Explanation

Given the equations:

1. 7x - 4y = 10

2. 2x + 3y = 65

Let's solve them using elimination or substitution. Multiplying equation 1 by 3 and equation 2 by 4 gives us a way to eliminate y:

1. 21x - 12y = 30

2. 8x + 12y = 260

Adding both equations:

29x = 290

x = 290 / 29

x = 10

Explanation

Given the sequence formula:

an = 3n + 5

To find the 7th term, substitute n = 7:

a7 = 3(7) + 5

= 21 + 5

= 26

Explanation

To find (-4a^2)^3:

(-4a^2)^3 = (-4)^3 * (a^2)^3

= -64 * a^(2*3)

= -64 * a^6

= -64a^6

Explanation

To divide (2x^3 - 5x^2y + 5xy^2 - 3y^3) by (2x - 3y), let's attempt polynomial long division or factorization if possible.

Given the form of the dividend and divisor, let's try to factor or directly apply division:

(2x^3 - 5x^2y + 5xy^2 - 3y^3) ÷ (2x - 3y)

Upon inspection or performing polynomial division, one notices:

2x^3 - 5x^2y + 5xy^2 - 3y^3 can be factored or divided as follows:

2x^3 - 3x^2y - 2x^2y + 3xy^2 + 2xy^2 - 3y^3

Which can be rearranged and factored:

x^2(2x - 3y) - xy(2x - 3y) + y^2(2x - 3y)

= (2x - 3y)(x^2 - xy + y^2)

Thus, (2x^3 - 5x^2y + 5xy^2 - 3y^3) ÷ (2x - 3y) = x^2 - xy + y^2

Explanation

"6 times a number" = 6x.

"Less than" means subtraction: 6x - 79 = x represents the statement.