Question

Question
Which of the following points is a solution to the linear inequality y>19x−29?(1 point)
Responses

(0,−13)
left parenthesis 0 comma negative Start Fraction 1 over 3 End Fraction right parenthesis

(0,−19)
left parenthesis 0 comma negative Start Fraction 1 over 9 End Fraction right parenthesis

(0,−49)
left parenthesis 0 comma negative Start Fraction 4 over 9 End Fraction right parenthesis

(0,−29)

Answer 1

Show which of the following points is part of the solution set for the inequality y≤25x+1.(1 point)
Responses

(10,5.5)
left parenthesis 10 comma 5.5 right parenthesis

(−10,6)
left parenthesis negative 10 comma 6 right parenthesis

(10,6)
left parenthesis 10 comma 6 right parenthesis

(10,4)

Answer 2

Kiani is shopping at a bookstore with a budget of $60. Hardbacks cost $12 and paperbacks cost $5. Write a two-variable inequality and determine the constraints of the problem. Which of the following points represents a viable solution?(1 point)
Responses

(1,4.5)
left parenthesis 1 comma 4.5 right parenthesis

(−2,6)
left parenthesis negative 2 comma 6 right parenthesis

(6,6)
left parenthesis 6 comma 6 right parenthesis

(2,4)

Answer 3

Use the image to answer the question.

The x- and y- axes of a coordinate plane range from 0 to 30 and 0 to 20 in increments of 5 and are labeled 'Lawns' and 'Dogs,' respectively. A line connects left parenthesis 0 comma 10 right parenthesis and left parenthesis 8 comma 0 right parenthesis.

This graph shows the inequality 25x+15y≥200, and represents Lina’s earnings for lawn mowing and dog walking where x represents the number of lawns mowed and y represents the number of dogs walked. Which of the labeled points is a viable solution in this context?

(1 point)
Responses

(10,10)
left parenthesis 10 comma 10 right parenthesis

(20,11.5)
left parenthesis 20 comma 11.5 right parenthesis

None of the points are a viable solution.
None of the points are a viable solution.

(2,3)

Answer 4

To determine which of the points is a solution to the linear inequality \( y > 19x - 29 \), we can substitute the x-coordinate of each point into the inequality and see if the y-coordinate satisfies it.

The inequality we are working with is \( y > 19x - 29 \).

Since all the given points have \( x = 0 \), we can simplify the inequality by substituting \( x = 0 \):

\[
y > 19(0) - 29 \\
y > -29
\]

Now we will check each point to see if it satisfies \( y > -29 \):

1. **Point (0, -13)**:
\(-13 > -29\) (True)

2. **Point (0, -\(\frac{1}{3}\))**:
\(-\frac{1}{3} > -29\) (True)

3. **Point (0, -19)**:
\(-19 > -29\) (True)

4. **Point (0, -\(\frac{1}{9}\))**:
\(-\frac{1}{9} > -29\) (True)

5. **Point (0, -49)**:
\(-49 > -29\) (False)

6. **Point (0, -29)**:
\(-29 > -29\) (False, because it is not greater)

Now, the points that satisfy the inequality \( y > -29 \) are:

- (0, -13)
- (0, -\(\frac{1}{3}\))
- (0, -19)
- (0, -\(\frac{1}{9}\))

Thus, any of the following points are solutions to the inequality:

- (0, -13)
- (0, -\(\frac{1}{3}\))
- (0, -19)
- (0, -\(\frac{1}{9}\))

The only point that does not satisfy the inequality is (0, -49) and (0, -29).

So, valid responses to the inequality include (0, -13), (0,-\(\frac{1}{3}\)), (0,-19), and (0,-\(\frac{1}{9}\)).

Answer 5

To determine which of the given points is part of the solution set for the inequality \( y \leq 25x + 1 \), we can substitute the \( x \) values of each point into the inequality and check if the corresponding \( y \) value satisfies it.

The inequality we are working with is:

\[
y \leq 25x + 1
\]

We will test each point:

1. **Point (10, 5.5)**:
Substitute \( x = 10 \) into the inequality.
\[
y \leq 25(10) + 1 \\
y \leq 250 + 1 \\
y \leq 251
\]
Since \( 5.5 \leq 251 \) (True), this point is part of the solution set.

2. **Point (−10, 6)**:
Substitute \( x = -10 \) into the inequality.
\[
y \leq 25(-10) + 1 \\
y \leq -250 + 1 \\
y \leq -249
\]
Since \( 6 \leq -249 \) (False), this point is NOT part of the solution set.

