<h2>Hey everybody, this is my first post so I hope i'm not breaking any posting rules by posting a Maths question here, maybe there's a section for it. I don't know.</h2>
<p>If b > 1. what is the slope of the line in the xy-plane that passes through the points (b,b^2) and (b^2,b^4)?
(A) -b^2 + 5b
(B) -b^2 + b
(C) -b^2 - b
(D) b^2 - b
(E) b^2 + b</p>
<p>I'd like an explanation for why the answer is actually (E), Thanks a lot.</p>
<p>EDIT*</p>
<h2>There’s another question ^,^</h2>
<p>If x>0, n is a nonnegative integer, and:
n+1 n+2 n+3
2x + x = x </p>
<p>(It’s written this way to clarify the exponents: 2 X x^n+1 / x^n+2 / x^n+3)
-which of the following must equal x^3?</p>
<p>Choices:
(A) 2+2x+x^2
(B) 2x+x^2
(C) 2+x^2
(D) 2+x
(E) 3x
Thanks again!</p>
<p>ok 1)
use the formula for slope: (y2-y1)/(x2-x1)
so
(b^4-b^2)/(b^2-b ) =>
(b^2-b)(b^2+b)/(b^2-b) => cancel it out
B^2+b/1 = E</p>
<p>i don’t really understand what you wrote for the second question, hope you understood my explanation for the first.</p>
<p>First problem:</p>
<p>The easiest way is to choose a value for b. A good value in this case is 10. That makes the points (b, b^2) and (b^2, b^4) into (10, 100) and (100, 10,000), respectively. Use the slope formula to get the equation: (10,000-100)/(100-10). This simplifies to 110. Then all you have to do is plug 10 into all of the answer choices to see which one equals 110. For instance, choice A is wrong because when you substitute 10 for b in the equation -b^2+5b, you get -50. Only choice E satisfies the equation, so </p>
<p>Choice (E) is correct.</p>
<p>Second problem:</p>
<p>This took some number sense for me to figure out. You should choose 2 as the value of x. When you do that, the first part of the equation, 2(2^(n+1)), becomes 2^(n+2) because you add the exponents when you multiply two of the same number. Then, you are left with 2^(n+2) + 2^(n+2) = 2^(n+3). The left side of the equation can be combined to 2(2^(n+2)), and using the same concept as before, to 2^(n+3).</p>
<p>Therefore 2^(n+3) = 2^(n+3). Obviously, n could therefore be any real number, which means that 2 satisfies the equation. Then, simply substitute 2 into the equation x^3 to get 8. Plug 2 into all of the answer choices and you will find that only choice B matches that, so</p>
<p>Choice (B) is correct.</p>
<p>I can algebraically reason out the second problem, but it is very hard for me to explain. </p>
<p>If you don’t understand my explanation, maybe someone else can give you a clearer one.</p>
<p>ahh, i understood the second question. it’s quite simple:
to get what x^3 gets just plug n=0 since n+3 = 3.</p>
<p>in other words
n+1 n+2 n+3
2x + x = x => 2x^1 + x^2 = x^3 => 2x+x^2 hence it’s b.
And I think learning algebra is better than plugging in numbers every question no offence, since usually plugging in 5 answers is usually just longer and might not work?</p>
<p>You should know how to do it algebraically, but plugging in numbers is very often the fastest and simplest way to solve high level problems.</p>
<p>Also, thenaga, the way you solved it wasn’t algebraically. All you did was plug in 0 for n.</p>
<p>I wrote out everything to help him in my explanation, so that may have made it seem drawn out. In reality, I finished both of these problems in 30-40 seconds each.</p>
<p>Well in regards to the second question, you kinda have to plug in n=0 as that is what the question asks you to do (x^3 = n^(0+3))</p>
<p>I was more referring to the first question where calculating from A -> E in calculator just takes too long imo and probably u will run into a mistake with the slip of a finger</p>
<p>Lol. I hope you don’t think I had to use a calculator with the method I described. </p>
<p>If you really believe the essence of what you said in the rest of your comment, then good luck with that LOL.</p>