Answer:
m<N = 76°
Step-by-step explanation:
Given:
∆JKL and ∆MNL are isosceles ∆ (isosceles ∆ has 2 equal sides).
m<J = 64° (given)
Required:
m<N
SOLUTION:
m<K = m<J (base angles of an isosceles ∆ are equal)
m<K = 64° (Substitution)
m<K + m<J + m<JLK = 180° (sum of ∆)
64° + 64° + m<JLK = 180° (substitution)
128° + m<JLK = 180°
subtract 128 from each side
m<JLK = 180° - 128°
m<JLK = 52°
In isosceles ∆MNL, m<MLN and <M are base angles of the ∆. Therefore, they are of equal measure.
Thus:
m<MLN = m<JKL (vertical angles are congruent)
m<MLN = 52°
m<M = m<MLN (base angles of isosceles ∆MNL)
m<M = 52° (substitution)
m<N + m<M° + m<MLN = 180° (Sum of ∆)
m<N + 52° + 52° = 180° (Substitution)
m<N + 104° = 180°
subtract 104 from each side
m<N = 180° - 104°
m<N = 76°
Answer: 1,365 possible special pizzas
Step-by-step explanation:
For the first topping, there are 15 possibilities, for the second topping, there are 14 possibilities, for the third topping, there are 13 possibilities, and for the fourth topping, there are 12 possibilities. This is how you find the number of possible ways.
15 * 14 * 13 * 12 = 32,760
Now, you need to divide that by the number of toppings you are allowed to add each time you add a topping.
4 * 3 * 2 * 1 = 24
32,760 / 24 = 1,365
There are 1,365 possible special pizzas
Answer:
Z=1
Step-by-step explanation:
Answer:
19.1 miles
Step-by-step explanation:
The situation given represents a right triangle.
Thus, we would use trigonometric function to find how far north the boat travelled.
Let's represent how far the boat travelled north with "x".
Thus:
Reference angle = 23°
Opposite = x
Adjacent = 45 miles
Apply TOA:
Tan 23° = Opp/Adj
Tan 23° = x/45
Multiply both sides by 45
45 × Tan 23° = x
x = 45 × Tan 23°
x = 19.1013667
x = 19.1 miles (nearest tenth of a mile)
