Is(4, 3)a solution to the inequality 3x + y ≥ 20?

Question

Yes or no

GPT-4o mini · Answer

To determine if (4, 3) is a solution to the inequality $3x + y \geq 20$, we can substitute $x = 4$ and $y = 3$ into the inequality:

\[ 3(4) + 3 \geq 20 \]

Calculating the left side:

\[ 12 + 3 = 15 \]

Now we check the inequality:

\[ 15 \geq 20 \]

This statement is false. Therefore, the point (4, 3) is not a solution to the inequality $3x + y \geq 20$.

So, the answer is no.

sunrise_lover09 · Answer

Doesthepoint(1, 10) satisfy the inequality y < 7x + 1? yes or no

GPT-4o mini · Answer

To determine if the point (1, 10) satisfies the inequality $ y < 7x + 1 $, we can substitute $ x = 1 $ and see if $ y $ is less than $ 7 \cdot 1 + 1 $.

First, calculate the right side:

\[ 7(1) + 1 = 7 + 1 = 8 \]

Now, we check the inequality:

\[ 10 < 8 \]

This statement is false. Therefore, the point (1, 10) does not satisfy the inequality $ y < 7x + 1 $.

So, the answer is no.

sunrise_lover09 · Answer

Does(2, 3)maketheinequality2x + 3y < 20true?

GPT-4o mini · Answer

To determine if the point (2, 3) satisfies the inequality $2x + 3y < 20$, we can substitute $x = 2$ and $y = 3$ into the inequality.

Calculating the left side:

\[ 2(2) + 3(3) < 20 \]

Now, compute the values:

\[ 4 + 9 < 20 \]

This simplifies to:

\[ 13 < 20 \]

This statement is true. Therefore, the point (2, 3) does satisfy the inequality $2x + 3y < 20$.

So, the answer is yes.

sunrise_lover09 · Answer

Is(4, 9)asolutiontotheinequalityy ≤ 2x + 1?

GPT-4o mini · Answer

To determine if the point (4, 9) satisfies the inequality $y \leq 2x + 1$, we can substitute $x = 4$ and $y = 9$ into the inequality.

First, calculate the right side:

\[ 2(4) + 1 = 8 + 1 = 9 \]

Now, we check the inequality:

\[ 9 \leq 9 \]

This statement is true. Therefore, the point (4, 9) is a solution to the inequality $y \leq 2x + 1$.

So, the answer is yes.

sunrise_lover09 · Answer

Doesthepoint(2, 5)satisfytheinequality14x + 20y ≥ 6?

GPT-4o mini · Answer

To determine if the point (2, 5) satisfies the inequality $14x + 20y \geq 6$, we can substitute $x = 2$ and $y = 5$ into the inequality.

Calculating the left side:

\[ 14(2) + 20(5) \geq 6 \]

Now, compute the values:

\[ 28 + 100 \geq 6 \]

This simplifies to:

\[ 128 \geq 6 \]

This statement is true. Therefore, the point (2, 5) does satisfy the inequality $14x + 20y \geq 6$.

So, the answer is yes.

sunrise_lover09 · Answer

Does(1, 7)maketheinequalityy < 7x + 10true?

GPT-4o mini · Answer

To determine if the point (1, 7) satisfies the inequality $y < 7x + 10$, we can substitute $x = 1$ and $y = 7$ into the inequality.

First, calculate the right side using $x = 1$:

\[ 7(1) + 10 = 7 + 10 = 17 \]

Now we check the inequality:

\[ 7 < 17 \]

This statement is true. Therefore, the point (1, 7) does satisfy the inequality $y < 7x + 10$.

So, the answer is yes.

sunrise_lover09 · Answer

Doesthepoint(1, 1)satisfytheinequality2x + 12y > 16?

GPT-4o mini · Answer

To determine if the point (1, 1) satisfies the inequality $2x + 12y > 16$, we can substitute $x = 1$ and $y = 1$ into the inequality.

Calculating the left side:

\[ 2(1) + 12(1) > 16 \]

Now, compute the values:

\[ 2 + 12 > 16 \]

This simplifies to:

\[ 14 > 16 \]

This statement is false. Therefore, the point (1, 1) does not satisfy the inequality $2x + 12y > 16$.

So, the answer is no.

sunrise_lover09 · Answer

Is(4, 5)asolutiontotheinequalityy ≥ 7x + 3?

GPT-4o mini · Answer

To determine if the point (4, 5) satisfies the inequality $y \geq 7x + 3$, we can substitute $x = 4$ and $y = 5$ into the inequality.

First, calculate the right side:

\[ 7(4) + 3 = 28 + 3 = 31 \]

Now we check the inequality:

\[ 5 \geq 31 \]

This statement is false. Therefore, the point (4, 5) is not a solution to the inequality $y \geq 7x + 3$.

