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lisabon 2012 [21]
3 years ago
15

Mark and heather starr are celebrating their 25th anniversary by having a reception at a local reception hall. they have budgete

d $3,000 for their reception. if the reception hall charges a $50 cleanup fee plus $32 per person, find the greatest number of people that they may invite and still stay within their budget.
Mark and heather can invite at most __ people to the reception.
Mathematics
2 answers:
pogonyaev3 years ago
7 0

Answer:

i think 90 people

Step-by-step explanation:

3,000 - 50 (clean up fee) - 64 (mark and heather) = 2886

32 x 10 = 320 ( cost of ten people )

2886 - (320 x 9) = 6

6 dollars left

den301095 [7]3 years ago
4 0
By most that they could invite is 90
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1. Write the equation for a line in point slope form that had a slope of 4 and passes through (1,1)
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Solution:

<u>Note that:</u>

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<u>Use the formula to convert the line in point slope form.</u>

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The equation of the line (In point slope form) is y - 1 = 4(x - 1).

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Solve for x:<br><br>5/7 = 4x/83​
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Step-by-step explanation:

\to  \dfrac{5}{7}  =  \dfrac{4x}{83}

By cross multiplication,

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HELP! Find the value of sin 0 if tan 0 = 4; 180 &lt; 0&lt; 270
BabaBlast [244]

Hi there! Use the following identities below to help with your problem.

\large \boxed{sin \theta = tan \theta cos \theta} \\  \large \boxed{tan^{2}  \theta + 1 =  {sec}^{2} \theta}

What we know is our tangent value. We are going to use the tan²θ+1 = sec²θ to find the value of cosθ. Substitute tanθ = 4 in the second identity.

\large{ {4}^{2}  + 1 =  {sec}^{2} \theta } \\  \large{16 + 1 =  {sec}^{2} \theta } \\  \large{ {sec}^{2}  \theta = 17}

As we know, sec²θ = 1/cos²θ.

\large \boxed{sec \theta =   \frac{1}{cos \theta} } \\  \large \boxed{ {sec}^{2}  \theta =  \frac{1}{ {cos}^{2}  \theta} }

And thus,

\large{  {cos}^{2}  \theta =  \frac{1}{17}}   \\ \large{cos \theta =  \frac{ \sqrt{1} }{ \sqrt{17} } } \\  \large{cos \theta =  \frac{1}{ \sqrt{17} }  \longrightarrow  \frac{ \sqrt{17} }{17} }

Since the given domain is 180° < θ < 360°. Thus, the cosθ < 0.

\large{cos \theta =   \cancel\frac{ \sqrt{17} }{17} \longrightarrow cos \theta =  -  \frac{ \sqrt{17} }{17}}

Then use the Identity of sinθ = tanθcosθ to find the sinθ.

\large{sin \theta = 4 \times ( -  \frac{ \sqrt{17} }{17}) } \\  \large{sin \theta =  -  \frac{4 \sqrt{17} }{17} }

Answer

  • sinθ = -4sqrt(17)/17 or A choice.
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3 years ago
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