The function is undefinded if the denominator, x-5, equals 0.
So
.
The domain is
.
In interval notation, this is (-infinity, 5) u (5, infinity).
5x-3=y 6x-3=y
x=1 x=1
51-3=y 61-3=y
51=5 61=6
5-3=y 6-3=y
2 3
y=2 y=3
The machine will make 24 robots
Answer:
m∠M = 79°
m∠N = 66°
Step-by-step explanation:
∠MPN is supplementary to ∠MPQ, so m∠MPN = 35
The sum of the measures of a triangle is 180.
So, m∠M + m∠N + m∠MPN = 180
5y + 4 + 4y + 6 + 35 = 180
9y + 45 = 180
9y = 135
y = 15
m∠M = 5y + 4 = 5(15) + 4 = 75 + 4 = 79
m∠N = 4y + 6 = 4(15) + 6 = 66
Another way to do this problem, which is easier, is to know that an exterior angle of a triangle is equal to the sum of the two remote interior angles.
That means 5y + 4 + 4y + 6 = 145
9y + 10 = 145
9y = 135
y = 15
From knowing the value of y you can now find the measures of angles M and N
5/9 because 15 + 12 = 27 and 15 are sunroofs so 15/27, I would simplify it to 5/9 but you can either have
15/27 or 5/9