Which graph represents the solution of 3x + 2y ≥ 4 and x + 3y ≤ 2?
2 answers:
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Answer:
12.1
Step-by-step explanation:
The dashed line joining M₁ and M₂ is the hypotenuse of a right triangle as shown in red below.
The base of the triangle is
x₂ - x₁ = 2 - (-3) = 2+ 3 = 5
The height of the triangle is
y₂ - y₁ = 16 - 5 = 11
We can now use Pythagoras' theorem to calculate distance between the two midpoints.
x² = 5² + 11² = 25 + 121 = 146
x = √146 = 12.1
The distance between M₁ and M₂ is 12.1.
Answer: x = 15, ∠K = 45.7°, ∠L = 45.7°, ∠M = 88.6°
<u>Step-by-step explanation:</u>
Since ∠K ≅ ∠L, then ΔKLM is an isoceles triangle with base KL
KM ≅ LM
3x + 23 = 7x - 37
23 = 4x - 37
60 = 4x
15 = x
KM = LM = 3x + 23
= 3(15) + 23
= 45 + 23
= 68
KL = 9x - 40
= 9(15) - 40
= 135 - 40
= 95
Next, draw a perpendicular bisector KN from K to KL. Thus, N is the midpoint of KL and ΔMNL is a right triangle.
- Since N is the midpoint of KL and KL = 95, then NL = 47.5
- Since ∠N is 90°, then NL is adjacent to ∠l and ML is the hypotenuse
Use trig to solve for ∠L (which equals ∠K):
cos ∠L =
cos ∠L =
∠L = cos⁻¹
∠L = 45.7
Triangle sum Theorem:
∠K + ∠L + ∠M = 180°
45.7 + 45.7 + ∠M = 180
91.4 + ∠M = 180
∠M = 88.6