Answer and Step-by-step explanation:
A Diophantine equation is simply an equation that relates whole numbers.
There are various types of Diophantine equations, but probably the most basic is the linear version: ax + by = c.
Different methods also abound for solving these types of equations:
- Coordinate geometry
- Modular arithmetic
- Induction
Hope this helps!
For
the first question; we have a problem dealing with translations.
Our goal is to translate
the word problem into an algebraic one. So our numbers are
60, 2, and 5. Our variable, or the letter holding the unknown
number's place
value, is
N. <span>
</span>The
problem states that 60 is MORE THAN the PRODUCT of 5 and N. Focus
on the words I bolded and capitalized. These are your key words that
tells you what operations
you need to use. Note that 'product' signals the operation of
multiplication (Since the answer you get from multiplying numbers is
called the 'product'.) and
'more than' signals the operation of addition (Because you are left
off with more than you originally had before adding). <span>
</span>Now
that we know that our algebraic expression contains multiplication,
addition, letter N and the numbers 2 and 5; we can start plugging the
numbers in.<span>
</span>60
= 2 (more than) + (product of) 5N. The answer for the first
attachment is
B. <span>
</span>_____________________________________________________________<span>
</span>All
we need to do for the AB problem (Question 25 on your material) is
solve AB.<span>
</span>Note
1: When a problem has no operation separating two letters or numbers,
this means multiplication.<span>
</span>Note
2: A and B are variables. Variables are letters that stand for and
hold the place of our unknown quantities. However, the values are not
unknown anymore given the fact that the question tells us that A= 42
and B = 2. Thus we substitute A with 42 and B with 2, then work from
there. 42 * 2 =84. Answer = A.
____________________________________________________________________
And
finally, for question 26, we use PEMDAS. P = parenthesis (), E =
exponent x^2, M/D = x or /, A/S means + or subtraction.
According
to PEMDAS, we first solve what's parenthesis, which is 77 – 32.
Using mental math, 77 – 32 = 45. ( 7 – 3 = 4 and 7 – 2 = 5.). 5/9
* 45 is what we have left. 5 divided by 9 =0.5555555555555556.
0.5555555555555556 * 45 = 25. Answer is D.
11, because 11 times 1 is 11 and 11 times 4 is 44.
