Answer:
Results are below.
Step-by-step explanation:
Giving the following information:
The expression 120+4x represents the cost of producing x items. The selling price is $5 for each item.
<u>The net income formula:</u>
y= (5 - 4)x - 120
(5-4)= contribution margin per unit sold (x)
120= fixed costs
<u>To calculate the break-even point in units, we need to use the following formula:</u>
Break-even point in units= fixed costs/ contribution margin per unit
Break-even point in units= 120 / 1
Break-even point in units= 120 units
Prove:
y= 1*120 - 120
y= 0
For a quadratic of the form

, we have the quadratic formula

,
where a is the coefficient (number before the variable) of the squared term, b is the coefficient of the linear term, and c is the constant term.
So, given

, we can get that

, and

. We substitute these numbers into the quadratic formula above.





This is our final answer.
If you've never seen the quadratic formula, you can derive it by completing the square for the general form of a quadratic. Note that the

symbol (read: plus or minus) represents the two possible distinct solutions, except for zero under the radical, which gives only one solution.
49 x 0.35=17.15. There are 17 classrooms total or 17.15
Let ‘s’ be the son’s age 12 years ago.
Let ‘f’ be the father’s current age.
4 years ago, the son was:
s-4
So, his father is currently:
3(s-4)
=
3s-12
Therefore:
f = 3s-12
In twelve years, the son will be:
s+12
And the father will be:
f+12
This can also be written as:
3s-12+12 as the fathers younger age would be f = 3s+12
=
3s
So, we know that s+12 is half the fathers current age, meaning the father is currently 2(s+12) which is equivalent to 2s+24. Also, we know that the father is currently 3 times the sons age 12 years ago, so 3s (proven by the calculations we made above). Therefore, 2s+24=3s which means 24=s. We can then substitute this, and we will receive 24+12 = 36
Son’s current age: 36
We then substitute the son’s age 12 years ago into 2s+24 to give us the father’s age.
2(24)+24 = 72
Father’s current age: 72