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
There are 4 cookies. James eat 3/8 of the cookies. How many cookies are left?
I: 635=dimes*10+quarters*25
or shorter
635=d*10+q*25
II: d=q*3+3
Substitute II (d=3q+3) into I to replace d:
635=d*10+q*25
635=(3q+3)*10+q*25
635=30+30q+25q
605=55q
11=q
-> 11 quarters
"What expression represents the number of dimes if q represent quarters"
insert q=11 into II:
II: d=q*3+3
d=11*3+3
d=33+3
d=36
Answer:
6
Step-by-step explanation:
im just gonna name these couples by numbers 1 , 2 and 3 and each couple will take up 2 seats together.
1 2 3
3 2 1
2 3 1
1 3 2
2 1 3
3 1 2
