Answer:
30.7 ft
Step-by-step explanation:
<em>An equilateral triangle with area 43.5 has a height of 8.68 not 8.5</em>
<em>I will do the problem as written even though it is not a possible equilateral triangle</em>
<em>---------------------------------------------</em>
a = (1/2)bh
43.5 = (1/2)b(8.5)
43.5 = 4.25b
b = 43.5/4.25
b = 10.2352941176
-----------------------
p = 3b
p = 3 * 10.2352941176
p = 30.7058823528
~ 30.7 ft
G(x) = 3x + 4
g(-4) = 3(-4) + 4
g(-4) = -12 + 4
g(-4) = -8
Step-by-step explanation:
<h3> new numbers are x+4 and x-1</h3>
so, x+4/x-1=11/16
16x+64=11x-11
16x-11x=-11-64
5x=-75
x = -15
also, x+1 = -14
(5x^2-15x) (-2x+6)
5x (x-3) -2 (x-3)
(5x-2) (x-3)
Part (a)
<h3>Answer: 12.1</h3>
-----------------------
Work Shown:
We'll apply the sine rule since we have a known opposite side of AB = 10 and an unknown hypotenuse we want to find BD.
Focus on triangle ABD
sin(angle) = opposite/hypotenuse
sin(D) = AB/BD
sin(56) = 10/x
x*sin(56) = 10
x = 10/sin(56)
x = 12.062179
x = 12.1
Make sure your calculator is in degree mode.
===================================================
Part (b)
<h3>
Answer: 15.1</h3>
-----------------------
Work Shown:
Draw an xy coordinate grid.
Place point A at the origin (0,0).
Point B is 10 units above this, so B is at (0,10).
Point C is at (18,10) since we move 18 units to the right of B.
Point D is at approximately (6.745085, 0). The 6.745085 is from solving tan(56) = 10/x for x.
Refer to the diagram below.
Apply the distance formula for the points C and D.
Segment CD is roughly 15.1 cm long.