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2 years ago

The width of a rectangle is three times its height. If it has an area of 60.75 square feet, what are its dimensions?

Mathematics

2 answers:

horrorfan [7]2 years ago

8 0

The answer is D my dude don’t over think. Since it’s are multiply your answer choices till you reach 60.75

LuckyWell [14K]2 years ago

3 0

Answer

d. 13.5 ft by 4.5 ft

Step-by-step explanation:

Let height of rectangle be x ft

Therefore, width = 3x ft

$area \: of \: rectangle = 60.75 \: {ft}^{2} \\ \therefore \: lw = 60.75 \\ \therefore \: 3x \times x = 60.75 \\ \therefore \: 3x^{2} = 60.75 \\ \therefore \: x^{2} = \frac{60.75}{3} \\ \therefore \: x^{2} = 20.25 \\ \therefore \:x = \sqrt{20.25} \\ \therefore \:x = 4.5 \: ft\\ \therefore \:3x =3 \times 4.5 = 13.5 \: ft$

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David wants to pack 574 cereal bars into bags of 10 and bags of 8 the number of bags of 8 is 2 more than the bags of 10. How man

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2 years ago

Which of the following matrices is the solution matrix for the given system of equations? x + 5y = 11 x - y = 5

givi [52]

<h2>The required solution is x = 6 and y = 11 </h2>

Step-by-step explanation:

Given system of equations are

x+5y = 11 and x-y =5

$A= \left[\begin{array}{cc}1&5\\1&-1\end{array}\right]$ $X=\left[\begin{array}{c}x\\y\end{array}\right]$

and $B= \left[\begin{array}{c}11\\5\end{array}\right]$

∴AX=B

$adj A = \left[\begin{array}{cc}{-1}&{-5}\\{-1}&1\end{array}\right]$

$A= \left|\begin{array}{cc}1&5\\1&-1\end{array}\right|=-6$

∴ $A^{-1} =\frac{adj A}{|A|}$

So, $A^{-1} =\frac{ \left[\begin{array}{cc}{-1}&{-5}\\{-1}&1\end{array}\right]}{-6}$

$A^{-1} ={ \left[\begin{array}{c \c} {{\frac{1}{6} }}&{\frac{5}{6}}\ \\ {{\frac{1}{6} }}&{\frac{-1}{6}} \end{array}\right]}$

$X =A^{-1}\times B$

⇒ $\left[\begin{array}{c}x\\y\end{array}\right] ={ \left[\begin{array}{c \c} {{\frac{1}{6} }}&{\frac{5}{6}}\ \\ {{\frac{1}{6} }}&{\frac{-1}{6}} \end{array}\right]} \times \left[\begin{array}{c}11\\5\end{array}\right]$

⇒ $\left[\begin{array}{c}x\\y\end{array}\right] ={ \left[\begin{array}{c} {6}\\ {11} \end{array}\right]}$

∴ x= 6 and y = 11

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