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Mademuasel [1]
3 years ago
10

The function f(x)=5x+4f(x)=5x+4 models the height of a tree, where x represents the years since the tree was planted for year 3

through year 10.
What is the practical range of the function?

integers from 3 to 10 inclusive

all real numbers between 19 and 54 inclusive

all integers

all real numbers between 3 and 10 inclusive
Mathematics
1 answer:
aliina [53]3 years ago
6 0

Answer:

all real numbers between 19 and 54 inclusive

Step-by-step explanation:

The correct answer is all real numbers between 19 and 54 inclusive

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  • 4x² - 13x + 8 = 0
  • 4x² - 11x + 5 = 0
  • 16x² - 41x + 1 = 0
  • x² + 5x + 4 = 0
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Step-by-step explanation:

<u>Given</u>

  • α and β are roots of 4x²-5x-1=0

<u>Then the sum and product of the roots are:</u>

  • α+b = -(-5)/4 = 5/4
  • αβ = -1/4

(i) <u>Roots are α + 1 and β + 1, then we have:</u>

  • (x - (α + 1))(x - (β + 1)) = 0
  • (x - α - 1)(x - β - 1) = 0
  • x² - (α+β+2)x + α+β+ αβ + 1 = 0
  • x² - (5/4+2)x +5/4 - 1/4 + 1 = 0
  • x² - 13/4x + 2= 0
  • 4x² - 13x + 8 = 0

(ii) <u>Roots are 2 - α and 2 - β, then we have:</u>

  • (x + α - 2)(x + β - 2) = 0
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(iii) <u>Roots are α² and β², then:</u>

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  • x² -(α²+β²)x + (αβ)² = 0
  • x² - ((α+β)² - 2αβ)x + (-1/4)² = 0
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  • x² - ( 25/16 + 1/2)x + 1/16 = 0
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(iv) <u>Roots are 1/α and 1/β, then:</u>

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