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3 years ago

Austen needs to buy a bathroom mirror that is 2 feet wide and 3 feet long. If the mirror

Mathematics

1 answer:

PtichkaEL [24]3 years ago

7 0

<h2><u>Question :-</u></h2>

Austen needs to buy a bathroom mirror that is 2 feet wide and 3 feet long. If the mirror sells for $5.00 per square foot, what will the total cost of the mirror be?

<h2><u>Solution :-</u></h2>

<h3><u>Given Information :-</u></h3>

<u>Length of the mirror Austen needs to buy ➢</u> 3 ft
<u>Width of the mirror Austen needs to buy ➢</u> 2 ft
<u>Cost of mirror per square foot ➢</u> $5.00

Total cost of the mirror Austen needs to buy.

<h3><u>Formula Used :-</u></h3>

Area of Mirror = Length × Width
Total cost of mirror = Area of mirror × Cost of mirror per square foot

<h3><u>Calculation :-</u></h3>

<u>Area of mirror :-</u>

<em><u>Substituting the values given in the 1st formula, We get, </u></em>

⇒ Area of mirror = ( 3 × 2 ) ft²

⇒ Area of mirror = 6 ft²

<u>Now finding the total cost of mirror,</u>

<em><u>Substituting the values calculated above in the 2nd formula, We get </u></em>

⇒ Total Cost of mirror = $ ( 6 × 5.00 )

⇒ Total Cost of mirror = $30

<h2><u>Final Answer :-</u></h2>

Total cost of the mirror Austen needs to buy will be $30

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Complete question :

The cost of a student ticket to the school play is $7. Write an equation that correctly relates the total cost, c, for a particular number, s, of student tickets purchased. Identify the independent and dependent variable.

Answer:

Dependent variable = Total cost

Independent variable = number of students

Step-by-step explanation:

The total cost equation is :

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The Independent variable also called the predictor variable is the number of students in the scenario described above as it is the variable upon which the total cost relies. It dictates the value of the output or dependent variable. As we vary the value of the Independent variable, number of students, the total cost which is the dependent variable also varies. The dependent variable on the other hand is the predicted value or variable which is controlled by the independent variable. The dependent variable in this case is the total cost, c

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<u>Your y-intercept is (0,-51).</u>

Next, using our equation plug the appropriate values into the quadratic formula:

$x=\frac{-24\pm \sqrt{24^2-4*3*(-54)}}{2*3}$

Next, solve the multiplications and exponent:

$x=\frac{-24\pm \sqrt{576-(-648)}}{6}\\\\x=\frac{-24\pm \sqrt{576+648}}{6}$

Next, solve the addition:

$x=\frac{-24\pm \sqrt{1224}}{6}$

Now, simplify the radical using the product rule of radicals as such:

Product Rule of Radicals: √ab = √a × √b

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Next, divide:

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Now to find the approximate values, solve this twice: once with the + symbol and once with the - symbol:

$x=-4+ \sqrt{34},-4- \sqrt{34}\\x\approx 1.83, -9.83$

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Answer with explanation:

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$A=\left[\begin{array}{ccc}1&1&-1\\1&0&1\\2&1&1\end{array}\right]\\\\ X=\left[\begin{array}{ccc}x\\y\\z\end{array}\right]\\\\B= \left[\begin{array}{ccc}2\\7\\13\end{array}\right]\\\\\rightarrow X=A^{-1}B\\\\\rightarrow X=\frac{Adj.A}{|A|}\times B\\\\a_{11}=-1,a_{12}=1,a_{13}=1,a_{21}=-2,a_{22}=3,a_{23}=1,a_{31}=1,a_{32}=-2,a_{33}=-1\\\\|A|=1\times(0-1)-1\times(1-2)-1\times(1-0)\\\\=-1+1-1\\\\|A|=-1\\\\Adj.A=\left[\begin{array}{ccc}-1&-2&1\\1&3&-2\\1&1&-1\end{array}\right]$

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