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2 years ago

An automobile travels 305 miles on 16 2/3 gallons of gasoline.

Mathematics

2 answers:

Nimfa-mama [501]2 years ago

6 0

Answer:

Step-by-step explanation:

Cost of a Road Trip Jesse's car gets 30 miles per gallon of gas. (a) If Las Vegas is 285 miles away, how many gallons of gas are needed to get there and then home? (b) If gas is $3.09 per gallon, what is the total cost of the gas for the trip.

AysviL [449]2 years ago

5 0

let's firstly convert the mixed fraction to improper fraction and then proceed from there.

$\stackrel{mixed}{16\frac{2}{3}}\implies \cfrac{16\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{50}{3}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{array}{ccll} miles&gallons\\ \cline{1-2} 305&\frac{50}{3}\\[1em] x&1 \end{array}\implies \cfrac{305}{x}=\cfrac{~~ \frac{50}{3}~~}{1}\implies \cfrac{305}{x}=\cfrac{50}{3}\implies 915=50x \\\\\\ \cfrac{305}{50}=x\implies \cfrac{183}{10}=x\implies 18\frac{3}{10}=x$

$\begin{array}{ccll} miles&gallons\\ \cline{1-2} 305&\frac{50}{3}\\[1em] 549&g \end{array}\implies \cfrac{305}{549}=\cfrac{~~ \frac{50}{3}~~}{g}\implies \cfrac{305}{549}=\cfrac{~~ \frac{50}{3}~~}{\frac{g}{1}}\implies \cfrac{305}{549}=\cfrac{50}{3}\cdot \cfrac{1}{g} \\\\\\ \cfrac{305}{549}=\cfrac{50}{3g}\implies 915g=27450\implies g=\cfrac{27450}{915}\implies g = 30$

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2 years ago

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2 years ago

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For a quadratic of the form $f(x)=ax^2+bx+c$ , we have the quadratic formula
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where a is the coefficient (number before the variable) of the squared term, b is the coefficient of the linear term, and c is the constant term.

So, given $2x^2-16x+27=0$ , we can get that $a=2, \ b=-16$ , and $c=27$ . We substitute these numbers into the quadratic formula above.

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If you've never seen the quadratic formula, you can derive it by completing the square for the general form of a quadratic. Note that the $\pm$ symbol (read: plus or minus) represents the two possible distinct solutions, except for zero under the radical, which gives only one solution.

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