Ineed with these quadratic applications.

1. d

2. c

Step-by-step explanation:

1. "You have a 12in by 14in picture you framed.  When you hung the picture, you found that the area is 261.44 square inches.  What is the width of the frame?"

If we call the width of the frame x, then the total width is w = 12 + 2x, and the total height is 14 + 2x.  Area is width times height, so:

A = wh

261.44 = (12 + 2x) (14 + 2x)

Distribute using FOIL (first outer inner last):

261.44 = 12×14 + 12×2x + 2x×14 + 2x×2x

261.44 = 168 + 24x + 28x + 4x²

261.44 = 168 + 52x + 4x²

0 = 4x² + 52x − 93.44

0 = x² + 13x − 23.36

Solve with quadratic formula:

x = [ -b ± √(b² − 4ac) ] / 2a

x = [ -13 ± √(169 + 93.44) ] / 2

x = (-13 ± 16.2) / 2

x = 1.6 or -14.6

Since x must be positive, x = 1.6 inches.

2. "A flower garden has been design with an L shaped walkway and viewing area around two sides as shown.  The garden itself is 5 yards by 8 yards.  The total area needed to build this landscape design is 60.9525 square yards.  What is the width of the walkway?"

If we call the width of the walkway x, then the total width is w = 5 + x and the total length is l = 8 + x.  Area is width times length, so:

A = wl

60.9525 = (5 + x) (8 + x)

Distribute using FOIL (first outer inner last):

60.9525 = 5×8 + 5×x + x×8 + x×x

60.9525 = 40 + 5x + 8x + x²

60.9525 = 40 + 13x + x²

0 = x² + 13x − 20.9525

Solve with quadratic formula:

x = [ -b ± √(b² − 4ac) ] / 2a

x = [ -13 ± √(169 + 83.81) ] / 2

x = (-13 ± 15.9) / 2

x = 1.45 or -14.45

Since x must be positive, x = 1.45 yards.

∠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.

the anwser is d) 75°

step-by-step explanation: