Question 1

Simplify the radical, if possible. If imaginary, rewrite in terms of i and simplify.

Accepted Answer

The answer of Simplify the radical, if possible. If imaginary,...

Question 2

Perform the addition. Write the result in a + bi form.
(5 - 8i) + (6 + 5i)

Accepted Answer

The answer of Perform the addition. Write the result in...

Question 3

Solve the absolute value inequality. Write your answer in interval notation.
|-5 - x| + 11 < 10

Accepted Answer

The answer of Solve the absolute value inequality. Write your...

Question 4

Write the complex number in the standard form a + bi and clearly identify the values of a and b.

Accepted Answer

The answer of Write the complex number in the standard...

Question 5

Multiply and write your answer in a + bi form. 4i(1 + 3i)

Accepted Answer

Distributing the 4i, we get 4i + 12i^2. Since i^2 is equal to -1, we can simplify the expression to 12 - 4i, which is in the form a + bi. Therefore, the answer is (C) -12 + 4i.

Question 6

Multiply and write your answer in a + bi form.
(5 - i)(4 + 3i)

Accepted Answer

The answer of Multiply and write your answer in a...

Question 7

Solve the absolute value inequality. Write solution in interval notation. 3|x + 7| + 9 < 15

Accepted Answer

First, simplify the inequality: 3|x + 7| + 9 < 15 becomes 3|x + 7| < 6, then |x + 7| < 2. Solving for x yields -2 < x + 7 < 2, which simplifies to -9 < x < -5.

Question 8

Write the complex number in the standard form a + bi.

Accepted Answer

The answer of Write the complex number in the standard...

Question 9

Write the complex number in the standard form a + bi and clearly identify the values of a and b.
-2

Accepted Answer

The answer of Write the complex number in the standard...

Question 10

Determine the domain for the expression. Write your answer in interval notation.

Accepted Answer

The answer of Determine the domain for the expression. Write...

Question 11

Perform the subtraction. Write the result in a + bi form. (-5 - 2i) - (-8 - 4i)

Accepted Answer

To perform subtraction, we need to distribute the negative sign to the second complex number:

(-5 - 2i) - (-8 - 4i) = -5 - 2i + 8 + 4i

Now we can combine like terms:

= 3 + 2i

So the answer is choice A.

Question 12

Solve the absolute value equation. Write the solution in set notation. -2|x - 9| + 10 = 2

Accepted Answer

The answer of Solve the absolute value equation. Write the...

Question 13

Solve the absolute value inequality. Write the solution in interval notation. |x + 6| ? 6

Accepted Answer

To solve the inequality |x + 6| ≤ 6, we consider two cases: x + 6 ≤ 6 and -(x + 6) ≤ 6. Solving the first gives x ≤ 0, and the second gives x ≥ -12. Combining these gives -12 ≤ x ≤ 0, which in interval notation is [-12, 0].

Question 14

An arithmetic student needs at least a 70% average to receive credit for the course. If she scored 70%, 64%, and 72% on the first three exams, what score must she get on the fourth exam to receive credit for the course?

Accepted Answer

To achieve at least a 70% average across four exams, the sum of the percentages must be at least 280% (since 70% * 4 = 280%). The student has already scored 70%, 64%, and 72%, which sum to 206%. Therefore, to reach at least 280%, the student needs at least 74% on the fourth exam (280% - 206% = 74%).

Question 15

Solve the absolute value inequality. Write the solution in interval notation.
|x + 2| > 9

Accepted Answer

The answer of Solve the absolute value inequality. Write the...

Question 16

Determine the domain for the expression. Write your answer in interval notation.

Accepted Answer

The expression is not defined when the denominator is zero. Therefore, we need to exclude the value -5 from the domain. The interval notation for the domain excluding -5 is [-5, ∞).

Question 17

Solve the absolute value inequality. Write the solution in interval notation. 3|x + 1| + 9 ? 18

Accepted Answer

To solve the inequality, first we isolate the absolute value term by subtracting 9 from both sides:

3|x + 1| ≥ 9

Then divide both sides by 3:

|x + 1| ≥ 3

This inequality has two cases:

Case 1: x + 1 ≥ 0
If x + 1 ≥ 0, then |x + 1| = x + 1, so we have:

x + 1 ≥ 3
x ≥ 2

Case 2: x + 1 < 0
If x + 1 < 0, then |x + 1| = -(x + 1), so we have:

-(x + 1) ≥ 3
-x - 1 ≥ 3
-x ≥ 4
x ≤ -4

Therefore, the solution to the inequality is:

x ≤ -4 or x ≥ 2

In interval notation, this is written as:

(-∞, -4] ∪ [2, ∞)

Only choice B matches this solution.

Question 18

Simplify the radical, if possible. If imaginary, rewrite in terms of i and simplify.

Accepted Answer

The answer of Simplify the radical, if possible. If imaginary,...

Question 19

Simplify the radical, if possible. If imaginary, rewrite in terms of i and simplify.

Accepted Answer

The answer of Simplify the radical, if possible. If imaginary,...

Question 20

Simplify the radical, if possible. If imaginary, rewrite in terms of i and simplify.

Accepted Answer

The answer of Simplify the radical, if possible. If imaginary,...

Quiz 1: Equations and Inequalities

Simplify the radical, if possible. If imaginary, rewrite in terms of i and simplify.

Perform the addition. Write the result in a + bi form. (5 - 8i) + (6 + 5i)

Solve the absolute value inequality. Write your answer in interval notation. |-5 - x| + 11 < 10

Write the complex number in the standard form a + bi and clearly identify the values of a and b.

Multiply and write your answer in a + bi form. 4i(1 + 3i)

Multiply and write your answer in a + bi form. (5 - i)(4 + 3i)

Solve the absolute value inequality. Write solution in interval notation. 3|x + 7| + 9 < 15

Write the complex number in the standard form a + bi.

Write the complex number in the standard form a + bi and clearly identify the values of a and b. -2

Determine the domain for the expression. Write your answer in interval notation. $Determine the domain for the expression. Write your answer in interval notation. A) y \in (-?, -4) \cup (-4, ?) B) y \in (-?, 4] C) y \in [4, ?) D) y \in (-?, -4]$

Perform the subtraction. Write the result in a + bi form. (-5 - 2i) - (-8 - 4i)

Solve the absolute value equation. Write the solution in set notation. -2|x - 9| + 10 = 2

Solve the absolute value inequality. Write the solution in interval notation. |x + 6| ? 6

An arithmetic student needs at least a 70% average to receive credit for the course. If she scored 70%, 64%, and 72% on the first three exams, what score must she get on the fourth exam to receive credit for the course?

Solve the absolute value inequality. Write the solution in interval notation. |x + 2| > 9

Determine the domain for the expression. Write your answer in interval notation. $Determine the domain for the expression. Write your answer in interval notation. A) m \in (-?, -5) \cup (-5, ?) B) m \in (-?, -5] C) m \in [-5, ?) D) m \in (5, ?)$

Solve the absolute value inequality. Write the solution in interval notation. 3|x + 1| + 9 ? 18

Simplify the radical, if possible. If imaginary, rewrite in terms of i and simplify.

Simplify the radical, if possible. If imaginary, rewrite in terms of i and simplify.

Simplify the radical, if possible. If imaginary, rewrite in terms of i and simplify.