Math Questions

Test Preparation SAT Preparation
1

<p>Hey guys, i was wondering if you could help me with two math problems.
1. x^2 + 16x + a= (x+b)^2
in the equation above, a and b are constants. If the equations is true for all values of x, what is the value of a?
answer: 64. i need to know how to do these kinds of problems</p>

<ol>
<li>In the xy coordinate system, a circle has a center at (6, 3.5). This circle has exactly one point in common with the x axis. If the point (3.5, t) is also a point on the circle, what is the value of it?
answer: 25</li>
</ol>

<p>I need help on how to do these kinds!
thanks</p>

2

<p>Ok, both these are tough questions. Here are the explanations.

  1. In order to do this problem, you must know how to FOIL. If you foil x^2 + 16x + a= (x+b)^2, you end up with x^2 +16x+ a= x^2 +2xb + b^2. Since you know that the left side of the equation must equal the right side of the equation, the constants must be the same and they must match up with the corresponding terms of the left side of the equation. So, you have to look at the right side of the equation in seperate parts. In other words, the first part of the right equation is x^2, which matches the first part of the left equation. Then the second part is 2xb and that has to match up with 16x; so you can set them equal to one another. 2xb=16x. The x’s cancel out and b=8. Then look at the third part of the right side of the equation, b^2, and that has to match with the left side of the equation, a; so you can set that equal to one another. b^2= a. Since you’ve found b already, just plug in. 8^2=a=64. You have your answer.</p>

<p>For the second one, i have the problem in my test booklet. I’ll look at it and tell u how to solve it ASAP.</p>

3

<p>Is the second asking for the value of t?</p>

4

<p>is the answer really 25??? i can’t seem to get it.</p>

5

<p>ohhh…on the circle??? i was thinking of on the CIRCUMFERENCE.</p>

6

<p>On the circle means that it’s on its circumference.</p>

7

<p>sorry, it was supposed to say 2.5</p>

8

<p>and yea, solve for t</p>

9

<p>For #2 (sorry I’m in a hurry)</p>

<p>You know that the circle is touches the x axis on one and only one point. So the point of intersection must be perpendicular to the x axis. Giving us the point (6, 0) - so the radius is 3.5. So the distance between the second point (3.5, t) and the center (6, 3.5) must be 3.5. Solve using the distance formula…</p>

10

<p>1) x^2 + 16x + a= (x+b)^2
in the equation above, a and b are constants. If the equations is true for all values of x, what is the value of a?</p>

<p>x^2 + 16x + a = x^2 + bx + bx + b^2 (expand the left side)
16x + a = 2bx + b^2 (cancel out x^2)</p>

<p>Now we have an ‘x’ term on both sides and a constant on both sides. Equate the ‘x’ term of one side with the other ‘x’ term, and then the two constants.</p>

<p>16x = 2bx (this is the ‘x’ term equation)
16 = 2b (cancel x’s)
b = 8</p>

<p>a = b^2 (this is the constant equation)
a = 8^2
a = 64</p>

<p>2) See spratley’s method</p>