Explanation

0.13 × P² = 13

Solve for P²:

P² = 13 / 0.13 = 100

Now take the square root:

P = √100 = 10

Explanation

Given x ∝ 1/y, so xy = k (constant).

When x = 3, y = 7, k = 3 × 7 = 21.

Now, when x = 5, 5y = 21.

y = 21/5 = 4.2.

Explanation

Given equation: x^2 - 3kx + 4k^2 = 0.

Sum of roots = 3k, Product of roots = 4k^2.

Sum of squares of roots = (sum of roots)^2 - 2(product of roots)

= (3k)^2 - 2(4k^2)

= 9k^2 - 8k^2

= k^2.

Given sum of squares = one of the options.

If sum of squares = 1, then k^2 = 1, so k = ±1

Explanation

Explanation

Let's factorize 2x^2 - 7x + 3. We need to find two numbers that multiply to 2 × 3 = 6 and add to -7. These numbers are -6 and -1.

So, 2x^2 - 7x + 3 = 2x^2 - 6x - x + 3

= 2x(x - 3) - 1(x - 3)

= (2x - 1)(x - 3)

Explanation

Explanation

Let's denote the number as x.

Given:

(1/3)x = 3(1/x)

Multiplying both sides by 3x:

x^2 = 9

Solving for x:

x = ±√9

x = ±3

Explanation

Given the equation:

78.36 = 78.36xy

Dividing both sides by 78.36:

1 = xy

The only option that satisfies xy = 1 is:

x = 1 and y = 1

Since 1 × 1 = 1.

The answer is x = 1 and y = 1.

Explanation

Given:

a + b = 4 ... (1)

a - b = 2 ... (2)

Add (1) and (2):

2a = 6

a = 3

Explanation

The expression x² - y² is a difference of squares, which can be factored as:

x² - y² = (x + y)(x - y).