1) Afew participles, such as concerning, considering, failing, and granting, function as prepositions and may be used to introduce a sentence without fear of dangling. Additionally, participial phrases, such as speaking of and judging by, may also work as introductory clauses without fear of dangling. A) After reading the pharmaceutical research, the report remained confusing.
B) Having completed the report in a timely manner, Jim met all his deadlines.
C) Being a very organized file keeper, Mr. Anthony was able to review.
D) Being the coordinator for the working mothers' co-op, Keisha's schedule is very busy.
E) When speaking clearly and slowly, the mike on the sound system works better.
2) Identify the independent clauses in the list below.
A) Jamal resigned.
B) The system was updated last week.
C) Marcia's poor typing.
3) Identify the dependent clauses in the list below.
A) Because he was job hunting.
B) Mr. Hu returned.
C) If Jimmy concludes today.
4) Identify the sentences with correct parallel structure.
A) As we prepared our presentation for the KLM proposal, Jim revised the PowerPoint, Linda double checked the numbers, and I created a handout.
B) Interpersonal communication, critical thinking, and the ability to problem solve are all qualities we look for in job candidates.
C) Below the lobby, on the first floor, and off to the left, you will find a check-in desk.
D) After the staff meeting, Lucas is always cranky, infocused, and wants a nap.
E) As receptionist, his duties include answering the phone, forwarding calls, and taking messages.

1. The Dangling Modifiers

Dangling modifiers modify a sentence but they do so without giving information as to who the subject of the action in the sentence. For example, After doing her homework, Hillary went to watch TV. Hillary is the subject here but the After does not show that.

The sentences with dangling modifiers therefore are;

A) After reading the pharmaceutical research, the report remained confusing.

D) Being the coordinator for the working mothers' co-op, Keisha's schedule is very busy.

E) When speaking clearly and slowly, the mike on the sound system works better.

2. Independent Clauses.

These are clauses that can be sentence on their own with no need for any additions.

The Independent Clauses are;

A) Jamal resigned.

B) The system was updated last week

3. Dependent Clauses

These cannot be a sentence on their own and require additions to be complete.

The dependent clauses are;

A) Because he was job hunting.

C) If Jimmy concludes today.

4. Parallel Structures

This is a sentence structure that aims to show that the clauses connected have the same importance. Coordinating conjunctions are used to connect the clauses such as or, and, for, etcetera.

The Parallel Structured sentences are;

A) As we prepared our presentation for the KLM proposal, Jim revised the PowerPoint, Linda double checked the numbers, and I created a handout.

C) Below the lobby, on the first floor, and off to the left, you will find a check-in desk.

E) As receptionist, his duties include answering the phone, forwarding calls, and taking messages.

start by isolating the variable on one side by adding 43w^2 to both sides.   the equation will read:

25w^2+5=0

*subtract 5 from both sides*

25w^2=-5

*divide both sides by 25*

w^2=-1/5

*take the square root of both sides*

w=√(-1/5)

the square root of -1 is i.   the square root of 5 remains √5

the answer is i/√5.

hope this