Answer:
7) a = 60; b = 100
8) c = 20
9) d = 45
Step-by-step explanation:
7)
a + 120 = 180
a = 60
b + 80 = 180
b = 100
8)
5c + 4c = 180
9c = 180
c = 20
9)
3d + d = 180
4d = 180
d = 45
tan 52 = 180/a; a = 180/tan 52
tan 43 = 180/b; b = 180/tan 43
you need to calculate, a-b = 180/tan 52 - 180/tan 43
substitute the value of tan thetas, and calculate it simply...
Answer:
<A= right
<B= acute
<C= obtuse
<D= acute
Step-by-step explanation:
Answer: 31 : 9
Step-by-step explanation:
Assume the following:
Alice's amount = P
Bob's amount = Q
Amount received = n
If Alice receives $n$ dollars from Bob ;then she will have $4$ times as much money as Bob.
P + n = 4(Q - n)
P + n = 4Q - 4n
P = 4Q - 4n - n
P = 4Q - 5n - - - - (1)
If, on the other hand, she gives $n$ dollars to Bob, then she will have $3$ times as much money as Bob
P - n = 3(Q + n)
P - n = 3Q + 3n
P = 3Q + 3n + n
P = 3Q + 4n - - - - - - (2)
Equating both equations - (1) and (2)
4Q - 5n = 3Q + 4n
4Q - 3Q = 4n + 5n
Q = 9n
Express P in terms of n, use either equation (1) or (2)
From equation 2:
P = 3Q + 4n
Substituting Q = 9n
P = 3(9n) + 4n
P = 27n + 4n
P = 31n
Alice's amount = P, Bob's = Q
Ratio = P:Q
31 : 9
