Question 1

Choose the one alternative that best completes the statement or answers the question.
Simplify the expression in terms of i:
-$\sqrt { - 49 }$
A) $7 i$
B) $49 i$
C) $i \sqrt { 7 }$
D) $- 7 i$

Accepted Answer

The square root of -49 can be simplified as $\sqrt{-49} = \sqrt{49} \cdot \sqrt{-1} = 7i$, where $i$ is the imaginary unit defined as $\sqrt{-1}$.

Question 2

Choose the one alternative that best completes the statement or answers the question.
-Aliyah earned an $6,000 bonus from her sales job for exceeding her sales goals. After paying taxes at a 30% rate, she invested the remaining money in two stocks. One stock returned the equivalent of
10% simple interest after 1 yr, and the other returned 4% at the end of 1 yr. If her investments
Returned $240.00 (excluding commissions) how much did she invest in each stock
A) $2,750 at 4% and $1,450 at 10%
B) $3,000 at 4% and $1,200 at 10%
C) $1,200 at 4% and $3,000 at 10%
D) $1,450 at 4% and $2,750 at 10%

Accepted Answer

After paying 30% taxes on her $6,000 bonus, Aliyah has $4,200 left to invest. Let x be the amount invested at 4% and (4200-x) be the amount invested at 10%. The equation for the total return is 0.04x + 0.10(4200-x) = 240. Solving this equation leads to x = $3,000 at 4% and $1,200 at 10%.

Question 3

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given a complex number a + bi, the expression a - bi is called the complex .

Accepted Answer

The answer of Write the word or phrase that best...

Question 4

Choose the one alternative that best completes the statement or answers the question.
-Suppose that a merchant buys a patio set from the wholesaler for $260. At what price should the merchant mark the patio set so that it may be offered at a discount of 25% but still give the merchant
A 20% profit on his $260 investment?
A) $325
B) $416
C) $377
D) $312

Accepted Answer

To achieve a 20% profit on a $260 investment, the merchant needs to sell the patio set for $260 * 1.20 = $312. To offer it at a 25% discount and still maintain this selling price, the marked price must be higher. Let x be the marked price. Then, x - 0.25x = $312, solving for x gives x = $416.

Question 5

Simplify the expression.
-$\frac { \sqrt { - 144 } } { \sqrt { - 36 } }$
A) $\frac { 1 } { 2 }$
B) 2
C) $2 i$
D) $- 2 i$

Accepted Answer

The expression simplifies to $\frac{\sqrt{-144}}{\sqrt{-36}} = \frac{12i}{6i} = 2$, where $i$ is the imaginary unit.

Question 6

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The imaginary number i is defined so that $i = \sqrt { - 1 } \text { and } i ^ { 2 } =$ .

Accepted Answer

The answer of Write the word or phrase that best...

Question 7

Simplify and write the result in standard form, a + bi.
-$$\frac { 4 + \sqrt { - 18 } } { 6 }$$
A) $\frac { 2 } { 3 } - \frac { \sqrt { 18 } } { 6 } i$
B) $\frac { 2 } { 3 } + \frac { \sqrt { 2 } } { 2 } i$
C) $\frac { 3 } { 5 } + \frac { \sqrt { 18 } } { 6 } i$
D) $\frac { 2 } { 3 } - \frac { \sqrt { 2 } } { 2 } i$

Accepted Answer

The answer of Simplify and write the result in standard...

Question 8

Choose the one alternative that best completes the statement or answers the question.
-One number is 33 more than another number. The quotient of the larger number and smaller number is 5 and the remainder is 1. Find the numbers.
A) 10 and 43
B) 8 and 41
C) 5 and 38
D) 11 and 44

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 9

Simplify the expression.
-$\sqrt { - 81 } \cdot \sqrt { - 3 }$
A) $- 27$
B) $9 \sqrt { 3 }$
C) $- 9 \sqrt { 3 }$
D) $9 \sqrt { - 3 }$

Accepted Answer

The answer of Simplify the expression.
-\(\sqrt { - 81 }...

Question 10

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given a complex number a + bi, the value of a is called the part and the value of b is
called the part.

Accepted Answer

The answer of Write the word or phrase that best...

Question 11

Simplify and write the result in standard form, a + bi.
-$\frac { 6 - \sqrt { - 18 } } { - 3 }$
A) $- 2 - 3 i \sqrt { 2 }$
B) $- 2 - i \sqrt { 2 }$
C) $- 2 + i \sqrt { 2 }$
D) $- 2 + 3 i \sqrt { 2 }$

Accepted Answer

The answer of Simplify and write the result in standard...

