Which equation results from applying the secant and tangent segment theorem to the figure? 12(a + 12) = 10^2 10 + 12 = a^2 10(a + 10) = 12^2 10(12) = a^2

The equation that results from applying the secant and tangent segment theorem to the figure is 12²  = 10(a+10)

According to the secant and tangent segment theorem, the square of the tangent line is equal to the product of the secant segments. Mathematically;

Tangent² = whole secant segment × External secant segment

DE² = AD × BD

Given

DE = 12

AD = a+10

BD = 10

Substitute into the formula:

12²  = 10(a+10)

Hence the equation that results from applying the secant and tangent segment theorem to the figure is 12²  = 10(a+10)

learn more on secant and tangent segment theorem here: link

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.