3. **Point (10, 6)**:
Substitute \( x = 10 \) into the inequality.
\[
y \leq 25(10) + 1 \\
y \leq 250 + 1 \\
y \leq 251
\]
Since \( 6 \leq 251 \) (True), this point is part of the solution set.

4. **Point (10, 4)**:
Substitute \( x = 10 \) into the inequality.
\[
y \leq 25(10) + 1 \\
y \leq 250 + 1 \\
y \leq 251
\]
Since \( 4 \leq 251 \) (True), this point is part of the solution set.

### Summary of Results:
- **(10, 5.5)**: True (part of the solution set)
- **(−10, 6)**: False (not part of the solution set)
- **(10, 6)**: True (part of the solution set)
- **(10, 4)**: True (part of the solution set)

Thus, the points (10, 5.5), (10, 6), and (10, 4) are part of the solution set for the inequality \( y \leq 25x + 1 \).

Answer 6

Let's define the variables for the problem:

- Let \( x \) represent the number of hardbacks purchased.
- Let \( y \) represent the number of paperbacks purchased.

The prices are as follows:
- Hardbacks cost $12 each.
- Paperbacks cost $5 each.

### Step 1: Write the two-variable inequality

Since Kiani has a budget of $60, the inequality representing this constraint is:

\[
12x + 5y \leq 60
\]

### Step 2: Determine the constraints of the problem

1. **Non-negativity**: Kiani cannot purchase a negative number of books, so:
\[
x \geq 0 \\
y \geq 0
\]

### Step 3: Identify viable solutions

Now we can test the proposed points to see if they satisfy the inequality \( 12x + 5y \leq 60 \) and the non-negativity constraints.

1. **Point (1, 4.5)**:
\[
12(1) + 5(4.5) = 12 + 22.5 = 34.5 \\
34.5 \leq 60 \quad \text{(True)}
\]
Both \( x \geq 0 \) and \( y \geq 0 \) are satisfied.

2. **Point (−2, 6)**:
\[
12(-2) + 5(6) = -24 + 30 = 6 \\
6 \leq 60 \quad \text{(True)}
\]
However, \( x = -2 \) does not satisfy \( x \geq 0 \) (False).

3. **Point (6, 6)**:
\[
12(6) + 5(6) = 72 + 30 = 102 \\
102 \leq 60 \quad \text{(False)}
\]
Both \( x \geq 0 \) and \( y \geq 0 \) are satisfied.

4. **Point (2, 4)**:
\[
12(2) + 5(4) = 24 + 20 = 44 \\
44 \leq 60 \quad \text{(True)}
\]
Both \( x \geq 0 \) and \( y \geq 0 \) are satisfied.

### Conclusion

The viable solutions among the proposed points are:

- **(1, 4.5)**: True
- **(−2, 6)**: False (not valid as \( x \) cannot be negative)
- **(6, 6)**: False
- **(2, 4)**: True

**Final Answer**: The viable solutions are (1, 4.5) and (2, 4).

Answer 7

To determine which of the labeled points is a viable solution for the inequality \( 25x + 15y \geq 200 \), we can substitute each of the proposed points into the inequality and see if the inequality is satisfied.

### Given inequality:
\[
25x + 15y \geq 200
\]

### Testing the points:

1. **Point (10, 10)**:
\[
25(10) + 15(10) = 250 + 150 = 400 \\
400 \geq 200 \quad \text{(True)}
\]

2. **Point (20, 11.5)**:
\[
25(20) + 15(11.5) = 500 + 172.5 = 672.5 \\
672.5 \geq 200 \quad \text{(True)}
\]

3. **Point (2, 3)**:
\[
25(2) + 15(3) = 50 + 45 = 95 \\
95 \geq 200 \quad \text{(False)}
\]

### Summary of Results:
- **(10, 10)**: Satisfies the inequality (True).
- **(20, 11.5)**: Satisfies the inequality (True).
- **(2, 3)**: Does NOT satisfy the inequality (False).

### Conclusion:
Both (10, 10) and (20, 11.5) are viable solutions to the inequality \( 25x + 15y \geq 200 \).

Given the responses:
- (10,10)
- (20,11.5)
- None of the points are a viable solution.
- (2,3)

Since at least one point is a viable solution, the correct response would be both (10,10) and (20,11.5). However, if the question allows only one selection, you can choose either (10, 10) or (20, 11.5) as a viable solution. If instructed to select just one, I would recommend selecting (10, 10) as it appears first. If you must choose only one option, please confirm if the interface restricts you from choosing multiple points.