1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
aliya0001 [1]
2 years ago
8

Student asked her maths teacher if he would reveal his age. Seeing an opportunity to test his student’s mental skills, the teach

er replied with a riddle: “My age in years is not a prime but is odd. Also, when the digits in my age are reversed and the new number added to my age, the result is a perfect square. Of course, if you prefer, you can take my age and reverse the digits and subtract that from my age and still get a perfect square.”
Although 51 is odd and not a prime, the teacher cannot be 51 years old, because neither (51 + 15) nor (51 -15) are perfect squares, and they both need to be perfect squares.
Mathematics
1 answer:
bixtya [17]2 years ago
7 0

Answer:

65 years old.

Step-by-step explanation:

If her age is 10 t + u (where t is the tens digit and u is the units digit) then reversing the digits gives 10 u + t. and the sum is 11 t + 11 u, which is a multiple of 11. We know this has to be a square number. Ong Xing Cong from Singapore sent in the following solution.

11 t + 11 u = 11 x 11 = 121

t + u = 11

65 - 56 = 3 x 3

She is 65 years old.

The best solutions do not need trial and improvement methods and they show that the answer or answers found are the only possible answers. Knowing the digits add up to 11 ( t + u = 11), you can also use (10 t + u ) - (10 u + t ) = 9 t - 9 u = 9( t - u ) As this is also a square number you know ( t - u ) is either 1, 4, or 9. The solutions for 4 and 9 don't give whole number values for t in 0  t  9.

You might be interested in
What are the multiples of 14?
Mrrafil [7]

14,28,42,56,70,84,98,112,126,140,154,168,182,196,210,224,238,252,266,280,294,308,

Is that enough?

7 0
2 years ago
Read 2 more answers
If the dimensions of the following cylinder are doubled, what factor will the surface area change by?
Vedmedyk [2.9K]

Answer:

probably 2 or 4

Step-by-step explanation:

7 0
3 years ago
Pizza is available with three kinds of cheese and four toppings. how many different ways can you order your pizza with one type
e-lub [12.9K]
You will choose 1 cheese 3 different ways because there are three types of cheeses.

You will choose your topings 6 different ways. 4!/(2!2!) = 4*3/2 = 6

Therefore you will be able to get 6 * 3 different pizzas = 18 pizza combinations.

To confirm the toppings, suppose they are (M)ushrooms (P)epperoni (O)nions and (B)acon

M P
M O
M B
P O
P B
O B

Total 6.The order doesn't matter here. M O is the same thing as OM
8 0
3 years ago
An airplane climbs at an angle of 16° with the ground. Find the ground
Tatiana [17]

Answer:

2403.2

Step-by-step explanation:

We get the length of the hypotenuse, and the base angle. To find the length of the base, we use the cosine of 16° since it is equal to the adjacent side length/ hypotenuse side length or cos 16°= x/2500. The isolate x by multiplying both sides by 2500. The cos 16° is around 0.96126, multiplied by 2500 (cos 16°(2500)) = 2403.1

6 0
3 years ago
Please help got stuck again with this one Thank you
Neko [114]
The answer is 2 cubed so B
4 0
3 years ago
Read 2 more answers
Other questions:
  • Can somebody please help me with 11 and 17
    12·1 answer
  • If y= 5/17 when x = 10, find y when x= 5. Show how you got your answer.
    10·1 answer
  • Can somebody please help me with 3 and 5. Please don’t answer if you are not sure. 17 points
    10·1 answer
  • Find the equation of the line shown.
    8·2 answers
  • It cost 13.80 for 5 tickets how much would it cost for 3 tickets
    8·1 answer
  • ONLY ANSWER CORRECTLY
    7·1 answer
  • You want to know about the dining habits of college students in the US. Since you do not have resources to survey all college st
    14·1 answer
  • Use <, >, or
    12·1 answer
  • 4. Find x<br> AB<br> (10x-51)<br> DC<br> (6x-11)
    11·1 answer
  • Find m26 if m/1 = 112°
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!