F(x) =1/2x+1/2 f-1(x) = [ ? ]x + [ ] - id121219725515, kylemartinez13

Question

Mathematics: F(x) =1/2x+1/2 f-1(x) = [ ? ]x + [ ]

kylemartinez13 · Accepted Answer

Area of triangle AMD is 32 square inches.

Area of triangle CMD is 8 square inches.

Area of triangle ACD is 40 square inches.

Step-by-step explanation:

In trapezoid ABCD with legs AB and CD.

Diagonal BD and AC intersect at M so that BM:MD=1:4

We are given ar(ABM)=8 in²

Ratio of area of two triangle is equal to ratio of their base.

$\dfrac{ar(ABM)}{ar(AMD)}=\dfrac{BM}{MD}$

$\dfrac{8}{ar(AMD)}=\dfrac{1}{4}$

$ar(AMD)=32\text{ in}^2$

Thus, Area of triangle AMD is 32 square inches.

If two triangles lie on same base and same parallel line then their area is equal.

$\therefore ar(ABD)=ar(ACD)$

ar(ACD)=ar(ACD)=ar(AMD)+ar(ABM)

$ar(ACD)=8+32\Rightarrow 40\text{ in}^2$

Thus, Area of triangle ACD is 40 square inches.

ar(CMD)=ar(ACD)-ar(AMD)

$ar(CMD)=40-32\Rightarrow 8\text{ in}^2$

Thus, Area of triangle CMD is 8 square inches.

F(x) =1/2x+1/2
f-1(x) = [ ? ]x + [ ]