So, the answer is no.

sunrise_lover09 · Answer

Does(1, 10)maketheinequalityy > 6x + 1true?

GPT-4o mini · Answer

To determine if the point (1, 10) satisfies the inequality $y > 6x + 1$, we will substitute $x = 1$ and $y = 10$ into the inequality.

First, calculate the right side:

\[ 6(1) + 1 = 6 + 1 = 7 \]

Now, check if the inequality holds:

\[ 10 > 7 \]

This statement is true. Therefore, the point (1, 10) does satisfy the inequality $y > 6x + 1$.

So, the answer is yes.

sunrise_lover09 · Answer

Is(–7, 7)asolutiontotheinequality y ≥ 1 7 x + 8 ?

GPT-4o mini · Answer

To determine if the point $(-7, 7)$ satisfies the inequality $$ y \geq \frac{1}{7}x + 8, $$ we can substitute $x = -7$ and $y = 7$ into the inequality. First, calculate the right side: $$ \frac{1}{7}(-7) + 8 = -1 + 8 = 7. $$ Now we check the inequality: $$ 7 \geq 7. $$ This statement is true. Therefore, the point $(-7, 7)$ is a solution to the inequality $$ y \geq \frac{1}{7}x + 8. $$ So, the answer is **yes**.

sunrise_lover09 · Answer

Doesthepoint(5, 3)satisfytheinequality2x + 3y > 13?

GPT-4o mini · Answer

To determine if the point (5, 3) satisfies the inequality $2x + 3y > 13$, we can substitute $x = 5$ and $y = 3$ into the inequality.

Calculating the left side:

\[ 2(5) + 3(3) > 13 \]

Now, compute the values:

\[ 10 + 9 > 13 \]

This simplifies to:

\[ 19 > 13. \]

This statement is true. Therefore, the point (5, 3) does satisfy the inequality $2x + 3y > 13$.

So, the answer is yes.

sunrise_lover09 · Answer

Does(–5, –8)maketheinequalityy < 10true?

GPT-4o mini · Answer

To determine if the point $(-5, -8)$ satisfies the inequality $y < 10$, we can substitute $y = -8$ into the inequality. Check the inequality: $$ -8 < 10. $$ This statement is true. Therefore, the point $(-5, -8)$ does satisfy the inequality $y < 10$. So, the answer is **yes**.

sunrise_lover09 · Answer

Doesthepoint(–1, 3)satisfytheinequality6x + 6y > 12?

GPT-4o mini · Answer

To determine if the point $(-1, 3)$ satisfies the inequality $6x + 6y > 12$, we can substitute $x = -1$ and $y = 3$ into the inequality. Calculating the left side: $$ 6(-1) + 6(3) > 12 $$ Now, compute the values: $$ -6 + 18 > 12 $$ This simplifies to: $$ 12 > 12. $$ This statement is **false** since $12$ is not greater than $12$. Therefore, the point $(-1, 3)$ does **not** satisfy the inequality $6x + 6y > 12$. So, the answer is **no**.

sunrise_lover09 · Answer

Is(5, 1)asolutiontotheinequalityy < 10x + 1?

GPT-4o mini · Answer

To determine if the point $(5, 1)$ satisfies the inequality $y < 10x + 1$, we can substitute $x = 5$ and $y = 1$ into the inequality. First, calculate the right side: $$ 10(5) + 1 = 50 + 1 = 51. $$ Now we check the inequality: $$ 1 < 51. $$ This statement is **true**. Therefore, the point $(5, 1)$ does satisfy the inequality $y < 10x + 1$. So, the answer is **yes**.

sunrise_lover09 · Answer

Doesthepoint(10, –8)satisfytheinequality5x + 6y ≤ 2?

GPT-4o mini · Answer

To determine if the point $(10, -8)$ satisfies the inequality $5x + 6y \leq 2$, we can substitute $x = 10$ and $y = -8$ into the inequality. Calculating the left side: $$ 5(10) + 6(-8) \leq 2 $$ Now, compute the values: $$ 50 - 48 \leq 2 $$ This simplifies to: $$ 2 \leq 2. $$ The statement is **true** since $2$ is equal to $2$. Therefore, the point $(10, -8)$ does satisfy the inequality $5x + 6y \leq 2$. So, the answer is **yes**.

sunrise_lover09 · Answer

Does(1, 7)maketheinequalityy ≥ 5x + 2true?

GPT-4o mini · Answer

To determine if the point $(1, 7)$ satisfies the inequality $y \geq 5x + 2$, we can substitute $x = 1$ and $y = 7$ into the inequality. First, calculate the right side: $$ 5(1) + 2 = 5 + 2 = 7. $$ Now we check the inequality: $$ 7 \geq 7. $$ This statement is **true**. Therefore, the point $(1, 7)$ does satisfy the inequality $y \geq 5x + 2$. So, the answer is **yes**.

sunrise_lover09 · Answer

s(1, 2)asolutiontotheinequality2x + 7y < 18?

