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3 years ago

What is the solution to the system of equations below?

Mathematics

1 answer:

Vanyuwa [196]3 years ago

8 0

Answer:

A. (–8, 2)

Step-by-step explanation:

(1) y = ½x + 6

(2) y = -¾x – 4 Set (1) = (2)

½x + 6 = -¾x – 4 Multiply each side by 4

2x + 24 = -3x – 16 Add 16 to each side

2x + 40 = -3x Subtract 2x from each side

40 = -5x Divide each side by -5

(3) x = -8 Substitute (2) into (1)

y = ½(-8) +6

= -4 + 6

= 2

The solution to the system of equations is (-8 ,2).

You can see the graphs of the two functions in the figure below. The two lines intersect at (-8, 2).

Check:

2 = ½(-8) + 6 2 = -¾(-8) - 4

2 = -4 +6 2 = 6 - 4

2 = 2 2 = 2

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3 years ago

The manufacturer of a CD player has found that the revenue R (in dollars) is R(p)= -4p2+1200p, when the unit price is p dollars.

qaws [65]

Answer: 9000$

Step-by-step explanation:

Let 's use the formula to find the vertex of the parabola:

ax²+bx+c=0

$\displaystyle x_v=-\frac{b}{2a} \\\\ Where :\\\\ y_v- maximum \ \ income \\\\ y_v=a(x_v)^2+bx_v+c \\\\ Then \ in \ \ our \ \ case : \\\\ -4p^2+1200p =0 \\\\ x_v=-\frac{1200}{-4\cdot 2} =150 \\\\ y_v=-4\cdot (150)^2+150\cdot 1200 \\\\ y_v=150\cdot 1200-150\cdot 600 \\\\ y_v=600\cdot 150=\bf 9000 \$