Who can do these three math questions?

Test Preparation SAT Preparation
1

<h1>1</h1>

<p>n = p^2 - 100p</p>

<p>n and p are prime numbers. What is the value of n?</p>

<h1>2</h1>

<p>2x - 5y = 8
4x + ky = 17</p>

<p>For which of the following values of k will the system of equations above have no solution?</p>

<p>A) -10
B) -5
C) 0
D) 5
E) 10</p>

<h1>3</h1>

<p>In triangle MPQ, the measure of angle M is 30 degrees and the measure of angle Q is 45 degrees. The length of segment MP is 10, what is the length of segment MQ?</p>

<p>And answer this: What do the symbols of a quadratic function (x^2 + by + c) determine in the shape of its graph? What do "x", "b", and "c" determine?</p>

2

<h1>2: -10 (A)</h1>

<h1>3: 5 + 5(root 3)</h1>

<p>Could you check if those are the correct solutions? I couldn’t figure out number 1. I’ll explain them to you if I am correct.</p>

3

<p>Both are correct. Kindly elaborate. :-)</p>

4

<p>PS. In the last question, I mean, what do the signs of each of the three terms determine? Like if it’s the x^2 is grouped with a negative coefficient, the parabola will be upside down, meaning that there will be a maximum point on the graph. And so on.</p>

5

<h1>2:</h1>

<p>2x - 5y = 8
y = (2/5)x - (8/5)
Now the other equation we have is 4x + ky = 17
To get something with “no solution” you have to eliminate the variable.
Basically, 4x + k(2/5)x = 0
So therefore k is -10, because 4x + -10(2/5)x = 0</p>

<h1>3:</h1>

<p>Draw a diagram, and use the sine rule.
(10)/(sin 45) = MQ/(sin 105)
Solve for MQ.</p>

<p>Oh and for you last question what I usually do is this:
Rearrange the equation in the form a(x - h) + k.
Then, “a” affects the orientation and width of the parabola, h represents the horizontal shift, and k represents the vertical shift. I’m sure there’s a more direct way for this, but I can’t seem to recall it!</p>

6

<p>Thank you for your explanations.
I understood #2, however, not so much with #3 since I’m not familiar with sin/cos/tan, if you have any other method, I’d be very grateful!</p>

<p>And for the last question, yep, there is a more direct approach I’m afraid, so we’ll have to wait for people like DrSteve to elaborate.</p>

<p>Thank you for your contribution! :-)</p>

7

<h1>1</h1>

<p>n = p^2 - 100p</p>

<p>n and p are prime numbers. What is the value of n?</p>

<p>n = p^2 - 100p
n = p(p - 100)</p>

<p>n and p MUST be prime numbers</p>

<p>so the answer is 101</p>

<p>-Solved-</p>

<p>PS: can n = p?</p>

8

<p>On the SAT, when it comes to ax^2 + bx + c, you only need to know a little:</p>

<p>The sign of the a value determines whether the parabola opens up or down. And bigger a values give narrower, steeper parabolas.</p>

<p>The c value is the y-intercept.</p>

<p>And the b value? Well, the math answer is that together with the a value, it determines the location of the vertex: x=-b/2a</p>

<p>But the SAT answer? I have never seen an SAT problem where you needed to know what the b value does. So don’t worry about it!</p>

9

<p>@Jwisgod, you are correct, and yes they can be equal. Thanks!</p>

<p>@pckeller, that was very enlightening, your explanation is appreciated.</p>

<p>Thanks everyone!</p>

10

<p>@SirWanksAlot:</p>

<p>You could just draw the diagram, and drop an altitude.
The triangles that formed are a 30-60-90 triangle and a 45-45-90 triangle. Just use the relations that you know for those triangles, and you will be able to solve it.</p>

11

<p>Ah, yes! And choose a value in between, right?</p>