the elevation of a deep-sea diver in relation to minutes passed. Using any two points on the graph, what is the rate of change in the diver’s elevation?
(1 point)
negative 110
feet per minute
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.
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)
$
The equation y=mx+b defines what type of function?(1 point)
Responses
a slope function
a slope function
a linear function
a linear function
a nonlinear function
a nonlinear function
an initial value function
The equation y=mx+b defines what type of function?(1 point)
a slope function
a linear function
a nonlinear function
an initial value function
The equation y= mx+b defines what type of function?
a slope function
a linear function
a nonlinear function
an initial value function
Use the table to answer the question.
x y
6 16
15 43
Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y=mx+b form.
(1 point)
We can use the formula for the slope of a line to find the slope of the line passing through the given points:
slope = (y2 - y1) / (x2 - x1)
= (43 - 16) / (15 - 6)
= 2.7
The equation of the line can be written in slope-intercept form as:
y = mx + b, where m is the slope and b is the y-intercept.
To find b, we can substitute the coordinates of one of the points into the equation:
16 = (2.7)(6) + b
Simplifying and solving for b, we get:
b = -0.2
Therefore, the equation of the linear function that models the relationship shown in the table is:
y = 2.7x - 0.2
Last year, Alayah ordered 4 cubic yards of soil and spent $220. This year, she orders 7 cubic yards of soil and spends $340. Write the equation of the linear function that models the relationship between the number of cubic yards of soil ordered and the total cost. Enter your answer in y=mx+b form.(1 point)
We can use the formula for the slope of a line to find the rate of change in the total cost with respect to the number of cubic yards of soil ordered:
slope = (change in y) / (change in x)
= (340 - 220) / (7 - 4)
= 40
The slope represents the additional cost per cubic yard of soil ordered.
To find the y-intercept, we can substitute the coordinates of one of the points into the equation:
220 = (40)(4) + b
Simplifying and solving for b, we get:
b = 80
Therefore, the equation of the linear function that models the relationship between the number of cubic yards of soil ordered and the total cost is:
y = 40x + 80
Here, x is the number of cubic yards of soil ordered, y is the total cost in dollars, 40 is the rate of change in cost per cubic yard of soil ordered, and 80 is the initial cost when no soil is ordered.
Use the table to answer the question.
Day of the Week Number of Children in the Car
Sunday 2
Monday 4
Tuesday 4
Wednesday 3
Thursday 4
Friday 3
Saturday 0
Describe the meaning of the word function in math. Then consider the table. Why does this table show a function?
(2 points)
In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output.
In the given table, the "Day of the Week" is the input (domain) and the "Number of Children in the Car" is the output (range). Each input (day of the week) has only one corresponding output (number of children in the car).
Therefore, this table shows a function because each input (day of the week) is related to exactly one output (number of children in the car).