Answer: a) Yes, there is enough fance
b) 58.1° and 47.9°
c) The city will not approve, because 1/3 of the area is just 2220.5ft²
Step-by-step explanation:
a) using law of cosines: x is the side we do not know.
x² = 126² + 110² - 2.126.110.cos74°
x² = 20335.3
x = 142.6 ft
So 150 > 142.6, there is enough fance
b) using law of sine:
sin 74/ 142.6 = sinα/126 = sinβ/110
sin 74/ 142.6 = sinα/126
0.006741 = sinα/126
sinα = 0.849
α = sin⁻¹(0.849)
α = 58.1°
sin 74/ 142.6 = sinβ/110
sin 74/ 142.6 = sinβ/110
0.006741 = sinβ/110
sinβ = 0.741
β = sin⁻¹(0.741)
β = 47.9°
Checking: 74+58.1+47.9 = 180° ok
c) Using Heron A² = p(p-a)(p-b)(p-c)
p = a+b+c/2
p=126+110+142.6/2
p=189.3
A² = 189.3(189.3-126)(189.3-110)(189.3-142.6)
A = 6661.5 ft²
1/3 A = 2220.5
So 2300 > 2220.5. The area you want to build is bigger than the area available.
The city will not approve
Answer:
Step-by-step explanation:
2b + 2c
Answer:
-4
Step-by-step explanation:
3+(-5)-2
3+-5-2
3-7
=-4
Answer:
Rotation
Step-by-step explanation:
Given:
Triangle DEF is congruent to Triangle GHJ by the SSS theorem
To find: transformation required to map Triangle DEF onto Triangle GHJ
Solution:
Two figures are said to be congruent if they overlap each other.
Two polygons are said to be congruent if they have same size and shape.
A rotation is a transformation that turns a figure about the center of rotation.
Rotation transformation is required to map Triangle DEF onto Triangle GHJ
Answer:
The sum of all real numbers x that are not in the domain of the function f(x) is 2.
Step-by-step explanation:
The given function is
The domain is the set of inputs. So, the domain of the given function is all real numbers except those numbers for which denominator values is equal to 0.
It means 
is not included in domain.
It means 2 is not included in domain.
It means 
is not included in domain.
The sum of all real numbers x that are not in the domain of the function f(x) is
Therefore the sum of all real numbers x that are not in the domain of the function f(x) is 2.
