Question

1. find gh.

19
$9x-3$
$5x+1$

1. find rs.

$2x+15$
$3x+5$
$6x-37$

Explanation:

For Problem 14:

Step1: Apply trapezoid midsegment theorem

The midsegment of a trapezoid equals the average of the two bases, so:
$$9x - 3 = \frac{19 + (5x + 1)}{2}$$

Step2: Simplify right-hand side

Combine like terms in the numerator:
$$9x - 3 = \frac{5x + 20}{2}$$
$$9x - 3 = \frac{5x}{2} + 10$$

Step3: Solve for x

Multiply all terms by 2 to eliminate fractions, then isolate x:
$$18x - 6 = 5x + 20$$
$$18x - 5x = 20 + 6$$
$$13x = 26$$
$$x = 2$$

Step4: Calculate GH

Substitute x=2 into GH's expression:
$$GH = 9(2) - 3$$

Step1: Apply trapezoid midsegment theorem

The midsegment equals the average of the two bases, so:
$$3x + 5 = \frac{(2x + 15) + (6x - 37)}{2}$$

Step2: Simplify right-hand side

Combine like terms in the numerator:
$$3x + 5 = \frac{8x - 22}{2}$$
$$3x + 5 = 4x - 11$$

Step3: Solve for x

Isolate x by rearranging terms:
$$11 + 5 = 4x - 3x$$
$$x = 16$$

Step4: Calculate RS

Substitute x=16 into RS's expression:
$$RS = 2(16) + 15$$

Answer:

15

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For Problem 15: