2 2/3 yards = how many feet

Solve the system by using a matrix equation

Sergeu [11.5K]

Answer:

Option A is correct (17,11).

Step-by-step explanation:

6x - 9y = 3

3x - 4y =7

it can be represented in matrix form as $\left[\begin{array}{cc}6&-9\\3&4\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}3\\7\end{array}\right]$

A= $\left[\begin{array}{cc}6&-9\\3&4\end{array}\right]$

X= $\left[\begin{array}{c}x\\y\end{array}\right]$

B= $\left[\begin{array}{c}3\\7\end{array}\right]$

i.e, AX=B

or X= A⁻¹ B

A⁻¹ = 1/|A| * Adj A

determinant of A = |A|= (6*-4) - (-9*3)

= (-24)-(-27)

= (-24) + 27 = 3

so, |A| = 3

Adj A= $\left[\begin{array}{cc}-4&9\\-3&6\end{array}\right]$

A⁻¹ = $\left[\begin{array}{cc}-4&9\\-3&6\end{array}\right]$ /3

A⁻¹ = $\left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right]$

X= A⁻¹ B

X= $\left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right] *\left[\begin{array}{c}3\\7\end{array}\right]$

X= $\left[\begin{array}{c}(-4/3*3) + (3*7)\\(-1*3) + (2*7)\end{array}\right]$

X= $\left[\begin{array}{c}-4+21\\-3+14\end{array}\right]$

X= $\left[\begin{array}{c}17\\11\end{array}\right]$

x= 17, y= 11

solution set= (17,11).

6 0

3 years ago

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In the Journal of Shell and Spatial Structures (December 1963), environmental researcher Vivek Ajmani studied the performance of

igomit [66]

Answer:

The standard deviation of the load distribution is of 5102.041 pounds.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 20000$

Also, the probability that the load is between 10,000 and 30,000 pounds is 0.95.

10,000 pounds and 30,000 pounds are equidistant from the mean. Due to this, and the probability of 0.95 of having a value in this range, 10000 is the (100-95)/2 = 2.5th percentile and 30000 is the (100+95)/2 = 97.5th percentile. Applying one of them, we find the standard deviation.

30,000 is the 97.5th percentile:

This means that when X = 30000, Z has a pvalue of 0.975. So when X = 30000, Z = 1.96. Then

$Z = \frac{X - \mu}{\sigma}$

$1.96 = \frac{30000 - 20000}{\sigma}$

$1.96\sigma = 10000$

$\sigma = \frac{10000}{1.96}$

$\sigma = 5102.041$

The standard deviation of the load distribution is of 5102.041 pounds.

8 0

3 years ago

Find the midpoint of the line segment joining the points (-2, -1) and (-8,12).

SCORPION-xisa [38]

x¹ = -2 x² = -8

y¹ = -1 y² = 12

Using midpoint formula,

M = ( x¹ + x²/2 ,y¹ + ý²/2)

or,M ={ -2+(-8)/2 , (-1) +12/2}

or, =( -10/2 , 11/2)

:M = ( -5 , 11/2)

6 0

3 years ago

Kathy needs money for a trip to Europe if she has US$300 in the bank but wants to withdraw half of it In British pounds and half

Aleks [24]

Answer: She has 21.63 more euros than pounds and has 1.23 times more euros than pounds.

Step-by-step explanation:

She has US$300, and she will withdraw half of it on pounds, and half of it in euros.

(half of US$300 is US$150)

We know that:

1 pound = US$1.6

(1 pound/US$1.6) = 1

Then US$150 = US$150*(1 pound/US$1.6) = (150/1.6) pounds = 93.75 pounds.

And we also know that:

1 euro = US$ 1.3

then:

(1 euro/US$ 1.3) = 1

This means that:

US$150 = US$150*(1 euro/US$ 1.3) = (150/1.3) euros = 115.38 euros.

This means that:

115.38 - 93.75 = 21.63

This means that she has 21.63 more euros than pounds.

and:

115.38/93.75 = 1.23

She has 1.23 times more euros than pounds.

6 0

3 years ago

How many terms are in the expression a3 + 3a2b - 4ab - 11b + 7? 7 4 5 6

rjkz [21]

There are 4 terms
Hope this helps

6 0

3 years ago

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