Explanation

The line y = 3 is a horizontal line that intersects the y-axis at y = 3.

Since it's horizontal, it's parallel to the x-axis.

Explanation

Given equations:

1. x - 2y = 5

2. 2x - y = 6

Step-by-Step Solution

Step 1: Solve one equation for one variable

From equation (2):

2x - y = 6

⇒ y = 2x - 6

Step 2: Substitute into the other equation

Substitute y = 2x - 6 into equation (1):

x - 2(2x - 6) = 5

x - 4x + 12 = 5

-3x + 12 = 5

Step 3: Solve for x

-3x = 5 - 12

-3x = -7

x = 7/3

Step 4: Solve for y

Substitute x = 7/3 back into y = 2x - 6:

y = 2(7/3) - 6

y = 14/3 - 6

y = 14/3 - 18/3

y = -4/3

Explanation

Given y varies directly with x, so y = kx.

Given y = 99 and x = 11,

99 = k × 11

k = 9

Now, y = 9x

When x = 3,

y = 9 × 3

y = 27

Explanation

Given x - 1/2x} = 6,

Cubing both sides gives x^3 - 1/8x^3 - 3.1/2.6 = 216.

This simplifies to x^3 - 1/8x^3 - 9 = 216.

So, x^3 - 1/8x^3 = 216 + 9 = 225.

Explanation

To factorize the quadratic expression 2x² + 5x + 2, we need to find two numbers whose product is 2 × 2 = 4 and whose sum is 5. These numbers are 4 and 1.

2x² + 5x + 2 = 2x² + 4x + x + 2

= 2x(x + 2) + 1(x + 2)

= (x + 2)(2x + 1)

Explanation

ax² − 2x + 2a = 0  

We are told: Sum of roots = Product of roots

Step 1: Use formulas  

For a quadratic equation ax² + bx + c = 0,  

- Sum of roots = −b/a

- Product of roots = c/a

So here:  

- Sum = −(−2)/a = 2/a  

- Product = (2a)/a = 2

Set them equal:  

2/a = 2

Multiply both sides by a:  

2 = 2a  

=> a = 1

Final Answer:  

a = 1

Explanation

If matrix A is 2x3 and matrix B is 3x3, then the order of the resulting matrix AB is 2x3. 

Explanation

If matrix A has an order of 3x4, then its transpose, denoted as AT, will have an order of 4x3

Explanation

 If matrix A has an order of 3x2, then the order of its transpose (A') will be 2x3. 

Explanation

The statement "P⇒Q is true if both are true" describes a conjunction, which is the logical "and" operation.