Question 12

Identify the real and imaginary parts of the complex number.
-$11 + 13 i$
A) Real: 11 ; imaginary: 13
B) Real: 24; imaginary: $i$
C) Real: 13; imaginary: 11
D) Real: 11 ; imaginary: $13 i$

Accepted Answer

The real part of the complex number $11 + 13i$ is 11, and the imaginary part is 13, without the $i$.

Question 13

Simplify the expression.
-$\frac { \sqrt { - 25 } } { \sqrt { 9 } }$
A) $- \frac { \sqrt { 5 } } { 3 }$
B) $\frac { 5 } { 3 }$
C) $\frac { 5 } { 3 } i$
D) $- \frac { 5 } { 3 }$

Accepted Answer

The expression simplifies to $\frac{\sqrt{-25}}{\sqrt{9}} = \frac{5i}{3}$, where $i$ is the imaginary unit, defined as $i = \sqrt{-1}$.

Question 14

Simplify and write the result in standard form, a + bi.
-$\frac { 14 - \sqrt { - 12 } } { 2 }$
A) $7 + 2 i \sqrt { 3 }$
B) $7 + i \sqrt { 3 }$
C) $7 - 2 i \sqrt { 3 }$
D) $7 - i \sqrt { 3 }$

Accepted Answer

The answer of Simplify and write the result in standard...

Question 15

Simplify.
-$$l ^ { 40 }$$
A) $- 1$
B) $i$
C) 1
D) $- i$

Accepted Answer

The expression $l^{40}$ seems to be a typo or misunderstanding. Assuming the intention was $i^{40}$, where $i$ is the imaginary unit defined as $i^2 = -1$, we can simplify $i^{40}$ by noting that $i^4 = 1$. Therefore, $i^{40} = (i^4)^{10} = 1^{10} = 1$.

Question 16

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-For a positive real number, b, the value $\sqrt { - b } =$ .

Accepted Answer

The answer of Write the word or phrase that best...

Question 17

Simplify and write the result in standard form, a + bi.
-$$\frac { - 8 - 10 i } { - 2 }$$
A) $4 + 10 i$
B) $4 - 5 i$
C) $4 - 10 i$
D) $4 + 5 i$

Accepted Answer

Dividing both the real part and the imaginary part of the numerator by the denominator gives $4 + 5i$.

Question 18

Simplify.
-$i ^ { 15 }$
A) $i$
B) $- 1$
C) 1
D) $- i$

Accepted Answer

The answer of Simplify.
-$i ^ { 15 }$
A) $i$
B) \(-...

Question 19

Identify the real and imaginary parts of the complex number.
-$\frac { 4 } { 7 }$
A) Real: $\frac { 4 } { 7 }$; imaginary: $i$
B) Real: 0 ; imaginary: $\frac { 4 } { 7 }$
C) Real: $\frac { 4 } { 7 }$; imaginary: 0
D) Real: 4 ; imaginary: 7

Accepted Answer

The given complex number is $\frac { 4 } { 7 }$ which does not have an imaginary part (i.e., a part with $i$). Therefore, its real part is $\frac { 4 } { 7 }$ and its imaginary part is 0.

Question 20

Choose the one alternative that best completes the statement or answers the question.
Simplify the expression in terms of i:
-$\sqrt { - 18 }$
A) $- 3 i \sqrt { 2 }$
B) $3 i \sqrt { 2 }$
C) $9 i \sqrt { 2 }$
D) $3 \sqrt { 2 i }$

Accepted Answer

The expression $\sqrt{-18}$ can be simplified to $\sqrt{18} \cdot \sqrt{-1}$. Since $\sqrt{-1} = i$ and $\sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2}$, the expression simplifies to $3i\sqrt{2}$.

Quiz 1: Equations and Inequalities

Choose the one alternative that best completes the statement or answers the question. Simplify the expression in terms of i: - $\sqrt { - 49 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a complex number a + bi, the expression a - bi is called the complex .

Simplify the expression. - $\frac { \sqrt { - 144 } } { \sqrt { - 36 } }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The imaginary number i is defined so that $i = \sqrt { - 1 } \text { and } i ^ { 2 } =$ .

Simplify and write the result in standard form, a + bi. - $\frac { 4 + \sqrt { - 18 } } { 6 }$

Choose the one alternative that best completes the statement or answers the question. -One number is 33 more than another number. The quotient of the larger number and smaller number is 5 and the remainder is 1. Find the numbers.

