Need help right now, big points 1, I thought of a two-digit number. The unit digit of my number is a prime number, and the tens digit is four times as big as the unit digit. What is my number?

2,I thought of a two-digit number. The digits of my number are different. The unit digit of my number is the tens digit raised to the third power. What is my number?

3,I thought of a two-digit number. The unit digit of my number is 7 more than the tens digit cubed. What is my number?

4. I thought of a three-digit number. Each digit to the left is the square of the previous digit. What is my number?

(Answer all the questions please, thank you very much!)

1) 82

2) 28

3) 18

4) 111

Step-by-step explanation:

1) a two digit number can be written as:

N = b*10 + c*1

where b and c must be single digit numbers

in this case, c is a prime number, and b = 4*c

The prime numbers are:

2, 3, 5...

if c = 2, then:

b = 4*2 = 8

And the two digit number is: 82.

if c = 3, then:

b = 4*3 = 12, and this leads to a 3 digit number.

And for any large value of c, b will not be a single digit number, then the only option here is 82.

2) same as before:

N = b*10 + c

c = b^3.

c ≠ b

Let's give different values for b, and see what happens.

b can not be zero, because that will lead to a single digit number, then we start with one.

b = 1 > c = 1^3 = 1 > (c = b, then this is not our number)

b = 2 > c = 2^3 = 8, then:

N = 2*10 + 8 = 28.

if b = 3 > c  = 3^3 = 28 (this is not a single digit number, then any value of b equal or larger than 3 does not work)

The only solution here is 28.

3) Same as before:

N = b*10 + c

c = b^2 + 7.

Same approach as before, let's give different values to b and see which one works:

b = 1 > c = 1^2 + 7 = 8

N = 1*10 + 8 = 18.

b = 2 ---> c = 2^2 + 7 = 4 + 7 = 11 (This is a two digit number, then any value of b equal or larger than 2 can be discarded)

The only option here is 18.

4) Now we have:

N = a*100 + b*10 + c.

where:

b = c^2

a = b^2.

Now let's give values to c. (here we can start with zero).

if c = 0 , then: b = 0^2 = 0, then: a = 0^2 = 0.

Then  N = 0*100 + 0*10 + 0 = 0 (this is not a 3 digit number)

if c = 1, then:   b = 1^2 = 1, then: a = 1^2

N = 1*100 + 1*10 + 1 = 111

If c = 2, then: b = 2^2 = 4, then: a= 4^2 = 16  (here a is not a single digit number, then values of c equal or larger than 2 can be discarded)

The only correct option here is 111.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)