In ΔGHI, the measure of ∠I=90°, GH = 96 feet, and IG = 25 feet. Find the measure of ∠H to the nearest tenth of a degree.
2 answers:
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The given information are the coordinates of points H, Z and B. So, the first step to do is to plot these points on a Cartesian plane as shown in the attached picture. We can deduce visually that horse Z is closer to the barns than horse H. But, to further justify the answer, we have to provide the magnitude of the distance of horses H and Z to barn B. In this approach, we use the distance formula:
d = √(x₂ - x₁)² + (y₂ - y₁)²
Use the coordinates of the two points to know their linear distances. These are represented by the red and green lines for each of the horses.
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = 19.4165
Since the scale is 1 unit = 100 meters, the actual distance between horse H and barn B is 19.416*100 = 1,941.65 meters
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = 16.4012
Since the scale is 1 unit = 100 meters, the actual distance between horse Z and barn B is 16.4012*100 = 1,640.12 meters
Comparing the distances: 1,941.65 meters > 1,640.12 meters. Therefore, it justifies that horse Z is nearer to the barn.
d = √(x₂ - x₁)² + (y₂ - y₁)²
Use the coordinates of the two points to know their linear distances. These are represented by the red and green lines for each of the horses.
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = 19.4165
Since the scale is 1 unit = 100 meters, the actual distance between horse H and barn B is 19.416*100 = 1,941.65 meters
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = 16.4012
Since the scale is 1 unit = 100 meters, the actual distance between horse Z and barn B is 16.4012*100 = 1,640.12 meters
Comparing the distances: 1,941.65 meters > 1,640.12 meters. Therefore, it justifies that horse Z is nearer to the barn.
Answer:
all of the functions have a unique range ⇒ answer 1
Step-by-step explanation:
* Lets revise how to find the domain and the range of the function
- The domain is all values of x that make the function defined
- The range is the set of all output values of a function
∵ f(x) = 3x²
- It is a quadratic function
- There is no values of x make this function undefined
∴ The domain of f(x) is all real numbers
- To find the range calculate the vertex of the function
∵ f(x) = ax² + bx + c
∵ f(x) = 3x²
∴ a = 3 , b = 0 , c = 0
∵ h = -b/2a
∴ h = 0/2(3) = 0/6 = 0
∵ k = f(h)
∴ k = f(0) = 3(0)² = 0
∴ The vertex of the cure is (0 , 0)
∵ k is the minimum value of the parabola
∴ The range of f(x) is all real numbers greater than or equal
to zero ⇒ (1)
∵ g(x) = 1/3x
- It is a rational function
- to find the values of x which make the function undefined equate
the denominator by 0
∵ 3x = 0 ⇒ divide both sides by 0
∴ x = 0
∴ The domain of g(x) is all real numbers except zero
∵ We can not put x = 0, then there is no value of g(x) at x = 0
∴ The range of the g(x) is all real number except zero ⇒ (2)
∵ h(x) = 3x
- It is a linear function
∵ There is no values of x make this function undefined
∴ The domain of h(x) is all real numbers
∴ The range of h(x) is all real numbers ⇒ (3)
* From (1) , (2) , (3) the answer is
all of the functions have a unique range
# Look to the attached graph to more understand
The red graph is f(x)
The blue graph is g(x)
The green graph is h(x)
