Explanation

2x + 9x = 11

Combine like terms:

11x = 11

Divide both sides by 11:

x = 1

So, the value of 'X' is 1.

Explanation

A group generated by one of its elements is called a cyclic group.

This means that the group can be generated by repeatedly applying the group operation to a single element, called the generator.

In other words, all elements of the group can be expressed as powers of the generator.

Explanation

A monoid is a set with an associative binary operation and an identity element.

A group is a monoid where every element has an inverse.

Explanation

3x² - 7x - 6 = 0

We can factor the equation:

(3x + 2)(x - 3) = 0

This gives us two possible solutions:

3x + 2 = 0 --> 3x = -2 --> x = -2/3

x - 3 = 0 --> x = 3

So, the roots of the equation are x = -2/3 and x = 3.

The correct answer is:

3, -2/3

Explanation

The quadratic equation whose roots are reciprocal of:

2x2 + 5x + 3 = 0 can be obtained by replacing x by 1/x.

Hence, 2(1/x)2 + 5(1/x) + 3 = 0

=> 3x^2 + 5x + 2 = 0

Explanation

Let the two consecutive positive integers be x and x + 1

x2 + (x + 1)2 - x(x + 1) = 91

x2 + x - 90 = 0

(x + 10)(x - 9) = 0 => x = -10 or 9.

As x is positive x = 9

Hence the two consecutive positive integers are 9 and 10.

Explanation

x + y = 67 ... (equation 1)

x - y = 3 ... (equation 2)

where x and y are the two numbers.

We can solve this system of equations by adding equation 1 and equation 2, which eliminates y:

2x = 70

Dividing both sides by 2 gives:

x = 35

Now that we have x, we can substitute it into equation 1 to find y:

35 + y = 67

Subtracting 35 from both sides gives:

y = 32

So, the two numbers are 35 and 32.

Explanation

To simplify the expression, we need to follow the rules of fractions and combine like terms:

X + 1/7 - X - 1/8

First, subtract X from X, which cancels out:

1/7 - 1/8

To subtract fractions, we need a common denominator, which is 56. So we can rewrite the fractions as:

(8/56) - (7/56)

Now we can subtract: 1/56

So the simplified result is:

1/56

Explanation

Explanation

3x - 15 - 6 = 0

3x = 21

X = 21/3

X = 7