Answer:
4x² -29x +51
Step-by-step explanation:
Put x-3 where x is in the original function definition, then "simplify". I think you'll find it convenient to rewrite the original function definition first.
... g(x) = 4x² -5x = x(4x -5)
Substituting, we have
... g(x-3) = (x -3)(4(x -3) -5)
... = (x -3)(4x -17) . . . . . simplify right factor
... = 4x² -12x -17x +51
... g(x -3) = 4x² -29x +51
Using the given exponential functions, it is found that the graph of g(x) will be less than than the graph of f(x) when x < 0.
<h3>What are the exponential functions?</h3>
The given exponential functions, f(x) and g(x), are respectively given by:
When x < 0, one possible value is x = -1, hence evaluating the functions at these values:
, hence, the graph of g(x) will be less than than the graph of f(x) when x < 0.
More can be learned about exponential functions at brainly.com/question/25537936
The equation of the central street PQ is -1.5x - 3.5y = -31.5 option (b) is correct.
<h3>What is a straight line?</h3>
A straight line is a combination of endless points joined on both sides of the point.
We have a straight line:
Convert it to the general form given below:
or
(Slope of AB line)
For the slope(m') of the PQ line:
( because AB and PQ are perpendicular to each other)
We know the:
Where (x', y') = (7, 6), we get:
(multiply by -1/2 on both sides)
Thus, the equation of the central street PQ is -1.5x - 3.5y = -31.5
Learn more about the straight line.
brainly.com/question/3493733
Hello!
You can make two expressions based on what you know
let x equal the larger number
let y equal the smaller number
x + y = 95
x + 2y = 120
We can use elimination to get rid of x
You can subtract the two equation to get rid of x
-y = -25
Since y is negative we can multiply both sides by -1 to make y positive
y = 25
Now we can put this into one of the other equations to find x
x + 25 = 95
subtract 95 from both sides
x = 70
The answers are 70 and 25
Hope this helps!
All are the exponential function.
<h2>Exponent</h2>
Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. c is the base and x is the power.
<h3>Which functions represent exponential growth?</h3>
1. y = f(x) is a exponential function.
Because the range of the exponential function is from 0 to ∞ for all values of x. And it is 1 at x = 0.
2. y = h(x) is a exponential function.
Because the range of the exponential function is from 0 to ∞ for all values of x. And it is 1 at x = 0.
3. y = g(x) is a exponential function.
Because the range of the exponential function is from 0 to ∞ for all values of x. And it is 1 at x = 0.
4. y = k(x) is a exponential function.
Because the range of the exponential function is from 0 to ∞ for all values of x. And it is 1 at x = 0.
Thus, all are the exponential function.
More about the exponent link is given below.
brainly.com/question/5497425
