Question

find the value of (3sqrt{x} + 7) if (x = 25).

a) 32
b) 82
c) -8
d) 22

question 10 (5 points)
which table correctly lists the three solutions for the equation (5x + y = 14)?

a)
\

$$\begin{tabular}{|c|c|c|c|} \\hline x & -1 & 0 & 1 \\\\ \\hline y & 9 & 14 & 19 \\\\ \\hline \\end{tabular}$$

b)
\

$$\begin{tabular}{|c|c|c|c|} \\hline x & -1 & 0 & 1 \\\\ \\hline y & -5 & 0 & 5 \\\\ \\hline \\end{tabular}$$

c)
\

$$\begin{tabular}{|c|c|c|c|} \\hline x & -1 & 0 & 1 \\\\ \\hline y & 19 & 14 & 9 \\\\ \\hline \\end{tabular}$$

d)
\

$$\begin{tabular}{|c|c|c|c|} \\hline x & -1 & 0 & 1 \\\\ \\hline y & 21 & 28 & 7 \\\\ \\hline \\end{tabular}$$

Explanation:

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<reasoning>

Evaluate the radical expression

Using the Algebraic Expression Evaluation knowledge point
\[

$$\begin{aligned} &x = 25\\ &3\sqrt{x} + 7 = 3\sqrt{25} + 7\\ &3(5) + 7 = 15 + 7 = 22 \end{aligned}$$

\]

Solve the linear equation for y

To find the solutions for the equation \(5x + y = 14\), we isolate \(y\) to make calculations straightforward.
\[
y = -5x + 14
\]

Test the x-values for the linear equation

We substitute the \(x\)-values \(-1\), \(0\), and \(1\) into our isolated equation to find the corresponding \(y\)-values.

• For \(x = -1\):

\[
y = -5(-1) + 14 = 5 + 14 = 19
\]

• For \(x = 0\):

\[
y = -5(0) + 14 = 14
\]

• For \(x = 1\):

\[
y = -5(1) + 14 = -5 + 14 = 9
\]

Match the calculated values to the options

The correct table must contain the pairs \((-1, 19)\), \((0, 14)\), and \((1, 9)\). Looking at the choices:

• Option A lists \(y\)-values: \(9, 14, 19\)
• Option B lists \(y\)-values: \(-5, 0, 5\)
• Option C lists \(y\)-values: \(19, 14, 9\)
• Option D lists \(y\)-values: \(21, 28, 7\)

Therefore, Option C is the correct table.
</reasoning>

<answer>

Question 1

<mcq-option>A) 32</mcq-option>
<mcq-option>B) 82</mcq-option>
<mcq-option>C) -8</mcq-option>
<mcq-correct>D) 22</mcq-correct>

Question 10

<mcq-option>A) Table with y-values: 9, 14, 19</mcq-option>
<mcq-option>B) Table with y-values: -5, 0, 5</mcq-option>
<mcq-correct>C) Table with y-values: 19, 14, 9</mcq-correct>
<mcq-option>D) Table with y-values: 21, 28, 7</mcq-option>
</answer>

<post_analysis>
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"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Linear Equation Solutions"
]
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</post_analysis>

Answer:

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<reasoning>

Evaluate the radical expression

Using the Algebraic Expression Evaluation knowledge point
\[

$$\begin{aligned} &x = 25\\ &3\sqrt{x} + 7 = 3\sqrt{25} + 7\\ &3(5) + 7 = 15 + 7 = 22 \end{aligned}$$

\]

Solve the linear equation for y

To find the solutions for the equation \(5x + y = 14\), we isolate \(y\) to make calculations straightforward.
\[
y = -5x + 14
\]

Test the x-values for the linear equation

We substitute the \(x\)-values \(-1\), \(0\), and \(1\) into our isolated equation to find the corresponding \(y\)-values.

• For \(x = -1\):

\[
y = -5(-1) + 14 = 5 + 14 = 19
\]

• For \(x = 0\):

\[
y = -5(0) + 14 = 14
\]

• For \(x = 1\):

\[
y = -5(1) + 14 = -5 + 14 = 9
\]

Match the calculated values to the options

The correct table must contain the pairs \((-1, 19)\), \((0, 14)\), and \((1, 9)\). Looking at the choices:

• Option A lists \(y\)-values: \(9, 14, 19\)
• Option B lists \(y\)-values: \(-5, 0, 5\)
• Option C lists \(y\)-values: \(19, 14, 9\)
• Option D lists \(y\)-values: \(21, 28, 7\)

Therefore, Option C is the correct table.
</reasoning>

<answer>

Question 1

<mcq-option>A) 32</mcq-option>
<mcq-option>B) 82</mcq-option>
<mcq-option>C) -8</mcq-option>
<mcq-correct>D) 22</mcq-correct>

Question 10

<mcq-option>A) Table with y-values: 9, 14, 19</mcq-option>
<mcq-option>B) Table with y-values: -5, 0, 5</mcq-option>
<mcq-correct>C) Table with y-values: 19, 14, 9</mcq-correct>
<mcq-option>D) Table with y-values: 21, 28, 7</mcq-option>
</answer>

<post_analysis>
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"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Linear Equation Solutions"
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