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The image shows four number lines, each representing different inequalities. The question asks which graph represents the compound inequality ( x \leq \frac{5}{4} ) or ( x \geq \frac{5}{2} ).

The first number line shows values greater than -0.5.
The second number line shows values less than or equal to 1.25.
The fourth number line shows values greater than -0.5 and less than or equal to 2.5.

i removed 3 because its not 3

9 answers

To represent the compound inequality \( x \leq \frac{5}{4} \) (which is \( x \leq 1.25 \)) or \( x \geq \frac{5}{2} \) (which is \( x \geq 2.5 \)), we need to identify a number line that reflects these two conditions.

  1. \( x \leq \frac{5}{4} \) includes all values up to and including 1.25.
  2. \( x \geq \frac{5}{2} \) includes all values starting from 2.5 and greater.

So, the combined solution will include:

  • All values \( x \) that are less than or equal to 1.25,
  • All values \( x \) that are greater than or equal to 2.5.

Looking at the number lines you mentioned:

  1. The first number line shows values greater than -0.5 (this does not represent either part of the compound inequality).
  2. The second number line shows values less than or equal to 1.25 (this represents one part, \( x \leq \frac{5}{4} \)).
  3. The fourth number line shows values greater than -0.5 and less than or equal to 2.5 (this does not represent the compound inequality because of the restriction on the upper limit).

Based on your description, the second number line represents \( x \leq \frac{5}{4} \). However, there should also be a line representing \( x \geq \frac{5}{2} \). If there is no number line for that portion, then none of the provided graphs fully represents the compound inequality \( ( x \leq \frac{5}{4} ) \) or \( ( x \geq \frac{5}{2} ) \).

To conclude, the second number line does represent part of the compound inequality (the left side), but without a number line showing \( x \geq \frac{5}{2} \) (the right side), none of the graphs fully depict the entire compound inequality. If a specific number line for the values \( x \geq 2.5 \) is available, that should be included to accurately satisfy the requirements of the compound inequality.

IT IS THE SECOND ONE YAY closed circle starting at somewhere between 1 and 1.5 going to the left and another point close circle starting at 2.5 going right

The image shows a compound inequality ( x < -8 ) or ( x \geq 3 ) and a number line ranging from -10 to 10. The number line has two points with arrows: one at -8 pointing left (indicating values less than -8) and one at 3 pointing right (indicating values greater than or equal to 3). There is also a draggable point currently placed at zero.

This visual representation helps to understand the solution set for the given compound inequality.

Great! It sounds like you correctly identified the second number line as representing the inequality \( x \leq \frac{5}{4} \) and the condition \( x \geq \frac{5}{2} \) for the first question, which means that it includes values less than or equal to \( 1.25 \) (with a closed circle at \( 1.25 \)) and starts at \( 2.5 \) and goes right (indicating all values equal to and greater than \( 2.5 \)).

For the new compound inequality \( ( x < -8 ) \) or \( ( x \geq 3 ) \):

  1. \( x < -8 \): This is represented on the number line with an open circle (or arrow) at -8 pointing left, indicating all values less than -8.

  2. \( x \geq 3 \): This is represented with a closed circle at 3 pointing right, indicating all values starting from 3 and going to the right (including all values greater than or equal to 3).

The number line you described effectively shows all numbers less than -8 to the left of -8, and all numbers greater than or equal to 3 to the right of 3.

This representation clearly visualizes the solution set for the compound inequality. If there is a draggable point at zero, it helps to illustrate that zero is neither part of the solution set (since it is not less than -8 and not greater than or equal to 3).

In summary, your understanding of both compound inequalities and their representations on number lines is correct! Thanks for sharing the details!

THANK YOUUU AAAAAA an open circle (or arrow) at -8 pointing left and a closed circle at 3 pointing right

Which are possible values for x? Check all that apply.

–10.2
3
–8
2.6
20

Given the compound inequality \( ( x < -8 ) \) or \( ( x \geq 3 ) \), we can determine which of the provided values for \( x \) satisfy either part of the inequality.

  1. –10.2: This is less than -8. Therefore, it satisfies \( x < -8 \).

  2. 3: This is equal to 3. Therefore, it satisfies \( x \geq 3 \).

  3. –8: This value is not less than -8 (since \( x < -8 \) does not include -8) and does not satisfy \( x \geq 3 \). So it does not satisfy either part of the inequality.

