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3 years ago

Find the value of x. if necessary, round to the nearest tenth a=47sq in

Mathematics

2 answers:

kirza4 [7]3 years ago

7 0

The answer is 9.7 in

..................................

kipiarov [429]3 years ago

3 0

the picture in the attached figure

we know that

area of the triangle is equal to

$A=(b*h)/2$

in this problem

A=47 in²

b=x

h=x

$47=x*x/2 \\ x^{2} =94 \\ x= \sqrt{94} \\ x=9.69 in \\ x=9.7in$

therefore

the answer is

x=9.7 in

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2 years ago

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2 years ago

In Exercises 40-43, for what value(s) of k, if any, will the systems have (a) no solution, (b) a unique solution, and (c) infini

svet-max [94.6K]

Answer:

If k = −1 then the system has no solutions.

If k = 2 then the system has infinitely many solutions.

The system cannot have unique solution.

Step-by-step explanation:

We have the following system of equations

$x - 2y +3z = 2\\x + y + z = k\\2x - y + 4z = k^2$

The augmented matrix is

$\left[\begin{array}{cccc}1&-2&3&2\\1&1&1&k\\2&-1&4&k^2\end{array}\right]$

The reduction of this matrix to row-echelon form is outlined below.

$R_2\rightarrow R_2-R_1$

$\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\2&-1&4&k^2\end{array}\right]$

$R_3\rightarrow R_3-2R_1$

$\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\0&3&-2&k^2-4\end{array}\right]$

$R_3\rightarrow R_3-R_2$

$\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\0&0&0&k^2-k-2\end{array}\right]$

The last row determines, if there are solutions or not. To be consistent, we must have k such that

$k^2-k-2=0$

$\left(k+1\right)\left(k-2\right)=0\\k=-1,\:k=2$

Case k = −1:

$\left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&-1-2\\0&0&0&(-1)^2-(-1)-2\end{array}\right] \rightarrow \left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&-3\\0&0&0&-2\end{array}\right]$

If k = −1 then the last equation becomes 0 = −2 which is impossible.Therefore, the system has no solutions.

Case k = 2:

$\left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&2-2\\0&0&0&(2)^2-(2)-2\end{array}\right] \rightarrow \left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&0\\0&0&0&0\end{array}\right]$

This gives the infinite many solution.

5 0

2 years ago

Christie needs 54.3 Square feet of laminate wood suppose each square foot of laminated wood cost $.60 find the amount she has to

Irina18 [472]

It will cost $33.

Since wood cost $ .60 sq ft, you can assume she needs to buy 55 sq ft because she will need to buy enough to have 54.3 square ft.

55 x $ .60 = $33

$32.58 would be he total for the 54.3 sq ft and .42 cents would be for the left over .7 sq ft that she didn’t use

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2 years ago

you know that five pizzas will feed 20 people. how many pizzas do you need to order to feed 88 people?

uysha [10]

5 pizzas feeding 20 people means 1 pizza to feed 4 people. 88/4=22 therefore 22 pizzas are needed to feed 88 people.

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2 years ago