Question

ok so the question is Write an expression to rubbers in the area of the figure the figure is a right triangle with 2X -2 and 4X plus 2 in the answer to that is 4X to the power of 2 - 2X -2 and that's part a and amp RP is what would the area be if X equals negative 2

Answer 1

ANSWERS

a) A = 4x² - 2x - 2

b) if x = -2, A = 18 units²

Step-by-step explanation

The area of a triangle is the length of the base, multiplied by its height and divided by 2:

`A=(b\cdot h)/(2)`

In this triangle, b = 4x + 2 and h = 2x - 2. The area is:

`A=((4x+2)(2x-2))/(2)`

We can simplify this expression. First we have to multiply the binomials in the numerator:

`\begin{gathered} A=(4x\cdot2x-4x\cdot2+2\cdot2x-2\cdot2)/(2) \\ A=(8x^2-8x+4x-4)/(2) \\ A=(8x^2-4x-4)/(2) \end{gathered}`

Now, using the distributive property for the division:

`\begin{gathered} A=(8x^2)/(2)-(4x)/(2)-(4)/(2) \\ A=4x^2-2x-2 \end{gathered}`

For part b, we just have to replace x with -2 in the expression above and solve:

`\begin{gathered} A=4(-2)^2-2(-2)-2 \\ A=4\cdot4+4-2 \\ A=16+2 \\ A=18 \end{gathered}`