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Using the equation t=13n+7

, create a sequence that corresponds from the 1st term to the 5th term.(1 point)
Responses

21, 22, 23, 24, 25
21, 22, 23, 24, 25

13, 26, 39, 50, 65
13, 26, 39, 50, 65

20, 33, 39, 59, 72
20, 33, 39, 59, 72

20, 33, 46, 59, 72

9 answers

To create a sequence based on the equation \( t = 13n + 7 \), we will substitute values of \( n \) from 1 to 5.

  1. For \( n = 1 \): \[ t = 13(1) + 7 = 13 + 7 = 20 \]

  2. For \( n = 2 \): \[ t = 13(2) + 7 = 26 + 7 = 33 \]

  3. For \( n = 3 \): \[ t = 13(3) + 7 = 39 + 7 = 46 \]

  4. For \( n = 4 \): \[ t = 13(4) + 7 = 52 + 7 = 59 \]

  5. For \( n = 5 \): \[ t = 13(5) + 7 = 65 + 7 = 72 \]

Thus, the sequence corresponding from the 1st term to the 5th term is: 20, 33, 46, 59, 72

So, the correct response is: 20, 33, 46, 59, 72.

Create a formula for the points (1,5)
, (2,7)
, (3,9)
, and (4,11)
.(1 point)
Responses

y=−2x+3
y equals negative 2 x plus 3

y=−2x−3
y equals negative 2 x minus 3

y=2x+3
y equals 2 x plus 3

y=2x−3

To determine a formula for the points (1,5), (2,7), (3,9), and (4,11), we can first identify the pattern in the \(y\)-values as \(x\) changes.

Looking at the points:

  • When \(x = 1\), \(y = 5\)
  • When \(x = 2\), \(y = 7\)
  • When \(x = 3\), \(y = 9\)
  • When \(x = 4\), \(y = 11\)

We can see that as \(x\) increases by 1, \(y\) increases by 2. This indicates a linear relationship with a slope of 2.

Let’s assume the equation of the line is in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

  1. Finding the slope (\(m\)): \[ m = \frac{change ; in ; y}{change ; in ; x} = \frac{7 - 5}{2 - 1} = 2 \]

  2. Finding the y-intercept (\(b\)): We can use one of the points. Let’s use (1, 5). \[ 5 = 2(1) + b \ 5 = 2 + b \ b = 3 \]

Putting it all together, the equation is: \[ y = 2x + 3 \]

Thus, the correct response is: y = 2x + 3.

When discussing the key features of a linear graph, which of the following statements is true?(1 point)
Responses

The points always have positive values.
The points always have positive values.

The rate of change can vary along the graph.
The rate of change can vary along the graph.

The points will make a straight line.
The points will make a straight line.

The initial value is always zero.

The key feature of a linear graph is that it represents a constant rate of change, which results in a straight line.

Among the options provided, the true statement is:

The points will make a straight line.

This is because linear graphs are defined by their linearity, where the relationship between the x and y values is consistent, leading to a straight line when plotted on a graph.

The other statements are not universally true:

  • The points may have both positive and negative values.
  • The rate of change (slope) is constant, not varying.
  • The initial value (y-intercept) can be any number, not just zero.

So, again, the correct response is: The points will make a straight line.

Create a sequence to show exponential growth where the population of 120 is doubling every day.(1 point)
Responses

120, 240, 480 . . .
120, 240, 480 . . .

120, 360, 1,080 . . .
120, 360, 1,080 . . .

120, 60, 30 . . .
120, 60, 30 . . .

120, 240, 480, 360, 480 . . .

To create a sequence that shows exponential growth where the population of 120 doubles every day, we can start with the initial population and multiply it by 2 for each subsequent day.

  1. Day 0: 120 (initial population)
  2. Day 1: \( 120 \times 2 = 240 \)
  3. Day 2: \( 240 \times 2 = 480 \)
  4. Day 3: \( 480 \times 2 = 960 \)

Thus, the sequence of populations is: 120, 240, 480, 960, ...

The closest match from your options is: 120, 240, 480 . . .

This correctly reflects the doubling pattern of exponential growth.

Select the response that creates an accurate formula for the sequence 2, 3.5, 6.125. 10.71875 . . .
.(1 point)
Responses

y=21.5x
y equals Start Fraction 2 over 1.5 x End Fraction

y=2+1.75x
y equals 2 plus 1.75 x

y=2(1.5)x
y equals 2 left parenthesis 1.5 right parenthesis superscript x baseline

y=2(1.75)x−1

To find the formula for the sequence \(2, 3.5, 6.125, 10.71875, \ldots\), we first look for a pattern.

Examining the ratios of consecutive terms:

  1. \( \frac{3.5}{2} = 1.75 \)
  2. \( \frac{6.125}{3.5} \approx 1.75 \)
  3. \( \frac{10.71875}{6.125} \approx 1.75 \)

This suggests that each term is approximately 1.75 times the previous term. This indicates an exponential growth behavior.

From this, the sequence can be modeled by the formula: \[ y = 2(1.75)^{x-1} \]

Here, \(2\) is the initial term, and \(1.75\) is the common ratio.

So, the correct response that creates an accurate formula for the sequence is: y = 2(1.75)^(x-1).