No, the first part is not a dangling modifier because it has an “it,” which clearly refers to the psychology class. Dangling modifiers will refer to a subject without using a noun or pronoun to represent the subject.
(A) and (B) don’t say who’s buying the car. (D) and (E) have wrong forms of the verb “have”—(D) has it as an infinitive for no reason, and (E) puts an incorrect “-ing” on it.
The rule about perpendicular line slopes tells you that (5, e) and (f, 7) are on a line with a slope of 5. So use the slope formula to write an equation, then solve it for e:
The “is why” is unnecessary. Fix it by replacing “is why” with a comma:
By incorporating Pueblo figures into her strongly geometric and abstract work, Pueblo artist Helen Hardin has had a significant impact on contemporary Native American art.
Sure, “their” refers to the enthusiasts, but that doesn’t make the structure correct. As long as it is, this is a fragment as written. We can fix that by giving it a main verb—changing “their having” to “they have.”
The problem with “their having” is that it suggests that the sentence will continue, e.g. “Many jazz enthusiasts would have to admit that their having overlooked Bennie Nawahi IS A MAJOR OVERSIGHT.” Now the sentence is complete, because it has a main verb: “is.”
Sentences 3 and 4 are both about how castles are fortified to keep unwanted people out. (A) is a total distraction—who cares who built the walls? (C) links the sentences nicely—the walls, moats, etc. were there to scare you away, but if you weren’t scared away, then the people in the castle would have a much easier time shooting you with arrows than you would shooting them.
That’s a syntax you’re probably not used to seeing, so it’s natural to be suspicious of it, but you can eliminate all the other choices for very legit reasons:
It’s not wrong because it’s not wrong. Change your thought pattern when you choose something that’s not an error: instead of wondering why it’s not wrong, file it away in your brain as an acceptable way to phrase things.
This is all about solving for expressions—one of the most important skills you can develop for SAT math dominance.
Foil out the first equation:
x^2 – 2xy + y^2 = 37
Note that you know xy, so you can substitute!
x^2 –2(4) + y^2 = 37
x^2 + y^2 = 45
Cool so far, right? But you’re not done. You need (x + y)^2, which is very much NOT the same thing as above. FOIL that out, too!
x^2 + 2xy + y^2 = ?
Awesomely, we already know what all those things are.
Rearrange and substitute:
x^2 + y^2 + 2xy
45 + 2(4)
I’ve done this one here.
If you post a pic of the figure in the comments, I will help you with this.
Nothing’s wrong with “the failure” by itself—the problem is “the failure at giving.” Idiomatically, we say “the failure to give.”
But there is a FANBOYS there: “and.” The therefore is set off by a comma on each side—it’s a little aside, not the main transition. Since the second part of the sentence has the same subject as the first, we don’t need a comma before “and.”
Here, check this out:
The new vaccine is effective at preventing certain forms of pneumonia and should be more widely used…
See—no comma needed.
So, like this?
The first thing you know is that, because AO and BO are radii, they’re equal to each other. Because we also know AB = AO, we know that triangle ABO is equilateral, and thus all its angles are 60 degrees.
We also know that angle ABC is 90 degrees, because it’s an inscribed angle corresponding to a diameter. I’ve never seen a real SAT question requiring this knowledge,
so I’m guessing this isn’t a real SAT question. (Edit: It is a real SAT question, and you don’t need that knowledge—see the comments below this post.)
So if angle BAC is 60 degrees and angle ABC is 90 degrees, then angle BCA must be 30 degrees.