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

Question

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

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

Cho
Cho

Trey
Trey

Amelia

Answer 1

To solve the equation \( x^2 + 9 = 45 \), we can start by isolating \( x^2 \):

1. Subtract 9 from both sides: \[ x^2 = 45 - 9 \] \[ x^2 = 36 \]

2. Next, take the square root of both sides: \[ x = \pm\sqrt{36} \] \[ x = \pm 6 \]

This gives us the solutions \( x = 6 \) and \( x = -6 \).

Now let's review the responses:

• Trey says the solution is {6}. (Incorrect, because there is another solution: -6.)
• Amelia says the solution is {−6, 6}. (Correct, as it includes both solutions.)
• Cho says the solution is {−6}. (Incorrect, because there is another solution: 6.)

The correct solution set is {−6, 6}, so the person who has found the correct solution set is Amelia.

Answer 2

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 parenthesis x equals negative 1 comma x equals 1 right parenthesis

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

{−1,1

Answer 3

The correct way to express the solution set for the values −1 and 1 in set notation is:

\[ {-1, 1} \]

So the correct response from the provided options is:

{−1,1}

Answer 4

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

{b:b>15}
left brace b colon b greater than 15 right brace

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

{b:b>3}

Answer 5

To express the solution set of the inequality \( 3(b-4) + 2b > 3 \) correctly, let's solve it first:

1. Distribute the 3: \[ 3b - 12 + 2b > 3 \]

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

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

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

The correct solution set for values of \( b \) that are greater than 3 can be expressed in set notation as:

\[ {b : b > 3} \]

So the correct response from the provided options is:

{b:b>3}

Answer 6

What value falls in the solution set of the inequality −3(4k+1)<15?(1 point)
Responses

−32
Start Fraction negative 3 over 2 End Fraction

−4
negative 4

−5
negative 5

−1

Answer 7

To solve the inequality \(-3(4k + 1) < 15\), we can start by distributing the \(-3\):

1. Distribute: \[ -12k - 3 < 15 \]

2. Add 3 to both sides: \[ -12k < 18 \]

3. Divide by \(-12\), and remember to flip the inequality sign: \[ k > -\frac{3}{2} \]

So, the solution set for the inequality is \( k > -\frac{3}{2} \).

Now, we need to find which of the provided options satisfies this inequality:

• −32: is less than \(-\frac{3}{2}\)
• Start Fraction negative 3 over 2 End Fraction (which is -1.5): is equal to \(-\frac{3}{2}\), but we need \(k\) to be greater than \(-\frac{3}{2}\)
• −4: is less than \(-\frac{3}{2}\)
• −5: is less than \(-\frac{3}{2}\)
• −1: is greater than \(-\frac{3}{2}\)

The value that falls in the solution set (i.e., satisfies \( k > -\frac{3}{2} \)) is:

−1