What can we infer about Billy based on the following text?

Question

But Mr. Greenslade at the head office in London had told him it was a splendid town. “Find your own lodgings,” he had said, “and then go along and report to the branch manager as soon as you’ve got yourself settled.”

(1 point)
Responses

He's tired
He's tired

He is traveling for work
He is traveling for work

He is the branch manager
He is the branch manager

He loves London

Answer 1

Based on the text provided, we can infer that:

He is traveling for work.

The context indicates that Billy has been instructed to find lodging and report to the branch manager, which suggests a work-related travel situation.

Answer 2

Use the table to answer the question.

x Substituted Evaluate True Statement?
−23

0
12
For the quadratic equation x2+20x=69
, complete the table by testing each of the given values to determine whether it is a solution. Identify which one of these values is in the solution set.

(1 point)
Only x=
is in the solution set.

Answer 3

To determine which value is a solution to the quadratic equation \(x^2 + 20x = 69\), we first rewrite the equation in standard form:

\[x^2 + 20x - 69 = 0\]

Now, we will substitute each value from the table into the equation and evaluate if it results in a true statement (i.e., whether the left side equals zero).

1. For \(x = -23\): \[ (-23)^2 + 20(-23) - 69 = 529 - 460 - 69 = 0 \] The statement is true.

2. For \(x = 0\): \[ (0)^2 + 20(0) - 69 = 0 - 69 = -69 \] The statement is false.

3. For \(x = 12\): \[ (12)^2 + 20(12) - 69 = 144 + 240 - 69 = 315 \] The statement is false.

Now, we summarize the results:

• For \(x = -23\), the statement is true (it equals 0).
• For \(x = 0\), the statement is false.
• For \(x = 12\), the statement is false.

Therefore, only \(x = -23\) is in the solution set.

So the final answer is:

Only x = -23 is in the solution set.

Answer 4

Use the table to answer the question.

x Substituted Evaluate True Statement?
7−11−−√

7
11−7–√

7+11−−√

11+7–√

For the quadratic equation (x−7)2=11
, complete the table by testing each of the given values to determine whether it is a solution. Identify the two solutions to the quadratic equation.

(1 point)
The smaller of the two solutions is x=
. The larger of the two solutions is x=
.

Answer 5

To solve the quadratic equation \((x - 7)^2 = 11\) and find the values for \(x\), we first take the square root of both sides to isolate \(x\):

\[ x - 7 = \pm \sqrt{11} \]

This gives us two equations:

1. \(x - 7 = \sqrt{11}\)
2. \(x - 7 = -\sqrt{11}\)

Now we can solve for \(x\) in both cases:

1. \(x = 7 + \sqrt{11}\)
2. \(x = 7 - \sqrt{11}\)

Next, we will use these solutions to complete the table and evaluate the given expressions:

1. For \(x = 7 - \sqrt{11}\):

   • Substitute: \(7 - \sqrt{11}\)
   • Evaluate: \((7 - \sqrt{11} - 7)^2 = (-\sqrt{11})^2 = 11\) (True statement)

2. For \(x = 7\):

   • Substitute: \(7\)
   • Evaluate: \((7 - 7)^2 = 0 \neq 11\) (False statement)

3. For \(x = 7 + \sqrt{11}\):

   • Substitute: \(7 + \sqrt{11}\)
   • Evaluate: \((7 + \sqrt{11} - 7)^2 = (\sqrt{11})^2 = 11\) (True statement)

4. For \(x = 11 + 7\):

   • Substitute: \(11 + 7 = 18\)
   • Evaluate: \((18 - 7)^2 = 11^2 = 121 \neq 11\) (False statement)

Now, summarizing the evaluations:

• \(x = 7 - \sqrt{11}\) is a true solution.
• \(x = 7 + \sqrt{11}\) is a true solution.
• \(x = 7\) is not a solution.
• \(x = 18 (11 + 7)\) is not a solution.

Identifying the Solutions:

• The smaller solution is \(x = 7 - \sqrt{11}\).
• The larger solution is \(x = 7 + \sqrt{11}\).

Final Answer:

• The smaller of the two solutions is \(x = 7 - \sqrt{11}\).
• The larger of the two solutions is \(x = 7 + \sqrt{11}\).

Thus, you can write:

The smaller of the two solutions is \(x = 7 - \sqrt{11}\). The larger of the two solutions is \(x = 7 + \sqrt{11}\).

Answer 6

How many solutions would the equation x2=−9
have? You do not need to solve for x.(1 point)
The equation would have
solution(s).

Answer 7

The equation \(x^2 = -9\) involves a square on the left side and a negative number on the right side.

In the real number system, the square of any real number is always non-negative (i.e., it cannot be negative). Since \(-9\) is negative, there are no real solutions to the equation.

However, if we consider complex numbers, we could find solutions. Specifically, we would find that \(x^2 = -9\) leads to \(x = 3i\) and \(x = -3i\) in the complex number system.

But since the problem does not specify the context (real or complex solutions) and is likely focused on the real number context, we conclude there are:

The equation would have 0 solution(s).

Answer 8

Assuming an equation with one side as a squared variable expression and the other side as a numeric expression, which of the following statements is correct?

Statement #1: If the numeric expression is greater than zero, there are two solutions.

Statement #2: If the numeric expression is greater than zero, there is one solution.

Statement #3: If the numeric expression is greater than zero, there are no solutions.

(1 point)
Statement #
is correct.

Answer 9

To analyze the statements regarding an equation of the form \(x^2 = k\) (where one side is a squared variable expression and the other side is a numeric expression \(k\)), we need to consider the value of \(k\):

1. If \(k > 0\):

   • The equation \(x^2 = k\) has two solutions: \(x = \sqrt{k}\) and \(x = -\sqrt{k}\).
   • So Statement #1 is correct.

2. If \(k = 0\):

   • The equation \(x^2 = 0\) has one solution, which is \(x = 0\).
   • So Statement #2 is correct in this specific case.

3. If \(k < 0\):

   • The equation \(x^2 = k\) has no real solutions since the square of a real number cannot be negative.
   • So Statement #3 is correct in this specific case.

Conclusion:

Since the question specifies the condition "if the numeric expression is greater than zero," the correct statement is:

Statement #1 is correct.

Statement #1: If the numeric expression is greater than zero, there are two solutions.