6, 2, -2 i could be wrong :/
Answer:
Number 1: $14.40
Number 2: $21.60
Step-by-step explanation:
They're not equivalent.
(vertical bars) represents the absolute value of x. How it works is that it turns negative numbers positive but leaves 0 and positive numbers alone (hence it gets a number's distance from 0 on the number line).
(square brackets) usually represents the floor function, which returns the largest integer that is less than or equal to x. (The floor of x can also be written as
--- it depends on what your textbook/source says).
To solve
, you first transform it into the equivalent equation
. Then by definition of absolute value, there are only two solutions for the first equation: x = 10 or x = -10.
[x] = 10 has infinitely many solutions. For example, the floor of 10 is 10, so
, thus a solution for the second equation is x = 10
The floor of 10.1 is 10, so
, thus another solution for the second equation is x = 10.1.
The two equations do not have the same solution set (as x = 10.1 does not solve |x| - 3 = 7 but solves [x] = 10), so they're not equivalent.
Answer:
Reflecting a function over any axis can be complicated if you do not know the proper way to do it, so I am going to use examples to show you.
If f(x)=x is your normal function, then flipping it across the y-axis would look like f(x)=-x.
Step-by-step explanation:
Placing a - sign before the X will make it flip across the y-axis. After the X, and it flips across the X-axis.
Answer:
(c) y < x^2 -5x
Step-by-step explanation:
A quadratic inequality is one that involves a quadratic polynomial.
<h3>Identification</h3>
The degree of a polynomial is the value of the largest exponent of the variable. When the degree of a polynomial is 2, we call it a <em>quadratic</em>.
For the following inequalities, the degree of the polynomial in x is shown:
- y < 2x +7 . . . degree 1
- y < x^3 +x^2 . . . degree 3
- y < x^2 -5x . . . degree 2 (quadratic)
<h3>Application</h3>
We see that the degree of the polynomial in x is 2 in ...
y < x^2 -5x
so that is the quadratic inequality you're looking for.
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<em>Additional comment</em>
When a term involves only one variable, its degree is the exponent of that variable: 5x^3 has degree 3. When a term involves more than one variable, the degree of the term is the sum of the exponents of the variables: 8x^4y3 has degree 4+3=7.