Given:
adults = x
male = 7x + 1
female = (7x + 1)/2
total number of people = 82
x + (7x + 1) + [(7x +1)/2] = 82
2x/2 + (14x + 2)/2 + (7x + 1)/2 = 82
2x + 14x + 2 + 7x + 1 = 82 * 2
23x + 3 = 164
23x = 164 - 3
23x = 161
x = 161/23
x = 7
adults = x = 7
males = 7x + 1 = 7(7) + 1 = 49 + 1 = 50
females = (7x+1)/2 = 50/2 = 25
7 + 50 + 25 = 82
Because we have two values of x, we can set the two expressions equal to each-other.
x^2 + 6x + 9 = x + 3
Subtract x and 3 from both sides.
x^2 + 5x + 6 = 0
Now that we have all terms on one side, we can find the values of x.
Using the AC method, we can simplify this equation to (x + 2)(x + 3)
The solutions to the system of equations presented are:
<h3>x = -2, x = -3.</h3>
Answer:
See solutions below
Step-by-step explanation:
From the given diagram;
AC = opposite
AB = 7 = hypotenuse
Angle of elevation = 70 degrees
Using SOH CAH TOA
Sin theta = opp/hyp
Sin theta = AC/AB
Sin 70 = AC/7
AC = 7sin70
AC = 7(0.9397)
AC = 6.58
Similarly
tan 70 = AC/BC
tan 70 = 6.58/BC
BC = 6.58/tan70
BC = 6.58/2.7475
BC = 2.39
tan m<A = BC/AC
tanm<A = 2.39/6.58
tan m<A = 0.3632
m<A = 19.96degrees
A foot is 12 in so a fraction could be 3/12
