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sweet-ann [11.9K]

1 year ago

13

Coupon B: 30% off of $63 shoes

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Svetlanka [38]1 year ago

6 0

$44.10

Original price: $
Discount percentage: %
Results
Discount:
Final Price:
Details
Discount = Original Price x Discount %/100
Discount = 63 × 30/100
Discount = 63 x 0.3
You save = $18.90

Final Price = Original Price - Discount
Final Price = 63 - 18.9
Final Price = $44.10

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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:

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

8 0

3 years ago

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4 x -6<br><br> How many groups?<br><br> A. 4<br> B. -6

Andreyy89

Answer:

2(2x - 3)

the grouping is [ ]

7 0

2 years ago

Which graph represents a function with a rate of change of 0.5? On a coordinate plane, a line with negative slope goes through p

Law Incorporation [45]

Answer:

C

Step-by-step explanation:

I took the test

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5 0

3 years ago

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jeyben [28]

Answer:

B

Step-by-step explanation:

-2 is greater than -3

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3 years ago

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What is the root of this equation? <br>2x^2 - 4x + 9 = 0

faust18 [17]

Answer:

x = 1 + i sqrt(7/2) or x = 1 - i sqrt(7/2)

Step-by-step explanation:

Solve for x:

2 x^2 - 4 x + 9 = 0

Divide both sides by 2:

x^2 - 2 x + 9/2 = 0

Subtract 9/2 from both sides:

x^2 - 2 x = -9/2

Add 1 to both sides:

x^2 - 2 x + 1 = -7/2

Write the left hand side as a square:

(x - 1)^2 = -7/2

Take the square root of both sides:

x - 1 = i sqrt(7/2) or x - 1 = -i sqrt(7/2)

Add 1 to both sides:

x = 1 + i sqrt(7/2) or x - 1 = -i sqrt(7/2)

Add 1 to both sides:

Answer: x = 1 + i sqrt(7/2) or x = 1 - i sqrt(7/2)

4 0

3 years ago