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3 years ago

WHat is the property for 5x+10=24-2x

Mathematics

1 answer:

____ [38]3 years ago

7 0

Answer:

x=2

Step-by-step explanation:

5x+10=24-2x

5x+10-10=24-2x-10

5x= -2x+14

5x+2x= -2x+14+2x

7x=14

7x/7=14/7

x=2

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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:

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

Solve the following system of equations by elimination. What is the value of x? x = 1.5 x = -1.5 x = 8 x = -8

Andru [333]

Using the elimination method, the value of x in the system of equations is calculated as: 8.

<h3>How to Solve a System of Equations by Elimination?</h3>

To solve a system of equations given using the elimination method, do the following:

Multiply 2x - 5y = 1 by 2 and multiply -3x + 2y = -18 by 5 to get the following:

4x - 10y = 2 --> eqn. 1

-15x + 10y = -90 --> eqn. 2

Add

-11x = -88

Divide both sides by -11

x = 8

Learn more about system of equations on:

brainly.com/question/14323743

#SPJ1

8 0

2 years ago

Help me 7th grade math please

Stolb23 [73]

Answer: 13.5 ounce bottle for $2.19

a 29.2 ounce bottle for $5.37

The 29.2 ounce bottle is better

Step-by-step explanation:

13.5 ounce bottle for $2.19

a 29.2 ounce bottle for $5.37

find the ratios

13.5/2.19 = $6.16 per unit

29.2/5.37 = $5.44 per unit

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2 years ago

Determine if the following relation is a function or not

Darya [45]

1 is not. 2 is. 3 is not. 4 is. 5 is. 6 is. 7 is not. 8 is.

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3 years ago

you make a salad and share with friends your sister eats 1/3 of it before they arrive (it is a a and b question pls help)

bagirrra123 [75]

Answer:

Sister Is a PIG

Step-by-step explanation:

and Your Friends Gets her Scraps

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3 years ago