Step-by-step explanation:
756 = 2² * 3³ * 7.
For 756n to be a perfect cube, all of its prime factors must have a power that is a multiple of 3.
How to get from 2² to 2³: Multiply by 2.
3³ has already a power that is a multiple of 3.
How to get from 7 to 7³: Multiply by 7².
Hence n = 2 * 7² = 98.
The answer is a. $35. First you multiply 25 by .40. Then you add the product to 25.
9514 1404 393
Answer:
(B) 4
Step-by-step explanation:
Consider the units column. The only sum of 3 and a single digit that will end in 1 is the sum ...
3 + 8 = 11
This tells you A = 8, so the top number is 1983, and the middle number is B78.
Considering the first two columns, we know that 83 +78 = 161, so there must be a carry of 1 into the third column. That makes it have the sum ...
1 + 9 + B = <something ending in 4>
We know the something cannot be 04 or 24, so must be 14. Then ...
10 + B = 14 ⇒ B = 4
__
So, the whole sum is ...
1983 +478 = 2461
and the letter values are ...
Answer:
41 years old.
Step-by-step explanation:
Let x represent age of younger child.
We have been given that a mother has two children whose ages differ by 5 years. So the age of older child would be
.
The sum of the squares of their ages is 97. We can represent this information in an equation as:

Let us solve for x.



Divide both sides by 2:






Since age cannot be negative, therefore, age of younger child is 4 years.
Age of older child would be 
Therefore, the age of older child would be 9 years.
We have been given that the square of the mother's age can be found by writing the squares of the children's ages one after the other as a four-digit number.
Square of 4: 
Square of 9:
.
Square of mother's age: 
To find mother's age, we need to take positive square root of 1681 as:

Therefore, the mother is 41 years old.