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Find and correct the error.

x4+6>3

x+6>12

x>6

(1 point)
Responses

6 should have been subtracted first before multiplying by 4 - the true answer should be x > -12

With inequalities you always flip the symbol at the end - the true answer should be x < 6
With inequalities you always flip the symbol at the end - the true answer should be x < 6

6 should have been added first before multiplying by 4 - the true answer should be x > 36
6 should have been added first before multiplying by 4 - the true answer should be x > 36

6 should have been subtracted first before multiplying by 4 - the true answer should be x > -3/4
6 should have been subtracted first before multiplying by 4 - the true answer should be x > -3/4
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11 answers

Let's analyze the steps in the equation to identify any errors. The initial inequality given is \( x + 6 > 12 \).

  1. Start with the inequality: \[ x + 6 > 12 \]

  2. To isolate \( x \), you subtract 6 from both sides: \[ x > 12 - 6 \]

  3. Simplifying that gives: \[ x > 6 \]

The steps taken are correct, and the solution \( x > 6 \) is valid.

Therefore, it appears that none of the responses correctly address any errors in this specific problem.

In summary, the answer derived from the initial inequality is indeed correct, and thus:

  • No correction is needed; \( x > 6 \) is the correct solution.
Answer the following questions regarding the graph:
the graph starts at (10, 0) and ends at (0, 25) and has a plot in the middle at the line on (5, 13)

(5 points)
a) Is this a proportional relationship?
no because the y intercept is at the origin
no, because the y-intercept isn't at the origin
yes, because the y-intercept goes through the origin
yes, because its a straight line
b) What is the y-intercept?
(0, -5/2)
(10, 0)
(0, 25)
c) What does the y-intercept mean in context of the scenario?
there is a $5 decrease on the gift card for every 2 coffees purchased.
the starting value of the gift card before buying any coffee is $25
you can buy 10 coffees with the gift card
d) What is the slope?
10
-5
-5/2
+5/2
25
e) What does the slope mean in context of the scenario?
there is a $5 increase on the gift card for every 2 coffees purchased.
the starting value of the gift card before buying an coffee is $25
there is a $5 decrease on the gift card for every 2 coffees purchased

Let's analyze the questions based on the provided graph information, which has points at \((10, 0)\), \((0, 25)\), and \((5, 13)\).

a) Is this a proportional relationship?

  • Answer: No, because the y-intercept isn't at the origin.
    A proportional relationship means the line goes through the origin (0, 0). Since the y-intercept is at (0, 25), it is not proportional.

b) What is the y-intercept?

  • Answer: (0, 25)
    The y-intercept is the point where the graph intersects the y-axis, which is (0, 25).

c) What does the y-intercept mean in context of the scenario?

  • Answer: The starting value of the gift card before buying any coffee is $25.
    The y-intercept represents the initial amount on the gift card before any purchases are made.

d) What is the slope?

To calculate the slope \(m\) between the two points \((10, 0)\) and \((0, 25)\), use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{25 - 0}{0 - 10} = \frac{25}{-10} = -\frac{5}{2} \]

  • Answer: -5/2

e) What does the slope mean in context of the scenario?

  • Answer: There is a $5 decrease on the gift card for every 2 coffees purchased.
    The slope indicates the change in the value of the gift card as the number of coffees purchased increases, showing a decrease of $5 for every 2 coffees.

Summary of Answers:

a) No, because the y-intercept isn't at the origin.
b) (0, 25)
c) The starting value of the gift card before buying any coffee is $25.
d) -5/2
e) There is a $5 decrease on the gift card for every 2 coffees purchased.

The cost of a gym membership can be represented by 25 + 5x, where x is the number of visits to the gym. (4 points)
a) The y-intercept is (response area). This means that (response area)
1st responses
(0, 5)
(0, 25)
2nd responses
it costs $5 per visit to the gym
the registration cost is $25
b) The slope is (response area). This means that (response area)
1st responses
5
25
2nd responses
the registration cost at the gym is $25
it costs $5 per visit to the gym

Let's analyze the given problem related to the cost of a gym membership represented by the equation \( C = 25 + 5x \), where \( C \) is the total cost and \( x \) is the number of visits.

a) The y-intercept

  1. The y-intercept:

    • When \( x = 0 \) (meaning no visits to the gym), the cost \( C \) is: \[ C = 25 + 5(0) = 25 \] Therefore, the y-intercept is: (0, 25).

  2. This means that:

    • The y-intercept indicates the initial cost (registration fee) before any gym visits, which is: the registration cost is $25.

b) The slope

  1. The slope:

    • The slope of the equation \( 5x \) indicates the rate of change in cost for each additional visit to the gym. Therefore, the slope is: 5.

  2. This means that:

    • The slope indicates that for each gym visit, the cost increases by $5, which translates to: it costs $5 per visit to the gym.

Summary of Responses:

  • a) The y-intercept is: (0, 25). This means that: the registration cost is $25.
  • b) The slope is: 5. This means that: it costs $5 per visit to the gym.
find the slope of y = -3/2x + 4

In the equation of a line given in the slope-intercept form \(y = mx + b\), the slope \(m\) is the coefficient of \(x\).

For the equation: \[ y = -\frac{3}{2}x + 4 \]

The slope \(m\) is: \[ m = -\frac{3}{2} \]

Therefore, the slope of the line is \(-\frac{3}{2}\).

using the graph find the y-intercept
weeks weight
0 1
1 5
2 9
3 13

To find the y-intercept from the provided data points, we can observe the relationship between the 'weeks' (x-values) and 'weight' (y-values). The y-intercept represents the point where the graph intersects the y-axis, which occurs when the x-value is 0.

From the data provided:

  • When weeks = 0, weight = 1.

Thus, the y-intercept is at the point \( (0, 1) \).

Summary:

The y-intercept is (0, 1).

what does the slope represent in this situation

To determine what the slope represents in the context of the given data, we first need to calculate the slope based on the provided points, then interpret its meaning.

Given Data Points:

  • (0, 1)
  • (1, 5)
  • (2, 9)
  • (3, 13)

Slope Calculation:

The slope \(m\) can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Choosing two points, for instance, (0, 1) and (1, 5):

  • \(y_2 = 5\), \(y_1 = 1\)
  • \(x_2 = 1\), \(x_1 = 0\)

So, the slope \(m\) is: \[ m = \frac{5 - 1}{1 - 0} = \frac{4}{1} = 4 \]

Interpretation of the Slope:

In this situation, the slope of 4 means that for every week that passes (an increase of 1 week), the weight increases by 4 units.

Summary:

The slope represents the rate of change of weight per week; specifically, the weight increases by 4 units for each week that goes by.