  4. 2.6: This value is not less than -8, and it is also not greater than or equal to 3. Therefore, it does not satisfy either part of the inequality.

  5. 20: This value is greater than 3, so it satisfies \( x \geq 3 \).

Possible values for \( x \) that satisfy the inequality:

  • –10.2
  • 3
  • 20

So the correct choices are –10.2, 3, and 20.

The image shows a number line with integers from -12 to -7. There are two closed circles at -11.25 and -8.75, indicating these values are included in the interval. The area between these points is highlighted, representing the range of values that satisfy a certain condition.

The compound inequality represented by the graph is: [ 0 < x \leq -11.25 \text{ or } x \geq -8.75 ]

“Which compound inequality is represented by the highlighted section on the number line?”

Based on your description of the number line with two closed circles at -11.25 and -8.75 and highlighting the area between these points, it seems the highlighted section represents values that are included between -11.25 and -8.75.

If we emphasize that the values between these two points are highlighted, the highlighted section indicates the range \( -11.25 \leq x \leq -8.75 \).

Therefore, the correct compound inequality represented by the highlighted section on the number line would be:

\[ -11.25 \leq x \leq -8.75 \]

This indicates all values \( x \) that are greater than or equal to -11.25 and less than or equal to -8.75.

So, in conclusion, the compound inequality represented by the highlighted section on the number line is:

\[ [-11.25 \leq x \leq -8.75] \]

Make sure you clarify that the original statement "[0 < x \leq -11.25 or x \geq -8.75]" is not accurate for the highlighted section if it indicates values between -11.25 and -8.75 on the number line.

It is "< x -11.25 or x > -8.75"

There are 30 calories in 1/4 cup of red seedless grapes.
How many calories are consumed if a person eats between 3/4 and 1 1/4 cups of grapes?

The number of calories in 3/4 cups of red seedless grapes is___

The number of calories in 1 1/4 cups of red seedless grapes is____

The inequality that could represent the number of calories when eating more than 3/4 but less than 1 1/4 cups of grapes is ____

To determine the number of calories consumed from red seedless grapes, we'll first calculate the number of calories in both \( \frac{3}{4} \) cups and \( \frac{1}{4} \) cup servings.

1. Calories Calculation

Since there are 30 calories in \( \frac{1}{4} \) cup of grapes:

  • Calories in \( \frac{3}{4} \) cup:

    \[ \text{Calories in } \frac{3}{4} \text{ cup} = 30 , \text{calories} \times 3 = 90 , \text{calories} \]

  • Calories in \( \frac{1}{4} \) cup:

    \[ \text{Calories in } \frac{1}{4} \text{ cup} = 30 , \text{calories} \]

  • Calories in \( 1 \) cup:

    \[ \text{Calories in } 1 \text{ cup} = 30 , \text{calories} \times 4 = 120 , \text{calories} \]

  • Calories in \( 1 \frac{1}{4} \) cups:

    \[ \text{Calories in } 1 \frac{1}{4} \text{ cup} = 120 + 30 = 150 , \text{calories} \]

Summary of Calculated Values

  • The number of calories in \( \frac{3}{4} \) cups of red seedless grapes is 90 calories.
  • The number of calories in \( 1 \frac{1}{4} \) cups of red seedless grapes is 150 calories.

2. Inequality Representation

Now to express the number of calories consumed when eating more than \( \frac{3}{4} \) cups but less than \( 1 \frac{1}{4} \) cups:

  • The calories for \( \frac{3}{4} \) cups is 90, and the calories for \( 1 \frac{1}{4} \) cups is 150.

Thus, the inequality representing the number of calories when eating more than \( \frac{3}{4} \) cups (90 calories) but less than \( 1 \frac{1}{4} \) cups (150 calories) would be:

\[ 90 < c < 150 \]

where \( c \) represents the number of calories consumed.

Final Answers

  • The number of calories in \( \frac{3}{4} \) cups of red seedless grapes is 90 calories.
  • The number of calories in \( 1 \frac{1}{4} \) cups of red seedless grapes is 150 calories.
  • The inequality that could represent the number of calories when eating more than \( \frac{3}{4} \) but less than \( 1 \frac{1}{4} \) cups of grapes is \( 90 < c < 150 \).