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Sagot :
To determine which ordered pair [tex]\((x, y)\)[/tex] is a viable solution, where [tex]\(x\)[/tex] represents the number of days a library book is late and [tex]\(y\)[/tex] represents the total fee, we need to verify which pairs satisfy the equation [tex]\( y = 0.30x \)[/tex].
Let's check each ordered pair:
1. Ordered pair [tex]\((-3, -0.90)\)[/tex]
- Here, [tex]\(x = -3\)[/tex] and [tex]\(y = -0.90\)[/tex].
- Checking the equation:
[tex]\[ y = 0.30x \implies -0.90 = 0.30 \times -3 \][/tex]
- Simplifying:
[tex]\[ -0.90 = -0.90 \][/tex]
- This pair satisfies the equation, so it is a viable solution.
2. Ordered pair [tex]\((-2.5, -0.75)\)[/tex]
- Here, [tex]\(x = -2.5\)[/tex] and [tex]\(y = -0.75\)[/tex].
- Checking the equation:
[tex]\[ y = 0.30x \implies -0.75 = 0.30 \times -2.5 \][/tex]
- Simplifying:
[tex]\[ -0.75 = -0.75 \][/tex]
- This pair satisfies the equation, so it is a viable solution.
3. Ordered pair [tex]\((4.5, 1.35)\)[/tex]
- Here, [tex]\(x = 4.5\)[/tex] and [tex]\(y = 1.35\)[/tex].
- Checking the equation:
[tex]\[ y = 0.30x \implies 1.35 = 0.30 \times 4.5 \][/tex]
- Simplifying:
[tex]\[ 1.35 = 1.35 \][/tex]
- This pair satisfies the equation, so it is a viable solution.
4. Ordered pair [tex]\((8, 2.40)\)[/tex]
- Here, [tex]\(x = 8\)[/tex] and [tex]\(y = 2.40\)[/tex].
- Checking the equation:
[tex]\[ y = 0.30x \implies 2.40 = 0.30 \times 8 \][/tex]
- Simplifying:
[tex]\[ 2.40 = 2.40 \][/tex]
- This pair satisfies the equation, so it is a viable solution.
In conclusion, the following ordered pairs are viable solutions:
- [tex]\((-3, -0.90)\)[/tex]
- [tex]\((-2.5, -0.75)\)[/tex]
- [tex]\((4.5, 1.35)\)[/tex]
- [tex]\((8, 2.40)\)[/tex]
However, if we need to select only the viable pairs from the list provided initially, the viable pairs are:
- [tex]\((-2.5, -0.75)\)[/tex]
- [tex]\((8, 2.40)\)[/tex]
Let's check each ordered pair:
1. Ordered pair [tex]\((-3, -0.90)\)[/tex]
- Here, [tex]\(x = -3\)[/tex] and [tex]\(y = -0.90\)[/tex].
- Checking the equation:
[tex]\[ y = 0.30x \implies -0.90 = 0.30 \times -3 \][/tex]
- Simplifying:
[tex]\[ -0.90 = -0.90 \][/tex]
- This pair satisfies the equation, so it is a viable solution.
2. Ordered pair [tex]\((-2.5, -0.75)\)[/tex]
- Here, [tex]\(x = -2.5\)[/tex] and [tex]\(y = -0.75\)[/tex].
- Checking the equation:
[tex]\[ y = 0.30x \implies -0.75 = 0.30 \times -2.5 \][/tex]
- Simplifying:
[tex]\[ -0.75 = -0.75 \][/tex]
- This pair satisfies the equation, so it is a viable solution.
3. Ordered pair [tex]\((4.5, 1.35)\)[/tex]
- Here, [tex]\(x = 4.5\)[/tex] and [tex]\(y = 1.35\)[/tex].
- Checking the equation:
[tex]\[ y = 0.30x \implies 1.35 = 0.30 \times 4.5 \][/tex]
- Simplifying:
[tex]\[ 1.35 = 1.35 \][/tex]
- This pair satisfies the equation, so it is a viable solution.
4. Ordered pair [tex]\((8, 2.40)\)[/tex]
- Here, [tex]\(x = 8\)[/tex] and [tex]\(y = 2.40\)[/tex].
- Checking the equation:
[tex]\[ y = 0.30x \implies 2.40 = 0.30 \times 8 \][/tex]
- Simplifying:
[tex]\[ 2.40 = 2.40 \][/tex]
- This pair satisfies the equation, so it is a viable solution.
In conclusion, the following ordered pairs are viable solutions:
- [tex]\((-3, -0.90)\)[/tex]
- [tex]\((-2.5, -0.75)\)[/tex]
- [tex]\((4.5, 1.35)\)[/tex]
- [tex]\((8, 2.40)\)[/tex]
However, if we need to select only the viable pairs from the list provided initially, the viable pairs are:
- [tex]\((-2.5, -0.75)\)[/tex]
- [tex]\((8, 2.40)\)[/tex]
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