The length of a rectangle is 6 centimeters more than its width. If x represents the width of the rectangle, wr

Question

1. The length of a rectangle is 6 centimeters more than its width. If x represents the width of the rectangle, write an algebraic expression in terms of x that represents its area and simplify the result

2. Simplify and write with positive exponents only: 4(xy^2)^2
All variables represent positive real numbers

3. Simplify and write with positive exponents only: a^-4b^3)^-3
All variables represent positive real numbers

4. Change to radical form: 3y^3/5

Answer 1

1. The length of a rectangle is 6 centimeters more than its width. If x represents the width of the rectangle, write an algebraic expression in terms of x that represents its area and simplify the result

Ans:
Let the breadth of the rectangle be x cm
therefore the length becomes, x + 6 cm
Area of a rectangle = length x breadth = x ( x+6) = x^2 + 6x cm square

2. Simplify and write with positive exponents only: 4(xy^2)^2
All variables represent positive real numbers

Ans: 4 (xy^2)^2 = 4(xy^4) = 4x^y^4 ( if its xy both raised to the power of 2) else its 4xy^4

3. Simplify and write with positive exponents only: a^-4b^3)^-3
All variables represent positive real numbers

Ans: (a^-4b^3)^-3
a^(-4x-3) b^(3 x -3) = a^12 b ^ -9

4. Change to radical form: 3y^3/5

Ans. Is the power 3/5 on 3 aswell? if yes, then the radical form is : Fifth root of 27y^3

if not then, its (3 x fifth root of y^3)

Answer 2

1.)
Let Area of Rectangle = A
Let width=x
Let length=x+6
A=x(x+6)
A=x^2+6x
2.) 4(x^2)(y^4)
3.) (a^12)/(b^9)
4.) (3y)^3/5 = fifthe root of (3y)^3
but 3(y^3/5) is 3 times fifth root of y^3

Answer 3

1. A = x(x + 6)
...(the factored form is generally considered the simplest)

2. 4x^2y^4

3. a^12/b^9

4. 3(y^3)^0.2

Answer 4

1) area = length*width
= x*(x+6)
=x^2 +6x

2)4(xy^2)^2=4(xy^2)(xy^2)=4x^2y^4

3)(a^-4b^3)^-3=a^12b^-9

4)3y^3/5 = 3*5throot(y^3)

Answer 5

A=LW A=(x+6)(2x+3) (Plug in expressions) A=2x^2 + 12x + 3x + 18 (multiply them which comprise FOIL) A=2x^2 + 15x + 18 (simplify like words) 2x^2 + 15x + 18 is your expression