X = y + 30 (I)
2x + 20 = 3y + 30
2x - 3y = 10 (II)
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2(y+30) - 3y = 10
2y + 60 - 3y = 10
-y = -50
y = 50
x = y + 30
x = 50 + 30
x = 80
Football team has 80 members, basketball team has 50 members.
Answer:
C and D
Step-by-step explanation:
i=√-1
n/4=x.5
since 2 is the remainder
n=2x
then i^n=i^2x
when x is even, i^n =1
when x is odd, i^n=-1
<h3>
Answer: A. 18*sqrt(3)</h3>
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Explanation:
We'll need the tangent rule
tan(angle) = opposite/adjacent
tan(R) = TH/HR
tan(30) = TH/54
sqrt(3)/3 = TH/54 ... use the unit circle
54*sqrt(3)/3 = TH .... multiply both sides by 54
(54/3)*sqrt(3) = TH
18*sqrt(3) = TH
TH = 18*sqrt(3) which points to <u>choice A</u> as the final answer
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An alternative method:
Triangle THR is a 30-60-90 triangle.
Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.
The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.
Now use the pythagorean theorem
a^2 + b^2 = c^2
(TH)^2 + (HR)^2 = (TR)^2
(x)^2 + (54)^2 = (2x)^2
x^2 + 2916 = 4x^2
2916 = 4x^2 - x^2
3x^2 = 2916
x^2 = 2916/3
x^2 = 972
x = sqrt(972)
x = sqrt(324*3)
x = sqrt(324)*sqrt(3)
x = 18*sqrt(3) which is the length of TH.
A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.
Answer:
The value of c from the equation is 5.
Step-by-step explanation:
c/5 - 4 = -3
Add 4 to both sides of the equation.
c/5 = 1
Multiply both sides by 5 to get c by itself.
c = 5
