Sam is practicing long track speed skating at an ice skating rink. The distance around the rink is 250 yards. He has skated arou
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The true about the domain and the range of the function is:
The domain is all real numbers, and the range is all real numbers
greater than or equal to -4 ⇒ 1st answer
Step-by-step explanation:
f(x) = (x + 2)(x + 6) is a quadratic function with 2 factors (x + 2) and (x + 6)
By multiplying its two factors we will find the form of the quadratic function
∵ (x)(x) = x²
∵ (x)(6) = 6x
∵ (2)(x) = 2x
∵ (2)(6) = 12
∴ f(x) = x² + 6x + 2x + 12
- By adding like terms
∴ f(x) = x² + 8x + 12
The quadratic function represented graphically by a parabola
Look to the attached figure
The x-coordinate of the vertex point of the parabola h =
where b is the coefficient of x and a is the coefficient of x²
∵ f(x) = x² + 8x + 12
∴ a = 1 and b = 8
∴ h =
The y-coordinate of the vertex point is k = f(h)
∵ h = -4
∴ k = f(-4)
∴ k = (-4)² + 8(-4) = 12 = 16 - 32 + 12
∴ k = -4
∴ The vertex point of the parabola is (-4 , -4)
∵ The parabola is opened upward
∴ Its vertex is minimum point
∴ The minimum value of f(x) is y = -4
∵ The domain of the function is the values of x
∵ The range of the function is the values of y corresponding to the
values of x
∵ x can be any real numbers
∴ x ∈ R, where R is the set of real numbers
∴ The domain of f(x) is all real numbers
∵ The minimum value of f(x) is y = -4
∴ y can be any real number greater than or equal to -4
∴ y ≥ -4
∴ The range is all real number greater than or equal to -4
The true about the domain and the range of the function is:
The domain is all real numbers, and the range is all real numbers
greater than or equal to -4
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Answer:
One watering system requires 36 minutes to complete the job alone while another watering system requires 12 minutes to complete the job alone.
Step-by-step explanation:
Given:
Both the system can complete the job = 9 minutes
We need find the time required by each system to do the job.
Solution:
Let the time required by another watering system to complete the job be 'x' mins.
Now given:
One watering system needs about three times as long to complete a job as another watering system.
Time required by one watering system =
Rate to complete the job by another watering system =
Rate to complete the job by One watering system =
Rate at which both can complete the job =
So we can say that;
Rate at which both can complete the job is equal to sum of Rate to complete the job by another watering system and Rate to complete the job by One watering system.
framing in equation form we get;
Now taking LCM to make the denominator common we get;
By Cross multiplication we get;
Dividing both side by 3 we get;
Time required by One watering system =
Hence One watering system requires 36 minutes to complete the job alone while another watering system requires 12 minutes to complete the job alone.