Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Our platform provides a seamless experience for finding reliable answers from a knowledgeable network of professionals. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
To determine whether the point [tex]\((1, -1)\)[/tex] satisfies the inequality [tex]\(40x - 22y \leq 50\)[/tex], we can follow these steps:
1. Substitute the coordinates of the point into the inequality:
Given the point [tex]\((x, y) = (1, -1)\)[/tex], substitute [tex]\(x = 1\)[/tex] and [tex]\(y = -1\)[/tex] into the inequality:
[tex]\[ 40(1) - 22(-1) \leq 50 \][/tex]
2. Simplify the left-hand side of the inequality:
Calculate the expression:
[tex]\[ 40(1) - 22(-1) = 40 + 22 \][/tex]
The two negatives in [tex]\(-22(-1)\)[/tex] cancel each other out, resulting in:
[tex]\[ 40 + 22 = 62 \][/tex]
3. Compare the simplified inequality:
Now we need to compare [tex]\(62\)[/tex] with the right-hand side of the inequality:
[tex]\[ 62 \leq 50 \][/tex]
4. Evaluate the truth of the statement:
Clearly, [tex]\(62\)[/tex] is not less than or equal to [tex]\(50\)[/tex]. Therefore, the inequality [tex]\(40x - 22y \leq 50\)[/tex] is not satisfied by the point [tex]\((1, -1)\)[/tex].
Conclusion: The statement that the point [tex]\((1, -1)\)[/tex] satisfies the inequality [tex]\(40x - 22y \leq 50\)[/tex] is False.
1. Substitute the coordinates of the point into the inequality:
Given the point [tex]\((x, y) = (1, -1)\)[/tex], substitute [tex]\(x = 1\)[/tex] and [tex]\(y = -1\)[/tex] into the inequality:
[tex]\[ 40(1) - 22(-1) \leq 50 \][/tex]
2. Simplify the left-hand side of the inequality:
Calculate the expression:
[tex]\[ 40(1) - 22(-1) = 40 + 22 \][/tex]
The two negatives in [tex]\(-22(-1)\)[/tex] cancel each other out, resulting in:
[tex]\[ 40 + 22 = 62 \][/tex]
3. Compare the simplified inequality:
Now we need to compare [tex]\(62\)[/tex] with the right-hand side of the inequality:
[tex]\[ 62 \leq 50 \][/tex]
4. Evaluate the truth of the statement:
Clearly, [tex]\(62\)[/tex] is not less than or equal to [tex]\(50\)[/tex]. Therefore, the inequality [tex]\(40x - 22y \leq 50\)[/tex] is not satisfied by the point [tex]\((1, -1)\)[/tex].
Conclusion: The statement that the point [tex]\((1, -1)\)[/tex] satisfies the inequality [tex]\(40x - 22y \leq 50\)[/tex] is False.
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.