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Svetllana [295]
2 years ago
6

What are the exact solutions of x2 − 3x − 5 = 0, where x equals negative b plus or minus the square root of b squared minus 4 ti

mes a times c all over 2 times a? x = the quantity of negative 3 plus or minus the square root of 29 all over 2 x = the quantity of 3 plus or minus the square root of 29 all over 2 x = the quantity of 3 plus or minus the square root of 11 all over 2 x = the quantity of negative 3 plus or minus the square root of 11 all over 2
Mathematics
1 answer:
Karo-lina-s [1.5K]2 years ago
7 0

Answer:

  • B. x = the quantity of 3 plus or minus the square root of 29 all over 2

Step-by-step explanation:

Given equation

  • x² - 3x - 5 = 0

The roots are

  • x=\cfrac{-b+- \sqrt{b^2-4ac} }{2a}

Substitute values into equation

  • x=\cfrac{3+- \sqrt{(-3)^2-4(1)(-5)} }{2(1)} =\cfrac{3+- \sqrt{9+20} }{2} =\cfrac{3+- \sqrt{29} }{2}

This is matching the option B

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A farmer want to fence in a rectangular field that encloses 3600 sq feet. The cost 3.50 per foot. Express the total cost c(x) of
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Answer:

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3 years ago
A local sorority sold hot dogs and bratwursts at the spring fling picnics. The first day they sold 8 dozen hot dogs and 13 dozen
kicyunya [14]

Answer:

1 hot dog costs $0.75

1 bratwurst costs $1.35

Step-by-step explanation:

Let x and y be the price per dozen of hot dogs and bratwursts respectively.

The first day they sold 8 dozen hot dogs and 13 dozen bratwursts for ​$282.60

8x + 13y = 282.60

The second day they sold 10 dozen hot dogs and 15 dozen bratwursts for a total of ​$333.00

10x + 15y = 333

and we have the linear system

<em>8x + 13y = 282.60 </em>

<em>10x + 15y = 333 </em>

which can be written in matrix form as

\bf \left(\begin{array}{cc}8&13\\10&15\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}282.60\\333\end{array}\right)

The solution would be given by

\bf \left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{cc}8&13\\10&15\end{array}\right)^{-1}\left(\begin{array}{c}282.60\\333\end{array}\right)

We have  

\bf \left(\begin{array}{cc}8&13\\10&15\end{array}\right)^{-1}=\left(\begin{array}{cc}-3/2&13/10\\1&-4/5\end{array}\right)

hence

\bf \left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{cc}-3/2&13/10\\1&-4/5\end{array}\right)\left(\begin{array}{c}282.60\\333\end{array}\right)=\left(\begin{array}{c}9\\ 16.2\end{array}\right)

Now,

if a dozen hot dogs cost $9, 1 hot dog costs 9/12 = $0.75

if a dozen bratwursts cost $16.2, 1 bratwurst costs 16.2/12 = $1.35

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