X = 30
hope that helps
180 - 108 = 72
180 - 72 -43 = 65
triangle on the left
Angles = 43,65,72
triangle on the right
180 - 65 = 115
180 - 115 - 35 = 30
so angles of triangle on the right = 30, 35, 115
x = 30 (vertical angles with the other angle of triangle on the right)
19^2 or 361 is the answer to the equation
Answer:
This is 0.14 to the nearest hundredth
Step-by-step explanation:
Firstly we list the parameters;
Drive to school = 40
Take the bus = 50
Walk = 10
Sophomore = 30
Junior = 35
Senior = 35
Total number of students in sample is 100
Let W be the event that a student walked to school
So P(w) = 10/100 = 0.1
Let S be the event that a student is a senior
P(S) = 35/100 = 0.35
The probability we want to calculate can be said to be;
Probability that a student walked to school given that he is a senior
This can be represented and calculated as follows;
P( w| s) = P( w n s) / P(s)
w n s is the probability that a student walked to school and he is a senior
We need to know the number of seniors who walked to school
From the table, this is 5/100 = 0.05
So the Conditional probability is as follows;
P(W | S ) = 0.05/0.35 = 0.1429
To the nearest hundredth, that is 0.14
We know that
case 1)
Applying the law of sines
a/Sin A=b/Sin B
A=56°
a=12
b=14
so
a*Sin B=b*Sin A----> Sin B=b*Sin A/a---> Sin B=14*Sin 56°/12
Sin B=0.9672
B=arc sin (0.9672)------> B=75.29°-----> B=75.3°
find angle C
A+B+C=180°-----> C=180-(A+B)----> C=180-(56+75.3)----> C=48.7°
find c
a/Sin A=c/Sin C----> c=a*Sin C/Sin A----> c=12*Sin 48.7°/Sin 56°)
c=10.87-----> c=10.9
the answer Part 1)
the dimensions of the triangle N 1
are
a=12 A=56°
b=14 B=75.3°
c=10.9 C=48.7°
case 2)
A=56°
a=12
b=14
B=180-75.3----> B=104.7°
find angle C
A+B+C=180°-----> C=180-(A+B)----> C=180-(56+104.7)----> C=19.3°
find c
a/Sin A=c/Sin C----> c=a*Sin C/Sin A----> c=12*Sin 19.3°/Sin 56°)
c=4.78-----> c=4.8
the answer Part 2)
the dimensions of the triangle N 2
are
a=12 A=56°
b=14 B=104.7°
c=4.8 C=19.3°
The -1 affects the coefficient of the entire term.
Without the -1,
the term has a positive coefficient.
(3a)² = 9a²
However, with the -1,
the term has a negative coefficient.
-(3a)² = -9a²
