A parallelogram has an area of 8x^2 - 2x -45. The height of the parallelogram is 4x + 9. I know the formula for a parallelogram is A=bh. Please work and explain how I get the length of the base of the parallelogram. Thanks

since a = bh and they give you a polynomial for a and h, you have to expect that b = a/h and (4x+9) divides (8x^2 - 2x -45)

In fact, 8x^2 - 2x -45 = (4x+9)(2x-5)

so, b = 2x-5

If they had given you numbers, you'd have had no trouble doing the division. Don't be confused by their efforts to cloak the underlying simplicity of the question.

Factor(unfoil) the area to get:

(2x-5)* (4x+9). When you divide that by the height, the result is the length of the base: (2x-5)
Not sure if you're solving for x, but I don't think that there's enough information. Let me know if this helps you!

I need help with lessons 15 measurement unit test

To find the length of the base of the parallelogram, we can use the formula for the area of a parallelogram which is A = b * h, where A is the area, b is the length of the base, and h is the height.

Given that the area of the parallelogram is 8x^2 - 2x - 45 and the height is 4x + 9, we can substitute these values into the formula:

8x^2 - 2x - 45 = b * (4x + 9)

Now, let's solve for b, the length of the base.

Step 1: Distribute the b to both terms inside the parentheses:
8x^2 - 2x - 45 = 4bx + 9b

Step 2: Rearrange the equation to put it in the form of a quadratic equation:
8x^2 - 2x - 45 - 4bx - 9b = 0

Step 3: Combine like terms:
8x^2 - (2 + 4b)x - 45 - 9b = 0

Step 4: Since the equation is quadratic, we need to set it equal to zero to solve for x.
8x^2 - (2 + 4b)x - 45 - 9b = 0 can be rewritten as:
8x^2 - (2 + 4b)x + (-45 - 9b) = 0

Step 5: Now, we can solve for x using factoring or the quadratic formula. If we can factor the quadratic equation, we can set each factor to zero and solve for x. If factoring is not possible, we can use the quadratic formula:

x = (-(2 + 4b) ± √((2 + 4b)^2 - 4(8)(-45 - 9b))) / (2(8))

Simplifying the equation:
x = (-(2 + 4b) ± √(4 + 16b + 4b^2 + 144 + 288b)) / 16

Step 6: Solve for x by simplifying the expression if possible, and then applying the quadratic formula.

Once you find the values of x, you can substitute them back into the equation to find the corresponding values of b, which will give you the length of the base of the parallelogram.