In the accompanying diagram of rhombus abcd, the lengths of the sides ab and bc are represented by 3x-4 and 2x+1, respectively. find the value of x.

x = 5

Explanation:
A rhombus is a quadrilateral in which all sides are equal.

Since ABCD is a rhombus, therefore:
AB = BC
3x - 4 = 2x + 1
3x - 2x = 1 + 4
x = 5

We can check:
AB = 3(5) - 4 = 11 units
BC = 2(5) + 1 = 11 units
They are equal

Hope this helps :)

1.   an exact solution requires a radical solution - no decimal approximation.2. (a)4x^3 = 756x^3 = 756/4 = 189x =   cube root of 189 =   5.74   to nearest hundredth answer(b)   189 = 3*3*3*7   so we can write the cube root of 189 as 3∛7 answerchecking (a) 4*(5.74^3 =   756.48   which is very close(b)   4* ((3∛3)^3   = 4*189   = 756   - spot on! 3. i would use solution b because the original question asked for an exact solution.