Logarhythm

ND = NE = NF
6x - 2 = 3x + 7

3x = 9

x = 3

This means NF = 6x - 2 = 6(3) - 2 = 18 - 2 = 16, which is your answer :)

Since they are similar, we can just take the proportions and apply it to each side :)

15/6 = 2.5, which means each side of the triangle LMN are 2.5 times longer than that of the other triangle.

20 ÷ 2.5 = 8

25 ÷ 2.5 = 10

This means the perimeter of triangle XYZ = 6 + 8 + 10, which gives 24cm, which is your answer :)

Hope this helps

Let b = cost of one binder, and n = cost of one notebook

3b + 10n = 875

3b + 4n = 485

----------------------

6n = 390

  n = 65

3b + 4n = 485

3b + 4(65) = 485

3b + 260 = 485

3b = 225

  b = 75

Notebooks cost 65 cents and binders cost 75 cents :)

Area of square = 144 cm², which means each side is √144 = 12 cm

Since the circle is inscribed in the square, the diameter is 12, so the radius is 6cm.

Area of circle = πr² = π * 6² = 36π cm², which is your answer :)

(x + 2)(3x² + x + 5)

= 3x³ + x² + 5x + 6x² + 2x + 10

= 3x³ + 7x² + 7x + 10

A = 3 

B = 7

C = 7

D = 10

A + B - C - D

= 3 + 7 - 7 - 10

= 10 - 17

= -7, which is your answer :)

√2, √10, 5√2...

5√2 = √(2 * 5²) = √50

The pattern is multiplying by 5 inside the square root.

To find the nth term, it would be:  nth term = √(2 * 5^{(n - 1)})

This means the 7th term = √(2 * 5^{(7 - 1)})

                                        = √(2 * 5⁶)

                                        = √(2 * 15625)

                                        = √31250, which is your answer :)

180 - 56 - 2x = 180 - 6x

124 - 2x = 180 - 6x

4x = 56

x = 14 

Hope this helps :)