Answer:
Step-by-step explanation:
Step 1:
Write the expression
Step 2: Expand
Step 3: Collect similar terms
Step 4: Factor 4 out of the expression to prove that the expression is a multiple of 4.
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1 answer:
9514 1404 393
Answer:
x = {-0.44, 1.69}
Step-by-step explanation:
Multiply by the denominator to eliminate the fraction.
3 = x(4x -5)
4x^2 -5x -3 = 0 . . . . . subtract 3 and put in standard form
Using the quadratic formula with a=4, b=-5, c=-3, we have the solutions as ...
Solutions rounded to hundredths are ...
x = -0.44
x = 1.69
_____
A graphing calculator can show the x-intercepts easily, so it works well to write the equation in the form
f(x) = 0
3/(4x -5) -x = 0
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Considering the vertex of the quadratic function, it is found that:
A robot traveling along the surface of the curved pit reaches a minimum depth of -22.25 feet.
<h3>What is the vertex of a quadratic equation?</h3>A quadratic equation is modeled by:
The vertex is given by:
In which:
Considering the coefficient a, we have that:
- If a < 0, the vertex is a maximum point.
- If a > 0, the vertex is a minimum point.
In this problem, the function is given by:
y = 0.75x² - 13.5x + 57.75.
Which means that the coefficients are a = 0.75 > 0, b = -13.5, c = 57.75.
Thus, the minimum value is given by:
Thus:
A robot traveling along the surface of the curved pit reaches a minimum depth of -22.25 feet.
More can be learned about the vertex of a quadratic function at brainly.com/question/24737967