<p>I am stuck at these problems can you please help me?
I will really appreciate your help. :D
It will be great if you can show the answer step by step.
Thanks!</p>
<p>1) If the length of AB is 5 and the length of BC is 6,
which of the following could be the length of AC ?
(A) 10
(B) 12
(C) 13
(D) 15
(E) 16</p>
<p>2) Let # be defined by a # b = ab + a + b for all numbers
a and b.</p>
<p>For what value of x is the statement x # y = x
always true?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2</p>
<p>Answer 1: A
Answer 2: B</p>
<p>1) By the Triangle Inequality Theorem, if you have three sides of a triangle a, b and c, a + b must be greater than c, b + c must be greater than a, and a + c must be greater than b. So, given the fact that two sides have length 5 and 6, the third side must have a length less than 11. The only choice that satisfies this is A) 10.</p>
<p>2) Since x # y = xy + x + y and this equals x, set both expressions equal.
xy + x + y = x -> subtract x from both sides
xy + y = 0 -> factor out y
y(x+1) = 0
This means that either y = 0 or x + 1 = 0. Since the questions asks about x, set x + 1 = 0. Thus x = -1 and the answer is B) -1.</p>
<p>@EngineBus2015 Thank you so much for you simple and detailed explanations! I really appreciate it.
Can you or anyone else help me with these problem?
Thank you 
</p>
<p>x f (x) z g(z)
4 5 5 4
8 a 10 b
12 9 20 7</p>
<p>The table above shows some values for the functions
f and g. If f and g are linear functions, what
is the value of a-b ?
(A) 0
(B) 1
© 2
(D) 3
(E) 4</p>
<p>Answer: C</p>
<p>Alright so for this one, try to look for a pattern:
For f(x), the increments of x are the same, which means the spacing between 5 and a is the same as the spacing between a and 9. What falls between 5 and 9? 7. Therefore, a = 7.</p>
<p>For g(z), the increments of z are not the same. The difference between 10 and 20 is twice the difference between 5 and 10. This means that the difference between b and 7 is twice the difference between 4 and b. The value of b that satisfies this is b = 5 because the difference between 4 and 5 is 1 and the difference between 5 and 7 is 2.</p>
<p>a - b = 7 - 5 = 2 -> Answer: C)</p>
<p>@EngineBus2015 Thank you SO MUCH!!!
I really appreciate your help, Thank you man.</p>