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t. a. =

T.A = 54 + 9/2 √3

Step-by-step explanation:

∵ The figure is triangular prism

∴ T.A = perimeter of the base × height + 2 × area of the base

∵ The base is an equilateral Δ with side length 3"

∴ The perimeter of the base = 3 × 3 = 9 inches

∴ The area of the base = 1/4 S² √3 = 1/4 (3)²√3 = 9/4 √3 inches²

∵ The length of the height of the prism = 6"

∴ T.A = 9 × 6 + 2 × 9/4 √3 = 54 + 9/2 √3

∴ T.A = 54 + 9/2 √3 inches²

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1