Answer:
x = 7/2 or x = -8/3
Step-by-step explanation:
Solve for x over the real numbers:
6 x^2 - 5 x = 56
Divide both sides by 6:
x^2 - (5 x)/6 = 28/3
Add 25/144 to both sides:
x^2 - (5 x)/6 + 25/144 = 1369/144
Write the left hand side as a square:
(x - 5/12)^2 = 1369/144
Take the square root of both sides:
x - 5/12 = 37/12 or x - 5/12 = -37/12
Add 5/12 to both sides:
x = 7/2 or x - 5/12 = -37/12
Add 5/12 to both sides:
Answer: x = 7/2 or x = -8/3
Answer:
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Step-by-step explanation:
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Answer:
B. Arithmetric
Step-by-step explanation:
Answer: The range is y ≥ 3.
Step-by-step explanation:
When we have an equation:
y = f(x)
The range is the set of the possible values of y.
In this case, we have:
y = f(x) = 2*x^2 - 20*x + 53
This is a quadratic equation, and the leading coefficient is positive. This means that the arms of the graph will open upwards.
Then the minimum value of y will be the vale at the vertex.
We know that for a quadratic equation of the form:
a*x^2 + b*x + c
The vertex is at:
x = -b/2a
Then in this case, the vertex will be at:
x = -(-20)/(2*2) = 20/4 = 5
Then the smallest value of this function will be:
f(5) = 2*5^2 - 20*5 + 53 = 3
This is the smallest value that y can take, and y can take any value greater than 3.
Then the range can be written as:
y ≥ 3.
