Nah it's fine haha I just graduated, so I have a lot of free time on my hands
7. So let's learn how each of the choices should look like in equation form.
Parabolas only have x^2. So things that (once simplified) should have a base equation of x^2+b=y. You can have 27052305x^2 + 91874917 = 19275175. That's still a parabola. Anything can change, there just can't be anymore higher degree variables than 2. So ONLY x^2.
Circles have a base formula of x^2+y^2=1. Honestly as long as the two squares are there and it equals 1 then it's a circle.
Hyperbolas have a base formula of ((x^2)/(a^2))-((y^2)/(b^2))=1. The a and b denotes slopes and vertices of each opposing parabola formed. Don't worry about those now cuz all we care about is what the equation is.
Ellipses are practically the same as hyperbolas except the minus is a plus.
Finally we look back at our equation.I'm gonna cheat because the other way is too long
We see that if we just purely remove EVERYTHING except for the x^2 and y^2, the correlation between those two is a minus, so it is x^2-y^2. Out of all the base equations I gave to you, the only one with a x^2-y^2 is hyperbolas, so the answer is C. You can try to simplify it, but it's gonna kill time which I'm sure you don't have.
8. For this, we try to cancel things out. Since we're trying to find the x, we try to cancel the y. To do this, we have to make the 2 ys from both equations cancel each other by being the negative form of the other. To do this we will multiply the first full equation by 2 to get 6x-2y=8. Now we can put the two equations on top of each other and cancel. 6x and 3x gives 9x. -2y and 2y gives 0. 8 and -5 gives 3. So the final equation is 9x=3 and x becomes 3, which is A.
9.Logs are stupid and retarded and I hate them but what must be done must be done. When logs add, that means they're multiplied. For example, log(xy)=logx+logy. SO for this we have logx+log(x+3) which means it's log(x(x+3))=1. What a log really means in this form is 10^1=x(x+3). If you ever see logs, sometimes they're log6(x)=1 (where the 6 is a subscript). That would mean 6^1=x, so x is 6. When there are no subscripts, it means a base of 10. So for our equation, it means 10^1=x(x+3). 10=x^2+3x or x^2+3x-10=0. We need to FOIL again, and we would get (x+5)(x-2)=0. We find that x=-5 and 2, so C.
10. This is just pretend the less than is an equal. (2x-5)(x+3)=0. x could be 5/2 or -3. Now we plug and chug. We plug in 3 numbers. One that is higher than our highest, one that is in the middle of the two numbers, and one that is lower than our lowest. I'm choosing 3, 0, and -4 because they're easy. Plugging in 3, we find that 6<0, which is false. Plugging in 0, we get that -15<0 which is true. Plugging in -4, we get 13<0, which is false. So now we know that any number above 5/2 and any number under -3 cannot be true. So, only numbers within those numbers are correct. Our choices are now B and C. Since we know that 5/2 and -3 would give us 0 which is not less than 0, we know that they cannot be the values, so the only answer is B.
11. Honestly, we can just plug in these two points into each equation and see if they work. If they work then that's the answer. BUT since we're learning
we need to make it ourselves. Their base equation is a line with a formula of y=mx+b where m is a slope and b is a constant. To find slope we do (y2-y1)/(x2-x1), so for us it is (6-8)/(3-9)=2/6=1/3. So now we know our equation is y=1/3x+b. Now we pick one of the points and plug it in. Let's do (3,6). We get 6=1+b. b as we find is 5. So our full equation is y=1/3x+5, which is C.
Hope you had fun learning