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Naddik [55]
3 years ago
9

(05.07 MC) A study analyzed the average yearly salt intake in the United States from 2012 thru 2017. The data is summarized in t

he table: Year Annual Salt Intake (grams) 2012 3,435 2013 3,501 2014 3,560 2015 3,626 2016 3,690 2017 3,744 The study found that the data after the year 2012 can be modeled by the function f(x) = 59.4x + 3,429, where x is the number of years since 2012 and f(x) is the total amount of salt ingested in grams. Describe the significance of 3,429.
Mathematics
2 answers:
pychu [463]3 years ago
7 0

Answer: An estimate of the average grams of salt used in 2012

gizmo_the_mogwai [7]3 years ago
5 0

Answer:

An estimate of the average grams of salt used in 2012

Step-by-step explanation:

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Im giving 100 Points to anyone who could solve this for me please.
myrzilka [38]

Answer:

AB = 27.2

BC = 33.5

AC = 50.4

∠A = 38°

∠ABC = 112°

Step-by-step explanation:

<u>Trigonometric ratios</u>

\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}

where:

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\implies \sf \cos(30^{\circ})=\dfrac{29}{BC}

\implies \sf BC=\dfrac{29}{\cos(30^{\circ})}

\implies \sf BC=\dfrac{58\sqrt{3}}{3}=33.5\:(nearest\:tenth)

\implies \sf \tan(30^{\circ})=\dfrac{BD}{29}

\implies \sf BD=29\tan(30^{\circ})

\implies \sf BD=\dfrac{29\sqrt{3}}{3}

\implies \sf \sin(38^{\circ})=\dfrac{BD}{AB}

\implies \sf AB=\dfrac{\dfrac{29\sqrt{3}}{3}}{\sin(38^{\circ})}

\implies \sf AB=27.2\:(nearest\:tenth)

\implies \sf \tan(38^{\circ})=\dfrac{BD}{AD}

\implies \sf AD=\dfrac{\dfrac{29\sqrt{3}}{3}}{\tan(38^{\circ})}

\implies \sf AD=21.4\:(nearest\:tenth)

\implies \sf AC=AD+DC=21.4+29=50.4

The interior angles of a triangle sum to 180°

⇒ ∠A + 52° + 90° = 180°

⇒ ∠A = 180° - 90° - 52°

⇒ ∠A = 38°

⇒ ∠ABC + 38° + 30° = 180°

⇒ ∠ABC = 180° - 38° - 30°

⇒ ∠ABC = 112°

**I have checked the measures using a graphing programme - see attached**

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