solve 3x=square root 5+4x

Question

1.solve 3x=square root 5+4x

 

2. write an equation in a standard form of the line passing through the given pair of point the line goes through the pair (2,5)(2,3)

 

3. the product of two consecutive positive integers is 11 more than their sum. find the integers.

 

4. find the product of 4y^3(2y+3)(y-4)

Answer 1

1. 3x = √(5 + 4x)

 

Square both sides, then rearrange and factor the quadratic:

 

9x² = 5 + 4x

9x² - 4x - 5 = 0

(9x + 5)(x - 1) = 0

x = -5/9    OR    x = 1

 

 

 

2. Standard Form of line through (2, 5) and (2, 3)

 

First, find the slope:

 

(5 - 3) / (2 - 2) = 2/0 = undefined

 

That means this line is actually a vertical line. Vertical lines have equations of the form x = __. Here, that's x = 2.

 

 

 

3. Word Problem

 

Call the two consecutive integers x and x + 1.

 

Since their product is 11 more than their sum...

 

x + (x + 1) + 11 = x(x + 1)

2x + 12 = x² + x

0 = x² - x - 12

0 = (x - 4)(x + 3)

x = 4    OR    x = -3

 

Since we've been told these are positive integers, x = 4 and x + 1 = 5.

 

 

 

4. Product of 4y³(2y + 3)(y - 4)

 

(8y⁴ + 12y³)(y - 4)

8y⁵ - 32y⁴ + 12y⁴ - 48y³

8y⁵ - 20y⁴ - 48y³