Explanation

Put a = 9 in a² + b² = 145

9² + b² = 145

81 + b² = 145

b² = 145 - 81

b² = 64

b = ±8

Last verified on 24-05-2026

Explanation

(10x + 6)/(x(x + 3)) decomposes as 2/x + 8/(x + 3)

Solution:

Let (10x + 6)/(x(x + 3)) = A/x + B/(x + 3)

Multiply both sides by x(x + 3)

10x + 6 = A(x + 3) + B(x)

Put x = 0

10(0) + 6 = A(0 + 3) + B(0)

6 = 3A

A = 2

Put x = -3

10(-3) + 6 = A(-3 + 3) + B(-3)

-30 + 6 = 0 - 3B

-24 = -3B

B = 8

So the decomposition is:

2/x + 8/(x + 3)

Last verified on 24-05-2026

Explanation

If f(x) = x² + 2x then f(2) + f(-2) = 8

Solution:

Put x = 2 in f(x) = x² + 2x

f(2) = 2² + 2_2

f(2) = 4 + 4 = 8

Put x = -2 in f(x) = x² + 2x

f(-2) = (-2)² + 2_(-2)

f(-2) = 4 - 4 = 0

Now add both values

f(2) + f(-2) = 8 + 0 = 8

Last verified on 24-05-2026

Explanation

If y ∝ 1/(x²) and y = 18 when x = 3, then y = 4.5 when x = 6

Solution:

Since y is inversely proportional to x², we can write  

y = k / x², where k is a constant.

When y = 18 and x = 3,

18 = k / 3²

18 = k / 9

k = 18 * 9 = 162

Now put k = 162 and x = 6 to find y,

y = 162 / 6²

y = 162 / 36

y = 4.5

So y = 4.5 when x = 6

Last verified on 24-05-2026

Explanation

Solve: (2x - 1)/3 = (x + 5)/2

Solution:

Step 1: Remove the denominators by cross multiplication

(2x - 1) _ 2 = (x + 5) _ 3

Step 2: Multiply out both sides

4x - 2 = 3x + 15

Step 3: Bring terms with x to left side and constants to right side

4x - 3x = 15 + 2

Step 4: Simplify

x = 17

Last verified on 24-05-2026