Respuesta :
Daily profit, y, as a function of T-shirts sold, x, is
y = -10x² + 160x - 430
In order to generate $50 in daily profits, the number of T-shirts sold is determined by solving the equation
-10x² + 160x - 430 = 50
Divide through by -10.
x² - 16x + 43 = -5
x² - 16x + 48 = 0
Answer:
This quadratic equation can be solved by factorization.
Explanation:
Note that
48 = 4 x 12, and
4 + 12 = 16
Therefore
x² - 16x + 48 = (x - 4 )(x - 12 ) = 0
The solutions are
x - 4 = 0 => x = 4, and
x - 12 = 0 => x = 12
y = -10x² + 160x - 430
In order to generate $50 in daily profits, the number of T-shirts sold is determined by solving the equation
-10x² + 160x - 430 = 50
Divide through by -10.
x² - 16x + 43 = -5
x² - 16x + 48 = 0
Answer:
This quadratic equation can be solved by factorization.
Explanation:
Note that
48 = 4 x 12, and
4 + 12 = 16
Therefore
x² - 16x + 48 = (x - 4 )(x - 12 ) = 0
The solutions are
x - 4 = 0 => x = 4, and
x - 12 = 0 => x = 12
a. The required equation is x² - 16x + 48 = 0
b. I would use factorisation to solve it and the selling prices that would generate a daily profit of $50 are $4 and $12 respectively.
a.
The required equation is x² - 16x + 48 = 0
The required equation
Since the quadratic function y = -10x² + 160x - 430 models a store’s daily profit (y) for selling a T-shirt priced at x dollars. Since we require a profit of $50, then y = 50.
So, y = -10x² + 160x - 430
-10x² + 160x - 430 = 50
-10x² + 160x - 430 - 50 = 0
-10x² + 160x - 480 = 0
Dividing through by -10, we have
x² - 16x + 48 = 0
So, the required equation is x² - 16x + 48 = 0
b.
I would use factorisation to solve it and the selling prices that would generate a daily profit of $50 are $4 and $12 respectively.
The method
To determine the method you would use to solve the equation, you would need to determine the value of the discriminant.
Discriminant
For a quadratic equation ax² + bx + c = 0, the discriminant is D = b² - 4ac
Since x² - 16x + 48 = 0 and its discriminant D = (-16)² - 4 × 48
= 256 - 192
= 48
= 64 > 0 and is a perfect square, so it is factorizable. The equation would have real and distinct roots,
So, x² - 16x + 48 = 0
x² - 4x - 12x + 48 = 0
x(x - 4) - 12(x - 4) = 0
(x - 4)(x - 12) = 0
x - 4 = 0 or x - 12 = 0
x = 4 or x = 12
I would use factorisation to solve it and the selling prices that would generate a daily profit of $50 are $4 and $12 respectively.
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