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MariettaO [177]

2 years ago

9

A pair of hikers, 18 miles apart, begin at the same time to hike toward each other. If one walks at a rate that is 1 mph faster

than the other , and if they meet 2 hours later , how fast is each one walking?

1 answer:

dsp732 years ago

3 0

Answer:

The chart below shows Mrs. Thompson's grocery bill. What is the average amount Mrs. Thompson spent on groceries?

A. $58

B. $68

C. $78

D. $340

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Express the system as AX = B; then solve using matrix inverses

Wittaler [7]

Answer with explanation:

1. The given equations are

3x -5 y=2

-x+2 y= 0

⇒The matrix in the form of , AX=B, is

$A=\left[\begin{array}{cc}3&-5\\-1&2\end{array}\right] ,\\\\ X=\left[\begin{array}{c}x&y\end{array}\right],\\\\B=\left[\begin{array}{c}2&0\end{array}\right]$

$\rightarrow X=A^{-1}B\\\\\rightarrow X=\frac{Adj.A}{|A|}\times B$

Adj.A=Transpose of cofactor of Matrix A

$Adj.A=\left[\begin{array}{cc}2&1\\5&3\end{array}\right] ,\\\\ |A|=6-5\\\\|A|=1\\\\\left[\begin{array}{c}x&y\end{array}\right]=\left[\begin{array}{cc}2&5\\1&3\end{array}\right] \times \left[\begin{array}{c}2&0\end{array}\right]\\\\x=4, y=2$

2.

The given equations are

x+y-z=2

x+z=7

2 x +y+z=13

⇒The matrix in the form of , AX=B, is

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

$\frac{Adj.A}{|A|}=\left[\begin{array}{ccc}1&2&-1\\-1&-3&2\\-1&-1&1\end{array}\right]\\\\X=A^{-1}B\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}1&2&-1\\-1&-3&2\\-1&-1&1\end{array}\right]\times\left[\begin{array}{ccc}2\\7\\13\end{array}\right]\\\\x=3,y=3,z=4$

7 0

3 years ago

What is the measure of an interior angle in a regular octagon?

Degger [83]

Answer:

135°

Step-by-step explanation:

(n-2) * 180 =

(8-2) * 180=

6*180= 1080

1080: 8 = 135

7 0

3 years ago

5. The dimensions, in inches, of a shipping box at We Ship 4 You can be expressed as width x, length x + 5, and height 3x - 1. T

meriva

The volume of a cuboid is given by length × width × height

We have:

Volume = 7.6 ft³
Height = 3x - 1
Length = x + 5
Width = x

Substituting these into the formula, we have:

7.6 = (3x - 1) (x + 5) (x)
7.6 = [3x² + 15x - x - 5] (x)
7.6 = [3x² + 14x - 5](x)
7.6 = 3x³ + 14x² - 5x
0 = 3x³ + 14x² - 5x - 7.6

Drawing the graph is one way of finding the solution (refer to the graph below):

We have three solutions (where the curve crosses the x-axis):
x = -4.9
x = -0.6
x = 0.8

Putting these solutions back into the context, since we are looking for the value of x which is part of measurement of length, we cannot have negative value, so we will take the value of x = 0.8 ft

Converting 0.8 ft into inches = 0.8 × 12 inches = 9.6 inches

Answer: x = 9.6 inches

7 0

2 years ago

Jill collected a total of 19 gallons of honey.if she distributes all of the honey equally between 9 jars,how much honey will be

sergeinik [125]

Answer:

2.1 gaallons of honey

Step-by-step explanation:

If you have to istrubute things then its obvous you need to divide something. To get 19 equally into 9 containers you divide 19 by 9 an get 2.1

I hope this helped

8 0

3 years ago

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julia-pushkina [17]

Felt

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5 0

3 years ago

Read 2 more answers