Answer- -6y-3
Distribute negative: 4x+(-2(x+3y)+(-1)(3)+-1(2x)
Distribute: 4x+-2x+-6y+-3+-2x
Combine like terms: (4x+-2x+-2x)+(-6y)+(-3)
You are left with -6y+-3 =-6y-3
When sorting fractions without expressing them as decimal values you have to keep in mind that the greater the denominator is, the smaller the value of the fraction.
For
The denominator in the first fraction is smaller than the denominator in the second one, so we know that the value of the first fraction is greater than the value of the second one.
To prove it you may express them as decimal values:
This inequation is true.
For
The denominator of the first fraction is greater than the denominator of the second one → 4>2, this means that the first fraction represents a value smaller than the second one.
This inequation is true
For
The denominator of the first equation is greater than the denominator of the second one 8>3, this means that the value the first fraction represents is less than the value of the second fraction.
This inequality is false.
For
The denominator of the first fraction is less than the denominator of the second one 2<7, this means that the first fraction is greater than the second one, so this inequation is false.
Answer: The company currently has 17 employees
Step-by-step explanation:
Let X represent the number of current employees in the company
From the first information, it can be expressed mathematically as
X + 3 ≥ 20
X ≥ 20 - 3
X ≥ 17
From the second information, it can be expressed mathematically as
X - 3 < 15
X < 15 + 3
X < 18
From the above solutions, it can be deduced that
17 ≤ X < 18
The only number that fulfils this criteria is 17.
Therefore, X = 17
Step-by-step explanation:
First, we want to find profit given revenue and cost. Because profit = revenue - cost, we can write the profit function, P(x), as R(x) - C(x) and go from there.
P(x) = R(x) - C(x)
P(x) = (-x²+24x) - ( 10x + 30)
P(x) = -x²+24x - 10x-30
P(x) = -x²+14x-30
In a quadratic function such as this, the graph opens downward (meaning that it goes from up to down) if the leading coefficient is negative and vice versa. Here, since -1 is attached to x², we can say that the graph opens downward. The point where the direction of the slope changes (when it goes from up to down), or the peak of the quadratic, is called the vertex.
The x value of the vertex is given by -b/(2a) in a quadratic of form ax²+bx+c. As a=-1 and b=14 here, we can say that -b/(2a) =
-14/(2*-1) = -14/-2
= 7
Therefore, the x value of the vertex, or the number of containers sold that maximizes profit, is 7.