Question

Which of the following is a point on the graph as described by the function y=(2x+1)2−4 ?(1 point) Responses (1,2) left parenthesis 1 comma 2 right parenthesis (0,−2) left parenthesis 0 comma negative 2 right parenthesis (−1,−5) left parenthesis negative 1 comma negative 5 right parenthesis (−1,−3)

Answer 1

To determine which point is on the graph of the function \( y = (2x + 1)^2 - 4 \), we can substitute the x-coordinates of the given points into the function and see if we get the corresponding y-coordinates.

1. For the point \( (1, 2) \): \[ y = (2(1) + 1)^2 - 4 = (2 + 1)^2 - 4 = 3^2 - 4 = 9 - 4 = 5 \] This point does not lie on the graph since \( 5 \neq 2 \).

2. For the point \( (0, -2) \): \[ y = (2(0) + 1)^2 - 4 = (0 + 1)^2 - 4 = 1^2 - 4 = 1 - 4 = -3 \] This point does not lie on the graph since \( -3 \neq -2 \).

3. For the point \( (-1, -5) \): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] This point does not lie on the graph since \( -3 \neq -5 \).

4. For the point \( (-1, -3) \): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] This point lies on the graph since \( -3 = -3 \).

Therefore, the point that is on the graph is \( (-1, -3) \).

Answer 2

Use the image to answer the question. Which of the following are the two quantities whose functional relationship is described in the given graph? (1 point) Responses The two quantities are the x -values and the y -values. The two quantities are the x -values and the y -values. The two quantities are the average rainfall in inches and the years. The two quantities are the average rainfall in inches and the years. The two quantities are inches and months of the year. The two quantities are inches and months of the year. The two quantities are the average rainfall in inches and the month of the year. The two quantities are the average rainfall in inches and the month of the year. Skip to navigation

Answer 3

Without seeing the specific graph, I can provide guidance based on common types of graphs that relate two quantities.

• If the graph typically represents how rainfall varies over a period, it would likely be a relationship between the average rainfall in inches and the years or the average rainfall in inches and the month of the year.
• If the graph instead presents a relationship that spans each month within a year, it might represent the average rainfall in inches and the month of the year.

Given these interpretations, if the graph indeed shows average rainfall over specific months, then the most appropriate response would be:

The two quantities are the average rainfall in inches and the month of the year.

If it spans multiple years, then the alternative might be suitable. However, based on your details, this would be my best educated guess.

Please review the graph and select the option that aligns best with its presentation of information!

Answer 4

Use the image to answer the question. Consider the given graph. Analyze the intervals during the months from June to December and describe how that corresponds to the average rainfall. (1 point) Responses the average rainfall increases the average rainfall increases the average rainfall increases then decreases the average rainfall increases then decreases the average rainfall remains constant the average rainfall remains constant the average rainfall decreases the average rainfall decreases Skip to navigation

Answer 5

Without seeing the specific graph, I will provide guidance based on typical behaviors of rainfall patterns during the months from June to December.

1. If the average rainfall is consistently going up from June to December, then the response would be: the average rainfall increases.

2. If the average rainfall increases for a certain period (e.g., June to September) and then starts to decrease thereafter (e.g., October to December), the appropriate response would be: the average rainfall increases then decreases.

3. If the average rainfall stays roughly the same through the months from June to December, it would be: the average rainfall remains constant.

4. If the average rainfall steadily decreases across these months, it would be: the average rainfall decreases.

To give the most accurate response, please consider the specific trends shown in the graph for the months from June to December. If you can summarize what the graph shows regarding the average rainfall in that period, I can help you choose the best answer!

Answer 6

Determine the rate of change in the following description. In Ms. Katy’s math class, a homework assignment is worth 100 points. If students turn the homework in late, there will be a deduction of 5 points per day. (1 point) Responses m=−100 m equals negative 100 m=5 m equals 5 m=100 m equals 100 m=−5

Answer 7

The scenario describes a homework assignment worth 100 points that incurs a deduction of 5 points for each day that it is turned in late.

To determine the rate of change, we see that for each day late, the total points decrease by 5. This can be expressed as:

• Rate of change = change in points / change in time (days late)

Since points are deducted, the change is negative. Thus, the rate of change is \(-5\) points per day.

Therefore, the correct response is:

m = -5.

Answer 8

Use the table to answer the question. x y 2.6 −6 3.2 3 Determine the rate of change of the linear function given as a table of values. (1 point) Responses m=−5 m equals negative 5 m=0.067 m equals 0.067 m=−15 m equals negative 15 m=15

Answer 9

To find the rate of change (slope) of the linear function represented by the table of values, we can use the formula for the slope \( m \) given two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

From the table, we have the points:

• \( (2.6, -6) \)
• \( (3.2, 3) \)

Now we can apply the values to the slope formula:

1. Assign the points:

   • \( x_1 = 2.6 \)
   • \( y_1 = -6 \)
   • \( x_2 = 3.2 \)
   • \( y_2 = 3 \)

2. Substitute into the slope formula:

\[ m = \frac{3 - (-6)}{3.2 - 2.6} \]

3. Simplify:

\[ m = \frac{3 + 6}{3.2 - 2.6} = \frac{9}{0.6} \]

4. Divide:

\[ m = \frac{9}{0.6} = 15 \]

Thus, the rate of change of the linear function given in the table is:

m = 15.

Answer 10

Find the initial value of the linear function, given that the rate of change is m=−47 , and (14,3) is an (x,y) value of the linear function.(1 point) Responses b=12.29 b equals 12.29 b=−5 b equals negative 5 b=15.71 b equals 15.71 b=11

Answer 11

To find the initial value (or y-intercept) of a linear function given the rate of change (slope) and a point on the function, we can use the point-slope form of the linear equation, which is:

\[ y = mx + b \]

Where:

• \( y \) is the output (dependent variable)
• \( m \) is the slope (rate of change)
• \( x \) is the input (independent variable)
• \( b \) is the y-intercept (initial value)

Given:

• The slope \( m = -47 \)
• The point \( (14, 3) \), where \( x = 14 \) and \( y = 3 \)

We can substitute these values into the equation to find \( b \):

\[ 3 = -47(14) + b \]

Now, calculate \( -47(14) \):

\[ -47(14) = -658 \]

Substituting this back into the equation:

\[ 3 = -658 + b \]

To solve for \( b \), add 658 to both sides:

\[ b = 3 + 658 \] \[ b = 661 \]

There seems to be a misunderstanding with the provided answer options since none of them match the calculated value of \( b = 661 \).

Please check for any other errors or if there's additional context, as the standard calculation based on the slope and given point leads to an initial value of 661. If any numbers or context have been misreported, please clarify!