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3 years ago

Solve for vertex f(x) = -(x-1)^2 +4

Mathematics

1 answer:

sergeinik [125]3 years ago

5 0

$f(x) = -(x-1)^2 +4 \\ f(x) = - {x}^{2} + 2x + 3$

$x_0 = \frac{ - b}{2a} \\ x_0 = \frac{ - 2}{2 \times ( - 1)} = 1$

$y_0 = - {(1)}^{2} + 2 \times 1 + 3 = 4$

Answer: (1, 4)

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3 years ago

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3 years ago

a company owns two dealerships, both of which sell cars and trucks. the first dealership sells a total of 164 cars and trucks. t

OLEGan [10]

Answer:

294 cars.

Step-by-step explanation:

Let x be the number of cars and y be the number of trucks.

We have been given that the first dealership sells a total of 164 cars and trucks. We can represent this information as:

$x+y=164...(1)$

The second dealership sells twice as many cars and half as many trucks as the first dealership. So the number of cars sold by 2nd dealership will be 2x and number of trucks sold by 2nd dealership will be y/2.

Further, the 2nd dealership sold a total of 229 cars and trucks. We can represent this information as:

$2x+\frac{y}{2}=229...(2)$

We can see that total number of cars sold on two dealerships will be $x+2x=3x$ .

We will use substitution method to solve for x. From equation (1) we will get,

$y=164-x$

Substituting this value in equation (2) we will get,

$2x+\frac{164-x}{2}=229$

Now let us have a common denominator.

$\frac{4x}{2}+\frac{164-x}{2}=229$

$\frac{4x+164-x}{2}=229$

Upon multiplying both sides of our equation by 2 we will get,

$2\times \frac{4x+164-x}{2}=2\times 229$

$4x+164-x=458$

$4x+164-164-x=458-164$

$4x-x=458-164$

$3x=294$

Therefore, the total number of cars sold by two dealerships is 294.

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4 years ago