Simplify the expression. - $\sqrt { - 81 } \cdot \sqrt { - 3 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a complex number a + bi, the value of a is called the part and the value of b is called the part.

Simplify and write the result in standard form, a + bi. - $\frac { 6 - \sqrt { - 18 } } { - 3 }$

Identify the real and imaginary parts of the complex number. - $11 + 13 i$

Simplify the expression. - $\frac { \sqrt { - 25 } } { \sqrt { 9 } }$

Simplify and write the result in standard form, a + bi. - $\frac { 14 - \sqrt { - 12 } } { 2 }$

Simplify. - $l ^ { 40 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -For a positive real number, b, the value $\sqrt { - b } =$ .

Simplify and write the result in standard form, a + bi. - $\frac { - 8 - 10 i } { - 2 }$

Simplify. - $i ^ { 15 }$

Identify the real and imaginary parts of the complex number. - $\frac { 4 } { 7 }$

Choose the one alternative that best completes the statement or answers the question. Simplify the expression in terms of i: - $\sqrt { - 18 }$

Quiz 1: Equations and Inequalities

Choose the one alternative that best completes the statement or answers the question. Simplify the expression in terms of i: - −49\sqrt { - 49 }−49​

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a complex number a + bi, the expression a - bi is called the complex .

Simplify the expression. - −144−36\frac { \sqrt { - 144 } } { \sqrt { - 36 } }−36​−144​​

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The imaginary number i is defined so that i=−1 and i2=i = \sqrt { - 1 } \text { and } i ^ { 2 } =i=−1​ and i2= .

Simplify and write the result in standard form, a + bi. - 4+−186\frac { 4 + \sqrt { - 18 } } { 6 }64+−18​​

Choose the one alternative that best completes the statement or answers the question. -One number is 33 more than another number. The quotient of the larger number and smaller number is 5 and the remainder is 1. Find the numbers.

Simplify the expression. - −81⋅−3\sqrt { - 81 } \cdot \sqrt { - 3 }−81​⋅−3​

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a complex number a + bi, the value of a is called the part and the value of b is called the part.

Simplify and write the result in standard form, a + bi. - 6−−18−3\frac { 6 - \sqrt { - 18 } } { - 3 }−36−−18​​

Identify the real and imaginary parts of the complex number. - 11+13i11 + 13 i11+13i

Simplify the expression. - −259\frac { \sqrt { - 25 } } { \sqrt { 9 } }9​−25​​

Simplify and write the result in standard form, a + bi. - 14−−122\frac { 14 - \sqrt { - 12 } } { 2 }214−−12​​

Simplify. - l40l ^ { 40 }l40

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -For a positive real number, b, the value −b=\sqrt { - b } =−b​= .

Simplify and write the result in standard form, a + bi. - −8−10i−2\frac { - 8 - 10 i } { - 2 }−2−8−10i​

Simplify. - i15i ^ { 15 }i15

Identify the real and imaginary parts of the complex number. - 47\frac { 4 } { 7 }74​

Choose the one alternative that best completes the statement or answers the question. Simplify the expression in terms of i: - −18\sqrt { - 18 }−18​

Choose the one alternative that best completes the statement or answers the question. Simplify the expression in terms of i: - $\sqrt { - 49 }$

Simplify the expression. - $\frac { \sqrt { - 144 } } { \sqrt { - 36 } }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The imaginary number i is defined so that $i = \sqrt { - 1 } \text { and } i ^ { 2 } =$ .

Simplify and write the result in standard form, a + bi. - $\frac { 4 + \sqrt { - 18 } } { 6 }$

Simplify the expression. - $\sqrt { - 81 } \cdot \sqrt { - 3 }$

Simplify and write the result in standard form, a + bi. - $\frac { 6 - \sqrt { - 18 } } { - 3 }$

Identify the real and imaginary parts of the complex number. - $11 + 13 i$

Simplify the expression. - $\frac { \sqrt { - 25 } } { \sqrt { 9 } }$

Simplify and write the result in standard form, a + bi. - $\frac { 14 - \sqrt { - 12 } } { 2 }$

Simplify. - $l ^ { 40 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -For a positive real number, b, the value $\sqrt { - b } =$ .

Simplify and write the result in standard form, a + bi. - $\frac { - 8 - 10 i } { - 2 }$

Simplify. - $i ^ { 15 }$

Identify the real and imaginary parts of the complex number. - $\frac { 4 } { 7 }$

Choose the one alternative that best completes the statement or answers the question. Simplify the expression in terms of i: - $\sqrt { - 18 }$