Due to the Triangle Angle Sum Theorem, we know that the sum of the interior angles of a triangle equals 180 degrees, therefore,
180 = m<1 + m<2 + m<3
180 - m<3 = m<1 + m<2
But, we also know that m<4 + m<3 = 180 degrees.
180 = m<3 + m<4
180 - m<3 = m<4
Both m<4 and m<1 + m<2 equals 180 - m<3
m<4 = m<1 + m<2
Answers:
x = 24
y = 8√3
Explanation:
1) Since, the given triangle is a right triangle, and you have both an angle and the hypotenuse length, you can use some trigonometric ratios to find the variables.
2) The variables given represent:
x: adjacent-leg to angle 30°
y: opposite length to angle 30°
3) sine ratio:
sin 30° = opposite-leg / hypotenuse = y / (16√3)
⇒ y = 16√3 sin 30° = 16√3 × (1/2) = 8√3
4) cosine ratio
cos 30° = adjacent-leg / hypotenuse = x / (16√3)
⇒ x = 16√3 cos 30° = 16√3 (√3 / 2) = 16 × 3 / 2 = 24
Answer:
Step-by-step explanation:
I dont know if its right but I think you have to subtract 30% from seven since the equation is not being specific and I came up with 4.9 but dont quote me on it im just giving a educational guess
Answer:
3d + 4p = $37.25
5d + 2p = $38.75
Actual Answer:
Bag of popcorn is $5
A drink is $5.75
Step-by-step explanation:
Let drinks = d
Let popcorn = p
Noah: 3d + 4p = $37.25
Other: 5d + 2p = $38.75
Choose a variable to eliminate (We'll choose p)
3d + 4p = $37.25
(5d + 2p = $38.75) -2
Distribute
-10d - 4p = -77.5
The -4p cancels out the 4p, then we combine
-7d = -40.25
Divide both sides by -7
-7d/-7 = -40.25/-7
d = 5.75
Back to 3d + 4p = $37.25
Substitute d with 5.75
3(5.75) + 4p = $37.25
17.25 + 4p = 37.25
Move the constant to the other side
17.25 + 4p = 37.25
-17.25 -17.25
4p = 20
Divide both sides by 4
4p/4 = 20/4
p = 5
Answer:
Step-by-step explanation:
