At a basketball game, an air cannon launches T-shirts into the crowd. The function y=−1/8x^2 + 4x represents the path of a T-shirt. The function 3y =2x − 14 represents the height of the bleachers. In both functions, y represents vertical height (in feet) and x represents horizontal distance (in feet). At what height does the T-shirt land in the bleachers?

The T-shirt lands in the bleachers at a height of 14 feet.

Step-by-step explanation:

The point where they meet is the solution of the simultaneous system of equations:

...........................................(1)

..............................................(2)

From (2),

.................................................(3)

Substituting (3) in (1),

Multiply through by 24 (the LCM of 3 and 8, the denominators of the fractions)

                OR        

                      OR        

The value of y represents the height.

Substituting for x in (3)

We discard the negative answer.

Hence, the T-shirt lands in the bleachers at a height of 14 feet.

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

d) 48

step-by-step explanation:

16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,256,272,288,304,320,336