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daser333 [38]
3 years ago
6

The product of this problem

Mathematics
1 answer:
Ganezh [65]3 years ago
5 0

See my steps answer is -12

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Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What is the function’s vertex?
BaLLatris [955]

Answer:

Vertex = (\frac{1}{2},\frac{7}{4})

Step-by-step explanation:

Given

f(x) = x^2 - x +2

Required

The vertex

We have:

f(x) = x^2 - x +2

First, we express the equation as:

f(x) = a(x - h)^2  +k

Where

Vertex = (h,k)

So, we have:

f(x) = x^2 - x +2

--------------------------------------------

Take the coefficient of x: -1

Divide by 2: (-1/2)

Square: (-1/2)^2

Add and subtract this to the equation

--------------------------------------------

f(x) = x^2 - x +2

f(x) = x^2 - x + (-\frac{1}{2})^2+2  -(-\frac{1}{2})^2

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

Expand

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

Factorize

f(x) = x(x - \frac{1}{2})- \frac{1}{2}(x - \frac{1}{2})+2  -\frac{1}{4}

Factor out x - 1/2

f(x) = (x - \frac{1}{2})(x - \frac{1}{2})+2  -\frac{1}{4}

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

f(x) = (x - \frac{1}{2})^2+ \frac{8 -1 }{4}

f(x) = (x - \frac{1}{2})^2+ \frac{7}{4}

Compare to: f(x) = a(x - h)^2  +k

h = \frac{1}{2}

k = \frac{7}{4}

Hence:

Vertex = (\frac{1}{2},\frac{7}{4})

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L + W 
length plus width

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A veterinarian randomly tested of her canine patients for Lyme disease and found that 2% of the canines tested positive for Lyme
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Ah?8$:83&:9&38:&393937488888’dixneidkd
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Help needed quickly
Rudiy27

Answer: your picture isn't popping up on my screen so when it pops up ill be more than welcomed to help .

Step-by-step explanation:

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3 years ago
Help. please read the instructions and Answer the questions​
Dominik [7]

9514 1404 393

Explanation:

We refer to the equations as [1] and [2]. We refer to the items as (1) – (4).

__

1. The terms to be eliminated have matching coefficients in (1) and (2). They can be eliminated by subtracting one equation from the other.

In (3) and (4), putting the equations in standard form* results in terms with opposite coefficients. Those terms can be eliminated by adding the equations.

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2. Terms to be eliminated will have matching or opposite coefficients.

__

3. In (1) and (2), the variable x can be eliminated by subtracting one equation from the other. In the attachment, we have indicated the subtraction that will result in the remaining variable having a positive coefficient.

__

4. In (3) and (4), the coefficients of the variables are not equal or opposite in the two equations, so no variable can be eliminated directly.

__

5. As suggested by the answer to Q4, an equivalent equation must be found that has an equal or opposite variable coefficient with respect to the other equation. The new equations are ...

  (3) [2] ⇒ x -y = 2

  (4) [1] ⇒ 2x +2y = 3

_____

Here are the solutions:

(1) [1] -[2]  ⇒  (x +y) -(x -y) = (-1) -(3)

  2y = -4  ⇒  y = -2

  x = y +3 = 1 . . . . from [2]

  (x, y) = (1, -2)

__

(2) [2] -[1]  ⇒  (x +2y) -(x +y) = (8) -(5)

  y = 3

  x = 5 -y = 2 . . . . from [1]

  (x, y) = (2, 3)

__

(3) [1] +[2]/2  ⇒  (x +y) +(x -y) = (1) +(2)

  2x = 3  ⇒  x = 3/2

  y = 1 -x = -1/2 . . . . from [1]

  (x, y) = (3/2, -1/2)

__

(4) [2] +[1]/2  ⇒  (5x -2y) +(2x +2y) = (4) +(3)

  7x = 7  ⇒  x = 1

  y = (3 -2x)/2 = 1/2

  (x, y) = (1, 1/2)

_____

* Equations in standard form have mutually prime coefficients. In (3) a factor of 2 can be removed from equation [2]. In (4), a factor of 2 can be removed from equation [1].

7 0
3 years ago
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