Question 1:
For this case we have that by definition, the GCF of two numbers is the largest number that is a factor of both numbers. For example, the number 10 is the biggest factor that 50 and 30 have in common.
We must find the GCF of the following expression:
We look for the prime factorization of each number:
The GCF of the three numbers is 
So:
Answer:
Option C
Question 2:
For this case we have that by definition of power properties of the same base, that:
That is, for multiplication of powers of the same base, the same base is placed and the exponents are added.
So:
ANswer:
Option A
Everyone would get 2 1/4 cupcakes because if you split up each cupcake by 4, (In four different pieces) everyone would get 9/4 slices. Change to a mixed number to get 2 1/4
3 is the greatest common denominator
You could easily change the 2 1/2 to a 2.5 and do 2.5-6=-3.5
The solution to the given algebraic equation 1000(7x - 10) = 50(292 + 100x) is; x = 12.3
<h3>How to simplify algebraic equations?</h3>
We want to simplify the algebraic equation;
1000(7x - 10) = 50(292 + 100x)
The first step is to use distributive property of equality to expand the bracket to get;
7000x - 10000 = 14600 + 5000x
7000x - 5000x = 14600 + 10000
2000x = 24600
Use division property of equality to divide both sides by 2000 to get;
x = 24600/2000
x = 12.3
Thus, we can conclude that the solution to the given algebraic equation 1000(7x - 10) = 50(292 + 100x) is; x = 12.3
Read more about algebraic equations at; brainly.com/question/723406
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