GPT-4o mini · Answer

To determine if the point $(1, 2)$ satisfies the inequality $2x + 7y < 18$, we can substitute $x = 1$ and $y = 2$ into the inequality. Calculating the left side: $$ 2(1) + 7(2) < 18 $$ Now compute the values: $$ 2 + 14 < 18 $$ This simplifies to: $$ 16 < 18. $$ This statement is **true**. Therefore, the point $(1, 2)$ does satisfy the inequality $2x + 7y < 18$. So, the answer is **yes**.

sunrise_lover09 · Answer

Does(8, –2)maketheinequalityx > –2true?

GPT-4o mini · Answer

To determine if the point $(8, -2)$ satisfies the inequality $x > -2$, we can simply check the value of $x$. Here, $x = 8$. Now, check the inequality: $$ 8 > -2. $$ This statement is **true**. Therefore, the point $(8, -2)$ does satisfy the inequality $x > -2$. So, the answer is **yes**.

sunrise_lover09 · Answer

Doesthepoint(–2, –5)satisfytheinequality y ≥ 1 2 x − 4 ?

GPT-4o mini · Answer

To determine if the point $(-2, -5)$ satisfies the inequality $$ y \geq \frac{1}{2}x - 4, $$ we will substitute $x = -2$ and $y = -5$ into the inequality. First, calculate the right side: $$ \frac{1}{2}(-2) - 4 = -1 - 4 = -5. $$ Now we check the inequality: $$ -5 \geq -5. $$ This statement is **true** since $-5$ is equal to $-5$. Therefore, the point $(-2, -5)$ does satisfy the inequality $$ y \geq \frac{1}{2}x - 4. $$ So, the answer is **yes**.

sunrise_lover09 · Answer

Is(–4, 2)asolutiontotheinequalityy > 4x + 10?

GPT-4o mini · Answer

To determine if the point $(-4, 2)$ satisfies the inequality $$ y > 4x + 10, $$ we can substitute $x = -4$ and $y = 2$ into the inequality. First, calculate the right side: $$ 4(-4) + 10 = -16 + 10 = -6. $$ Now we check the inequality: $$ 2 > -6. $$ This statement is **true**. Therefore, the point $(-4, 2)$ does satisfy the inequality $$ y > 4x + 10. $$ So, the answer is **yes**.

sunrise_lover09 · Answer

Does(–2, –5)maketheinequality2x − 20y ≥ –5true?

GPT-4o mini · Answer

To determine if the point $(-2, -5)$ satisfies the inequality $$ 2x - 20y \geq -5, $$ we can substitute $x = -2$ and $y = -5$ into the inequality. Calculating the left side: $$ 2(-2) - 20(-5) \geq -5. $$ Now compute the values: $$ -4 + 100 \geq -5. $$ This simplifies to: $$ 96 \geq -5. $$ This statement is **true**. Therefore, the point $(-2, -5)$ does satisfy the inequality $$ 2x - 20y \geq -5. $$ So, the answer is **yes**.

sunrise_lover09 · Answer

Doesthepoint(10, 10)satisfytheinequality20x − 17y ≥ –12?

GPT-4o mini · Answer

To determine if the point $(10, 10)$ satisfies the inequality $$ 20x - 17y \geq -12, $$ we can substitute $x = 10$ and $y = 10$ into the inequality. Calculating the left side: $$ 20(10) - 17(10) \geq -12. $$ Now compute the values: $$ 200 - 170 \geq -12. $$ This simplifies to: $$ 30 \geq -12. $$ This statement is **true**. Therefore, the point $(10, 10)$ does satisfy the inequality $$ 20x - 17y \geq -12. $$ So, the answer is **yes**.

sunrise_lover09 · Answer

Does(–5, –8)maketheinequalityy < –4true?

GPT-4o mini · Answer

To determine if the point $(-5, -8)$ satisfies the inequality $$ y < -4, $$ we can simply check the value of $y$. Here, $y = -8$. Now, check the inequality: $$ -8 < -4. $$ This statement is **true**. Therefore, the point $(-5, -8)$ does satisfy the inequality $y < -4$. So, the answer is **yes**.

sunrise_lover09 · Answer

Doesthepoint(2, –2)satisfytheinequalityy ≤ 3x − 8?

GPT-4o mini · Answer

To determine if the point $(2, -2)$ satisfies the inequality $$ y \leq 3x - 8, $$ we can substitute $x = 2$ and $y = -2$ into the inequality. First, calculate the right side: $$ 3(2) - 8 = 6 - 8 = -2. $$ Now we check the inequality: $$ -2 \leq -2. $$ This statement is **true** since $-2$ is equal to $-2$. Therefore, the point $(2, -2)$ does satisfy the inequality $$ y \leq 3x - 8. $$ So, the answer is **yes**.