Some math questions

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1

<p>If (a-10b)^2=a^2+ 100b^2,
what is a^2b^4</p>

<p>I distributed the exponent on the left, but it just gives you that both sides are equal to each other, which doesn't help solve at all. No idea whatsoever what to do with this problem.</p>

<ol>
<li>The surface of a three-dimensional solid consists of faces, each of which has the shape of a polygon. What is the least number of such faces a solid can have?
A 2
B 3
C 4
D 5
E 6</li>
</ol>

<p>I put 2, because I thought of a cone, which has the two triangular bases or whatever and the circles, and circles aren't polygons so yeah. But I am absolute garbage at 3D geometry so I'm most likely wrong. </p>

<ol>
<li>The five digits 1,2,3,4,5 are used to form 5-digit numbers in which no digit is repeated. How many such five-digit numbers greater than 40,000 are possible?
24
48
64
96
120</li>
</ol>

<p>I got 48, but it's impossible to be 100% confident on these types of problems so I have to ask here.</p>

2

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</p>

<p>(a-10b)(a-10b)=a²+100b²
a²-20ba+100b² = a² + 100b²
-20ba = 0 (b or a has to be 0)
(a^2)(b^4) = 0</p>

<p>I think you made a mistake. It doesn’t give you that both sides are equal to each other.</p>

3

<p>Well I did something right…0 is what I put for my ‘meh it’s free-response need to put something down’ answer, lol. Unconfident guessing ftw.</p>

<p>OOOOOH you’re supposed to foil it…wow I usually catch stuff like that.</p>

4

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</p>

<p>Think of it this way: A triangle is a 2D polygon with least vertices. Make this into a 3D solid, you get a triangular pyramid which has 4 faces.</p>

5

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</p>

<p>First, there are 5 options for each digit places. (ten thousands place, thousands place, hundreds… so on)
The number has to be greater than 40,000 (which means the ten thousands place only has 2 choices.)</p>

<p>2 options in ten thousands place,
4, 3, 2, and 1 option(s) in other places.</p>

<p>2<em>4</em>3<em>2</em>1 = 48 numbers greater than 40,000 with no repeating digits.</p>