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Mathematics

1 answer:

Svetradugi [14.3K]3 years ago

8 0

Answer:

Answer: a = - 12

Step-by-step explanation:

We have here two equations, one 18x + 12y = 36, the other ax - 8y = - 24;

Now if we were to consider making these two equations have a common y co - efficient, we would multiply the top equation by 2, the bottom consecutively by - 3. This would make a standard 24y ;

2 * ( 18x + 12y = 36 ), ⇒ 36x + 24y = 72

+ - 3 * ( ax - 8y = - 24 ) + - 3ax + 24y = 72

As you can see, all terms are equivalent, besides that of the co - efficient of x. Knowing that, it would be ax must be multiplied by - 3 to receive 36x, as the bottom equation is multiplied by - 3, where all terms are equivalent to the top terms;

- 3 * ax ⇒ 36x, - 3 * - 12x = 36x,

Answer: a = - 12

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Raina must choose a number between 55 and 101 that is a multiple of 2, 8 and 10. Write all the numbers that she could choose. If

Aleonysh [2.5K]

Answer:

The only possible number is $80$ .

Step-by-step explanation:

The number in question needs to be a multiple of all three of $2$ , $8$ , and $10$ . As a result, it must also be a multiple of the least common multiplier (lcm) of the three number.

Start by finding the least common multiplier of the three numbers.

Factor each number into its prime components:

$2$ is a prime number itself.
$8 = 2^3$ .
$10 = 2 \times 5$ .

The only prime factors are $2$ and $5$ .

The greatest power of $2$ among the three numbers is $3$ .
The greatest power of $5$ among the three numbers is $1$ .

Therefore, the least common multiplier of the three number should be the product of $2^3$ and $5$ . That's equal to $2^3 \times 5 = 8 \times 5 = 40$ .