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Trey, Amelia, and Cho are discussing the solution set to the equation x2+9=45 .

Trey says the solution is {6} .

Amelia says the solution is {−6,6} .

Cho says the solution is {−6} .

Which person has found the correct solution set?

(1 point)
Responses

Trey
Trey

None of them are correct.
None of them are correct.

Amelia
Amelia

Cho

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To solve the equation \( x^2 + 9 = 45 \), we first isolate \( x^2 \):

\[
x^2 + 9 = 45
\]
\[
x^2 = 45 - 9
\]
\[
x^2 = 36
\]

Next, we take the square root of both sides:

\[
x = \pm 6
\]

This means the solutions are \( x = 6 \) and \( x = -6 \).

Now, let's review what each person said:

- Trey says the solution is {6}. (Incorrect, as it should include both solutions.)
- Amelia says the solution is {−6, 6}. (Correct, as it includes both solutions.)
- Cho says the solution is {−6}. (Incorrect, as it should include both solutions.)

The correct answer is **Amelia**.

anonymous anonymous answered
1 month ago

The values −1 and 1 make the equation 3x2+7=10 true. Use set notation to express the solution to the equation.(1 point)

Responses

(−1,1)
left parenthesis negative 1 comma 1 right parenthesis

​ {x=−1,x=1}
​ left brace x equals negative 1 comma x equals 1 right brace

(x=−1,x=1)
left parenthesis x equals negative 1 comma x equals 1 right parenthesis

{−1,1}

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

The solution to the equation can be expressed in set notation. Since the values \(-1\) and \(1\) are the solutions, the correct answer in set notation would be:

\[
\{−1, 1\}
\]

Therefore, the correct choice is **{−1, 1}**.

anonymous anonymous answered
1 month ago

The solution set of the inequality 3(b−4)+2b>3 is the set of values of b greater than three. Which set notation correctly expresses the solutions?(1 point)

Responses

{b:b<15}
left brace b colon b less than 15 right brace

{b:b<3}
left brace b colon b less than 3 right brace

{b:b>3}
left brace b colon b greater than 3 right brace

{b:b>15}

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To express the solution set of the inequality \(3(b - 4) + 2b > 3\), we first need to solve the inequality.

1. Expand the left side:
\[
3b - 12 + 2b > 3
\]

2. Combine like terms:
\[
5b - 12 > 3
\]

3. Add 12 to both sides:
\[
5b > 15
\]

4. Divide by 5:
\[
b > 3
\]

The solution is \(b > 3\).

In set notation, this is expressed as:

\[
\{b : b > 3\}
\]

Therefore, the correct choice is **{b:b>3}**.