Suppose line AT bisects ∠CAR. if ∠CAT = 5x and ∠CAR = 9x +7, what is ∠TAR

∠TAR =  35°

Step-by-step explanation:

∠TAR = ∠CAR - ∠CAT = (9x + 7) - 5x = 4x + 7

AT bisect ∠CAR       ∠TAR = ∠CAT

4x + 7 = 5x

x = 7

∠TAR = 4 x 7 + 7 = 35

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

a triangular prism is a 3 dimensional shape composed of triangles and rectangles. it is made from two triangular bases and three rectangular sides.