Help me plzzz with my math

A four-digit number N leaves a remainder of 10 when divided by 21, a remainder of 11 when divided by 23, and a remainder of 12 w

aksik [14]

Answer:

16

Step-by-step explanation:

There may be a formal way to solve simultaneous Diophantine equations, but I don't know what it is. So, I addressed this by solving them 2 at a time.

First of all, we want to find a relation between integers p and q such that ...

21p+10 = 23q +11

21p -23q = 1 . . . . . . subtract 23q+10

Using the extended Euclidean algorithm or trial and error or astute observation, we find that (p, q) = (11, 10) is a solution to this equation. Then we can write p and q as ...

p = 23n+11
q = 21n+10

for some integer n.

Then our original numbers become ...

21p+10 = 21(23n+11)+10 = 483n +241 . . . . for some integer n

For this to be a 4-digit number, we must have n such that

1000 ≤ 483n +241 ≤ 9999

1.6 < n < 20.2

__

Modulo 25, the number (483n+241) is ...

8n +16

and we want that value to be 12:

(8n +16) mod 25 = 12

(8n +4) mod 25 = 0 . . . . . subtract 12

4(2n+1) mod 25 = 0 . . . . factor out 4

For this to be true, we must have 2n+1 be a multiple of 25. The only value of n that is in the required interval [2, 20] is n=12.

__

When n=12, 483n+241 = 6037. The sum of digits of 6037 is 16.

3 0

3 years ago

Please help! 3 Questions please show how you solved the problem

Masteriza [31]

Answer:

1) $(-y^2-4y-8+4y^2+6y-3)$

2) $32x^5y^4z^2$

3) $x^3-9x^2+14x+24$

Step-by-step explanation:

Given the expression we have to simplify the expression

1) $(-y^2-4y-8)-(-4y^2-6y+3)$

⇒ $(-y^2-4y-8+4y^2+6y-3)$

Combining like terms, we get

⇒ $3y^2+2y-11$

2.) $(2x^2y^3z^2)(4xy.4x^2)$

⇒ $(2x^2y^3z^2)(16x^3y)$

⇒ $32x^5y^4z^2$

3.) $(x-4)(x^2-5x-6)$

⇒ $x^3-5x^2-6x-4x^2+20x+24$

⇒ $x^3-9x^2+14x+24$

5 0

3 years ago

Which of the following is a situation in which an equation cannot be solved

Klio2033 [76]

Answer:

B One term of the polynomial has a degree of 3

3 0

3 years ago

Read 2 more answers

The difference between the two numbers is 48. The ratio of the two numbers is 7:3. What are the two numbers?

OlgaM077 [116]

Let the bigger no. be X and the smaller no. be Y

X-Y=48

7-3=4

48÷4=12

X=12×7=84

Y=12×3=36

6 0

3 years ago

Read 2 more answers

Given that D(x) = 2x, select all of the following that are true statements

Keith_Richards [23]

Answer:

D(x) is a function

D(x) is a direct variation

D(x) is a rule for the set of points (5.10). (6, 12) and (-2,-4)

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem

$D(x)=2x$

D(x) is a direct variation (linear function)

The variable x is the independent variable or input value

The variable D(x) is the dependent variable or output value

<u><em>Verify each statement</em></u>

case 1) D(x) is a function

The statement is true

see the explanation

case 2) x is the dependent variable

The statement is false

The variable x is the independent variable or input value

case 3) D(x) is a direct variation

The statement is true

see the explanation

case 4) D(x) is a rule for the set of points (5.10). (6, 12) and (-2,-4)

The statement is true

Because

For x=5

substitute in the linear equation

$D(x)=2(5)=10$ ---> is ok

For x=6

substitute in the linear equation

$D(x)=2(6)=12$ ---> is ok

For x=-2

substitute in the linear equation

$D(x)=2(-2)=-4$ ---> is ok

6 0

3 years ago