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tensa zangetsu [6.8K]
3 years ago
13

A catering company charges $300 plus $40 per guest for a wedding. Sarah and Eric do not want to spend more than $5,000 on cateri

ng. Write and solve an inequality in terms of the number of guests, g, that can be invited.
Mathematics
2 answers:
Nezavi [6.7K]3 years ago
8 0
40g+300 is less than or equal to 5000
g is less than or equal to 117.5
So that is 117 guests max can be invited

Effectus [21]3 years ago
5 0

Answer:

117 guests can be invited!!!! HOPE I HELPED

Step-by-step explanation:

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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?
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Answer:

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Step-by-step explanation:

Given

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Required

The vertex

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First, we express the equation as:

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So, we have:

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

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

Take the coefficient of x: -1

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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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