X was the case, so/but/since/because Y happened [closed]
First of all, none of those choices are particularly good, but some are better than others. This answer is more along the lines of general multiple-choice strategy than an explanation of grammar, but I'll try to explain why the best choice is B.
Generally, cars tend to stop moving when they hit trees, and so the best way to combine the two sentences would either be to say that the car was going 100 MPH when it hit the tree, or that the car was going 100 MPH until it hit the tree.
C and D mean the same thing (the car was propelled to a speed of over 100 mph as a result of hitting the tree), so they're obviously both wrong.
A could be correct in the context of there being some sort of barrier that would have prevented objects moving slower than 100 mph from hitting the tree - "the blue car was going fast enough to break through the barrier, and therefore it hit the tree."
B, while poorly written, is most likely the correct answer, as it could be read as "the blue car was going at over 100 mph... but then it hit a tree." Since this answer requires fewer assumptions than answer A, it is a better choice.
None of the answers is correct. "The car dashed the tree" is not correct English, and no variations on it are going to be correct.
When used with an object, to "dash" something means to strike with it. So "I dashed the glass on the floor". If "the car dashed the tree", it means the car picked up the tree and hit something with it. That is obviously not what is meant.
(There are other meanings of dash, such as to go fast, or to draw a line with dashes, but none of them are applicable here. Ancient writers also used 'dashed' in this way, but if you are learning to speak modern English I really don't recommend it - most people you speak to will assume you are incorrect in using 'dashed' this way)
Some sentences that might be correct, and mean the car struck the tree:
- The car dashed against the tree
- The car dashed into the tree
However 'dashed' is not the best word to use in this case. Most English speakers would use 'crashed'.
To deal with the prepositions, which is what your question is about, either "so" or "but" would be applicable. "So" means that the 100mph speed was the reason for it striking the tree; "but" means that striking the tree caused it to stop going at 100mph. 'Since' and 'because' both would mean that crashing into the tree was the reason it was going 100mph, which is obviously wrong.
There is no answer given that is surely correct. Answers A or B in some cases might be, but we do not know.
Even if you would use "dash into" and left out "blue" in the answers there is no expression that is known to be correct.
Definitely correct only a combination with and or before would be, because
The car dashed the tree. It was going at over 100mph.
only gives little information:
- Car dashed tree
- Car was faster than 100mph some time before the crash (directly or before it left the street or if it even was on one is not known)
The car was going at over 100mph and dashed into the tree.
The car was going at over 100mph before it dashed into the tree.
A closer look why all answer can be or must be wrong.
A) The (blue) car was going 100mph, so it dashed 'into' the tree.
So? Is the dash a result of going 100mph? Would it not have crashed into it with lesser speed? Would it have been possible to miss the tree even with 100mph?
B) The (blue) car was going at over 100mph, but it dashed 'into' the tree.
Why but? What did the crash prevent the car from? Reaching the finish line? Getting over 110mph?
C) The (blue) car was going at over 100mph, since it dashed 'into' the tree.
Since? It definitely did not go at over 100mph as a result of the dash.
D) The (blue) car was going at over 100mph because it dashed 'into' the tree.
Because? Same as answer C.