Answer:
6√3
Step-by-step explanation:
6^2+x^2=12^2
36+x^2=144
-36 -36
x^2=108
x=6√3
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Answer:
24 premium tickets were sold.
Step-by-step explanation:
Let :
Deluxe ticket = x
Regular tickets = x + 78
Premium tickets = y
x + (x + 78) + y = 208
4x + 2(x+78) + 10y = 714
2x + y = 208 - 78
4x + 2x + 156 + 10y = 714
2x + y = 130 - - - - - (1)
6x + 10y = 558 - - - - (2)
Now we can solve the simultaneous equation using elimination method :
From (1)
y = 130 - 2x
Put y = 130 - 2x in (2)
6x + 10(130 - 2x) = 558
6x + 1300 - 20x = 558
- 14x = 558 - 1300
-14x = - 742
x = 742 / 14
x = 53
Put x = 53 in y = 130 - 2x
y = 130 - 2(53)
y = 130 - 106
y = 24
The given triangle has two sides marked equal and hence is an isosceles triangle.In isosceles triangle base angles are equal <A=<B=50.
Sum of angles in any triangle is 180 degrees.
<A+<B+<C=180°
50+50+5y+10=180
Adding like terms :
110+5y=180
Subtracting 110 on both sides:
5y=70
Dividing both sides by 5:
y=14.
Answer:
Base of the ladder is 3 meters away from the building.
Step-by-step explanation:
Let's use Pythagoras theorem to solve.
Pythagoras theorem says,
Here let horizontal distance is "a''
Vertical distance of window is 4 m
So, b=4
The Rafi leans 5 m ladder against the wall. So, c=5.
Simplify it
Subtract both sides 16
Take square root on both sides
a=±3
So, base of the ladder is 3 meters away from the building.
