Hank orders popcorn while watching a movie. the popcorn was served in a trapezoidal bucket. the height of the bucket is 10x-9 cm, and the length of its broad bases are 10x-2 cm and 16x+10cm. which of th following formulas can be used to find the area, A, of the broad side of the trapezoidal bucket

Area of the trapezoidal bucket, A is 130x² - 77x - 36 cm²

Step-by-step explanation:

Sum of parallel sides = (10x - 2) + (16x + 10)

                                   = 26x + 8 = 2(13x + 4)

Height = 10x - 9

⇒ Area of the bucket = 1/2 × 2(13x + 4) (10x - 9)

                                    = (13x + 4)(10x - 9) cm²

                                    = 130x² - 117x + 40x - 36

                                A = 130x² - 77x - 36

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

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step-by-step explanation:

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