Answer:
12<x<16
Step-by-step explanation:
if c^2 > a^2 + b^2
then the triangle is obtuse
since 20 is the longest side
20^2 > x^2 + (x+4)^2
simplify
400 > x^2 + (x+4)(x+4)
FOIL
400 > (x^2 ) + (x^2 + 4x+4x+16)
combine like terms
400 > (2x^2 + 8x+16)
divide by 2
400/2 > 2x^2 /2 + 8x/2 + 16/2
200 > x^2 + 4x +8
subtract 200 from each side
0> x^2 + 4x +8-200
0> x^2 +4x-192
Factor
0 > (x-12) ( x+16)
using the zero product property
0> x-12 0 > x+16
12>x -16>x
x must be greater than 12
we know the longest side is 20
x+4 < 20
subtract 4
x< 16
x>12 and x < 16
12<x<16
4800 divide by 3=1600 (2 cars 1 truck)
4600-1600-3000 (6 cars)
3000 divide by 3 = 1000(2cars)
1000 times 2=2000(4 cars )
4800-2000-2800 (2 cars 3 trucks)
$2,800 is your answer
Answer:
∠x = 13.43°
Step-by-step explanation:
area ΔABC = 1/2 ( BD x AC) = 1/2 (22 x AC) = 42
22 x AC = 84 AC = 84/22 = 42/11 = 3.82
CD = BD - BC = 22 - 6 = 16
AD² = AC² + CD² = (3.82)² + 16² = 270.59
AD = 16.45
sin ∠x = AC / AD = 3.82 / 16.45 = 0.2322
∠x = 13.43°
Using thereoms/postulates, we know that the 60° angle and the (5z - 85)° angle are congruent
so to first find z..
now that we know z, we can find x
simply replace the z in (5z - 85) with 29
and add the entire angle to x to equal 180
(supplementary angles)
