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

Question

Responses

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

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

(10,4)
left parenthesis 10 comma 4 right parenthesis

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

Answer 1

To determine which of the given points satisfies the inequality \( y \leq 25x + 1 \), we need to substitute the x-value of each point into the equation \( y = 25x + 1 \) and see if the corresponding y-value is less than or equal to the calculated value.

1. For the point (10, 5.5):

   • \( x = 10 \)
   • Calculate \( y = 25(10) + 1 = 250 + 1 = 251 \)
   • Check: \( 5.5 \leq 251 \) (True)

2. For the point (10, 6):

   • \( x = 10 \)
   • Calculate \( y = 25(10) + 1 = 250 + 1 = 251 \)
   • Check: \( 6 \leq 251 \) (True)

3. For the point (10, 4):

   • \( x = 10 \)
   • Calculate \( y = 25(10) + 1 = 250 + 1 = 251 \)
   • Check: \( 4 \leq 251 \) (True)

4. For the point (−10, 6):

   • \( x = -10 \)
   • Calculate \( y = 25(-10) + 1 = -250 + 1 = -249 \)
   • Check: \( 6 \leq -249 \) (False)

Based on this analysis, all points except for (−10, 6) satisfy the inequality \( y \leq 25x + 1 \). Therefore, the points that are part of the solution set are (10, 5.5), (10, 6), and (10, 4).

Answer 2

which one

Answer 3

Among the given points, we need to select just one point that satisfies the inequality \( y \leq 25x + 1 \).

After evaluating the points:

1. (10, 5.5): Satisfies the inequality.
2. (10, 6): Satisfies the inequality.
3. (10, 4): Satisfies the inequality.
4. (−10, 6): Does not satisfy the inequality.

Since all three of the first points satisfy the inequality, you can choose any one of them.

If you need to pick just one point, you could choose:

(10, 5.5).

This is a valid point in the solution set for the inequality.