<span>1. Martina is given to be 14 years older than Joey who is x years old. Hence, the age of Martina can be expressed as,
x + 14
2. If Joey's current age is x then in 5 years he will become x+5 years old.
3. Martina's age will be her current age added with 5 making it, x+14+5 or x + 19.
4. The equation that would best represent the given scenario in this item is:
x + 19 = 3(x + 5)
5. From the given above, the value of x is equal to 2. This is Joey's current age.
6. The current age of Martina is x + 14 which is equal to 16.</span>
Answer:
-1
Step-by-step explanation:
See the attachment for the polynomial long division. The constant in the quotient is -1.
_____
Here, there is a remainder of -x. If there were no remainder the constant in the quotient is the ratio of the constant in the dividend to the constant in the divisor: -2/2 = -1.
That could be a first guess in a "guess and check" solution approach.
<em>Guess</em>: first term of binomial quotient is (2x^3)/x^2 = 2x; last term of binomial quotient is -2/2 = -1. So, the quotient is guessed to be (2x -1).
<em>Check</em>: (2x -1)(x^2 -x +2) = 2x^3 -3x^2 +5x -2
Subtracting this from the actual dividend gives a remainder of -x. This has a lower degree than the divisor, so no further adjustment of the quotient is required.
Answer:
$22.5.
Step-by-step explanation:
The total revenue that is gained from the sales of the cakes is determined by multiplying the number of cakes by the price. If we let x be the number of $1 that should be deducted from the price and y be the total revenue,
y = (25 - x)(100 + 5x)
Simplifying,
y = 2500 + 25x - 5x²
We get the value of x that will give us the maximum revenue by differentiating the equation and equating the differential to zero.
dy/dx = 0 = 25 - 10x