Given :
A cashier at Giorgio's Grocery Store gets paid $8 per hour for shifts of 6 hours or less.
And $12 per hour for working shifts over 6 hours long.
To Find :
A function best represents this situation.
Solution :
Let, number of hours is h and amount paid is y .
For, h ≤ 6
y = 8h
For, h > 6
y = 12h
Therefore, function representing this is :
y( h ) = 8h , x ≤ 6
12h , x > 6
Hence, this is the required solution.
Answer:
4d
Step-by-step explanation:
i think any variable alone with no coefficient equals one
so this problem is like adding the terms 3d + 1d
so 1+3=4
and you use the variable d at the end
therefore the answer would be 4d
hope this helped<3
(a) When f is increasing the derivative of f is positive.
f'(x) = 15x^4 - 15x^2 > 0
15x^2(x^2 - 1)> 0
x^2 - 1 > 0 (The inequality doesn't flip sign since x^2 is positive)
x^2 > 1
Then f is increasing when x < -1 and x > 1.
(b) The f is concave upward when f''(x) > 0.
f''(x) = 60x^3 - 30x > 0
30x(2x^2 - 1) > 0
x(2x^2 - 1) > 0
x(x^2 - 1/2) > 0
x(x - 1/sqrt(2))(x + 1/sqrt(2)) > 0
There are four regions here. We will check if f''(x) > 0.
x < -1/sqrt(2): f''(-1) = -30 < 0
-1/sqrt(2) < x < 0: f''(-0.5) = 7.5 > 0
0 < x < 1/sqrt(2): f''(0.5) = -7.5 < 0
x > 1/sqrt(2): f''(1) = 30 > 0
Thus, f''(x) > 0 at -1/sqrt(2) < x < 0 and x > 1/sqrt(2).
Therefore, f is concave upward at -1/sqrt(2) < x < 0 and x > 1/sqrt(2).
(c) The horizontal tangents of f are at the points where f'(x) = 0
15x^2(x^2 - 1) = 0
x^2 = 1
x = -1 or x = 1
f(-1) = 3(-1)^5 - 5(-1)^3 + 2 = 4
f(1) = 3(1)^5 - 5(1)^3 + 2 = 0
Therefore, the tangent lines are y = 4 and y = 0.
Given:
Solution:
Here, we need to find the property illustrated by this equation.
It the given equation, we write (x+y) as (y+x).
According to the Commutative Property of Addition, if a and b are two real numbers, then
It means, Commutative Property of Addition is illustrated by the given equation.
Therefore, the correct option is b, i.e., Commutative Property of Addition.
Answer:
- B solving by factoring
- A the quadratic formula
Step-by-step explanation:
<h3>1.</h3>
The "zero product principle" or "zero product rule" tells you a product will be zero if and only if one or more of the factors is zero. This fact is used to solve quadratic equations by factoring.
Factoring the equation y = ax² +bx +c to the form y = a(x -r)(x -s) allows you to immediately identify the solutions of y=0 as x=r and x=s. These are the values of x that make the factors zero, hence making the product zero.
Finding the values of x that satisfy ax² +bx +c = 0 by rearranging it to the form a(x -r)(x -s) = 0 is called "solving by factoring."
<h3>2.</h3>
When the process of "completing the square" is applied to the standard-form quadratic y = ax² +bx +c, the result is a formula for the two solutions to y = 0:
This quadratic formula tells you the solutions based on the coefficients of the original equation, so <em>does not require rearranging</em> the equation in any way.
