<p>Please fully explain the answer and how to reach it. I feel I'm lacking some important skill when it comes to these types of problems. Please help me solve these, I'll check back tommarow. More than one response to the same question is fine, I like seeing different approaches and explanations. Thanks. Any tips or suggestions for solving a similar problem would be greatly appreciated.</p>
<ol>
<li>If -g(x)=g(-x) for all values of x, then which of the following could be g(x)?</li>
</ol>
<p>A. g(x)=x-1
B. g(x)=x+1
C. g(x)=x
D. g(x)=-x^2
E. g(x)=x^2</p>
<ol>
<li>The cube shown above has edge e. If X is the center of the cube, what is the length of AX in terms of e? (A is the bottom left corner of the cube), so AX would be like half the diagonal)</li>
</ol>
<p>A. (e radical 3)/2
b. (e radical 2)/3
C. e radical 2
D. e radical 3
E. 2e radical 3</p>
<ol>
<li><p>Six different points, A, B, C, D, E, and F, are labeled on a line in that order. The length of AD is 5.75 and the length of BF is 7.5. If the length of BC is 3, what is one possible length of CD? (Grid in)</p></li>
<li><p>For a quadratic function h(x), h(x)=t(x+5)(x-5) where t is constant. If h(d+3.6)=0, and d is a positive number, what is d?</p></li>
<li><p>A rectangular box is constructed from 10 square tiles, each of which has a perimeter of 24 centimeters. If the box is formed so that the tiles do not overlap, what is the volume of the box in cubic centimeters?</p></li>
</ol>
<ol>
<li>If -g(x)=g(-x) for all values of x, then which of the following could be g(x)?</li>
</ol>
<p>For whatever reason, I had a hunch that g(x) might be just x. So lets try it out.</p>
<p>Let g(x) = x
-g(x) = g(-x)
-x = -x …(substitution)</p>
<p>All things check out, so [C]</p>
<ol>
<li>For a quadratic function h(x), h(x)=t(x+5)(x-5) where t is constant. If h(d+3.6)=0, and d is a positive number, what is d?</li>
</ol>
<p>h(d + 3.6) = 0 = t<em>(d + 3.6 + 5)(d + 3.6 - 5)
0 = t</em>(d + 8.6)(d - 2.6)
For this to be true, t=0 or d = -8.6 or d = 2.6</p>
<p>They tell us ‘d’ is positive, so d = [2.6]</p>
<ol>
<li>A rectangular box is constructed from 10 square tiles, each of which has a perimeter of 24 centimeters. If the box is formed so that the tiles do not overlap, what is the volume of the box in cubic centimeters?</li>
</ol>
<p>Hard to do this in your head at 1:04 AM, but I’ll try. </p>
<p>I’m assuming the rectangular box is 3D. The only possible permutation of this box is such that 2 tiles on top, 2 tiles on bottom, 2 tiles on one side, 2 tiles on the other, and 1 on each side.
/__
/<em>/</em>/</p>
<p>I did my best to draw it ^
Each tile has a side length of 24/4 = 6 cm
So the dimensions are, 6x6x12 = [432 cm3]</p>
<ol>
<li>Six different points, A, B, C, D, E, and F, are labeled on a line in that order. The length of AD is 5.75 and the length of BF is 7.5. If the length of BC is 3, what is one possible length of CD? (Grid in)</li>
</ol>
<p>I’ll attempt to draw the line.</p>
<p>A<em>__B</em><em>3</em><em>C</em>____<strong><em>D</em></strong><em>E</em>____F (the measurements are arbitrary) </p>
<p>Find CD</p>
<p>AD= 5.75
BF= 7.5
BC = 3</p>
<p>BF-BC = CF = 4.5, which means that CD + DF = 4.5, so CD<4.5</p>
<p>So let CD = 4.4 ( I choose 4.4, because there could be another bound that I didn’t find)</p>
<ol>
<li>The cube shown above has edge e. If X is the center of the cube, what is the length of AX in terms of e? (A is the bottom left corner of the cube), so AX would be like half the diagonal)</li>
</ol>
<p>The length of a diagonal of a rectangular prism with side lengths A,B,C is sqrt(A^2 + B^2 + C^2).</p>
<p>So the length of this diagonal is just sqrt(3e^2)</p>
<p>We want half of this, so answer is sqrt(3e^2)/2 or e*sqt(3)/2</p>
<p>[A]</p>
<p>Greedisgood has the right idea for #4 but also a minor subtraction error:</p>
<p>(d + 3.6 - 5) = (d-1.4) and the answer is 1.4</p>
<p>BTW, the diagram for #5 is excellent!</p>
<ol>
<li>Six different points, A, B, C, D, E, and F, are labeled on a line in that order. The length of AD is 5.75 and the length of BF is 7.5. If the length of BC is 3, what is one possible length of CD? (Grid in)</li>
</ol>
<p>A_<strong><em>B</em></strong><em>C</em><strong><em>D</em></strong><em>E</em>___F</p>
<p>B_________________<strong><em>F = 7.5
A</em></strong>________<strong><em>D = 5.75
B</em></strong>_C = 3</p>
<p>B to F (7.5) - B to C (3) = 4.5
4.5 is the total distance between C to D, D to E, and E to F.
A to D (5.75) - B to C (3) = 2.75
2.75 is the total distance between A to B and C to D.
This means C to D is less than 2.75.</p>
<p>**Answer:<a href=“0,%202.75”>/b</a></p>
<ol>
<li>If -g(x)=g(-x) for all values of x, then which of the following could be g(x)?</li>
</ol>
<p>A. g(x)=x-1
B. g(x)=x+1
C. g(x)=x
D. g(x)=-x^2
E. g(x)=x^2</p>
<p>When I initially read the problem I’m like oh boy going to have to plug in a number for all 5 answers, but when I read it again I realized any “x” to an odd power will yield the same answer. It doesn’t matter if it’s x to the first like in C or x to the 2133131 power.</p>
<ol>
<li>A rectangular box is constructed from 10 square tiles, each of which has a perimeter of 24 centimeters. If the box is formed so that the tiles do not overlap, what is the volume of the box in cubic centimeters?</li>
</ol>
<p>1) Ignore the 24 centimeters until you form your box with the 10 identical tiles.
2) A basic box has 6 sides or 6 tiles that leaves you with four left over.
3) Make four sides rectangles by adding a piece to each side.
4) Dimensions of the box are now: 2 tile sides by 1 tile side by 1 tile side.
5) 24 cm is equal to 1 sqr tile. 24 / 4 = 6 cm per side
6) 12x6x6</p>
<p>Answer: 12x6x6 = 432cm^3</p>
<ol>
<li>For a quadratic function h(x), h(x)=t(x+5)(x-5) where t is constant. If h(d+3.6)=0, and d is a positive number, what is d?</li>
</ol>
<p>Going into this problem first isolate the variable “t” with the initial equation because you are solving for “d” and having two variables could be tricky.</p>
<p>Solve for t:
0 = h(d+3.6)
0 = t(d+3.6+5)(d+3.6-5)
Divide by (d+3.6+5)
0 = t(d+3.6-5)
Divide by (d+3.6-5)
0 = t
t = 0</p>
<p>Solve for d:
h(d+3.6) = t(d+3.6+5)(d+3.6-5) = 0
0 = t(d+3.6+5)(d+3.6-5)
Divide by t
0 = (d+3.6+5)(d+3.6-5)
0 = (d + 8.6)(d - 1.4)
d = -8.6
d = 1.4</p>
<p>Answer: d has to between (0,∞) so d = 1.4</p>