Explanation

Given equation: 3x - 2y = 9

Substitute x = 5 into the equation:

3(5) - 2y = 9

15 - 2y = 9

Subtract 15 from both sides to isolate -2y:

-2y = 9 - 15

-2y = -6

Divide by -2 to solve for y:

y = -6 / -2

y = 3

Explanation

If one root of the equation is 2, then we can factor the left-hand side of the equation as (x - 2)(x^2 - 4x + 3) = (x - 2)(x - 1)(x - 3) = 0.

This tells us that the other two roots are 1 and 3.

Explanation

• The number  is a decimal number without repetition, that is, it has infinite decimal places, thus it is irrational.

Explanation

The cube roots of unity are:  

1, ω, and ω², where:

- ω = -1/2 + (√3/2)i  

- ω² = -1/2 - (√3/2)i  

These are the complex cube roots of unity, and they satisfy:

1 + ω + ω² = 0  

and  

1 × ω × ω² = 1

Explanation

Explanation

• A Row Matrix has only one row and multiple columns.

  $$[1 1 1] quad text{→ 1 row, 3 columns}$$

• Identical Matrix (probably meant "Identity Matrix") → has 1s on the diagonal and 0s elsewhere (square matrix).

Explanation

To simplify the expression 5x(2x-5),

we can use the distributive property to multiply each term inside the parentheses by 5x.

First, distribute 5x to both terms inside the parentheses:

5x * 2x = 10x^2

5x * -5 = -25x

Now we have:

10x^2 - 25x

Explanation

Use integration by parts:
Let $u=x$, $dv=\cos (x)dx$

Then:

$$\int x\cos (x)dx=x\sin (x)-\int \sin (x)dx=x\sin (x)+\cos (x)$$

Evaluate from $0$ to π/2

$$= left( frac{pi}{2} cdot 1 + cosleft( frac{pi}{2} right) right) - left( 0 + cos(0) right) = frac{pi}{2} - 1$$

π/2​−1

Explanation

The expansion of (1 + x)⁵ can be found using the Binomial Theorem.

(1 + x)⁵ = 1 + 5x + 10x² + 10x³ + 5x⁴ + x⁵

Sum of coefficients = 1 + 5 + 10 + 10 + 5 + 1 = 32

Alternatively, we can find the sum by substituting x = 1:

(1 + 1)⁵ = 2⁵ = 32

Explanation

Subtract 7 from both sides:

3x+7−7<22−7

3x<15

Divide both sides by 3:

x< 15/3

​x<5