Answer:
Price of widget to break even= $37.9
Step-by-step explanation:
We are told that the equation representing the amount of profit, y, made by the company, in relation to the selling price of each widget, x is;
y = -8x² + 348x - 1705
Now, the company will break even when it has made no profit. That is when, y = 0
Thus;
0 = -8x² + 348x - 1705
Rearranging,
8x² - 348x + 1705 = 0
Using quadratic formula ;
x = [-b ± √(b² - 4ac)]/2a
x = [-8 ± √(-348² - 4•1•1705)]/(2 x 8)
x = $5.63 or $37.87
We'll use $37.87 because it is the highest price for which no profit is made, and higher price means that we could sell least number of products to earn a certain amount of money.
We are told to approximate to nearest cent. Thus,
Price of widget = $37.87 ≈ $37.9
Answer:
C. In y^2-y=6, 6 should have been subtracted on both sides first.
Step-by-step explanation:
It is a quadratic equation so you subtract the 6 and create
y^2-y-6=0
Then you factor it to:
(y-3)(y+2)=0
The solutions then are:
y-3=0, y=3 and y+2=0, y=-2
{-2,3}
Answer:
(3x - 4)(8x - 3)
Step-by-step explanation:
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 24 × 12 and sum = - 41
The required factors are - 32 and - 9
Use these factors to split the x- term
24x² - 32x - 9x + 12 ( factor the first/second and third/fourth terms )
= 8x(3x - 4) - 3(3x - 4) ← factor out (3x - 4) from each term
= (3x - 4)(8x - 3) ← in factored form
Answer:
The other endpoint would be (-13, -11)
Step-by-step explanation:
In order to find the coordinates of an end point, we need to note that the midpoint would be the average of the two values. We'll call the unknown point P and we'll start by looking at the x values only.
(1 + Px)/2 = -6 ----> multiply by 2
1 + Px = -12 -----> subtract 1
Px = -13
Now we can do the same with the y values.
(7 + Py)/2 = -2 ----> multiply by 2
7 + Py = -4 ------> subtract 7
Py = -11
Question:
Diners frequently add a 15% tip when charging a meal to a credit card. What is the price of the meal without the tip if the amount charged is $20.70? How much was the tip?
Answer:
Price of meal = $18
Tip price = $2.70
Step-by-step explanation:
Let the price of the meal be <em>y</em>;
Let the tip be <em>t</em>
<em></em>
<em>From the question;</em>
15% of <em>y </em>is the tip charge (<em>t</em>). i.e
t = 15%y
=> t = 0.15y --------(i)
<em>The total amount charged is $20.70 (This means that the sum of the price of the meal and the tip is $20.70)</em>
=> y + t = 20.70 [substitute the value of t=0.15y from equation (i)]
=> y + 0.15y = 20.70
=> 1.15y = 20.70
=> y = 
=> y = $18
Therefore the price of the meal, y, is $18.
From equation (i),
t = 0.15y [substitute the value of y = $18]
t = 0.15(18)
t = $2.70
Therefore the tip was $2.70
