What ordered pair is a solution of the equations y = 4x + 3?

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

The required solution is x = 6 and y = 11

7 0

2 years ago

Please help asap

FromTheMoon [43]

Answer: $9

Step-by-step explanation:

10 percent of 9 or 90 broken into 10 parts is 9 also 90 divided by 10 is 9

3 0

2 years ago

Some transportation experts claim that it is the variability of speeds, rather than the level of speeds, that is a critical fact

scZoUnD [109]

Answer:

Explained below.

Step-by-step explanation:

The claim made by an expert is that driving conditions are dangerous if the variance of speeds exceeds 75 (mph)².

(1)

The hypothesis for both the test can be defined as:

H₀: The variance of speeds does not exceeds 75 (mph)², i.e. σ² ≤ 75.

Hₐ: The variance of speeds exceeds 75 (mph)², i.e. σ² > 75.

(2)

A Chi-square test will be used to perform the test.

The significance level of the test is, α = 0.05.

The degrees of freedom of the test is,

df = n - 1 = 55 - 1 = 54

Compute the critical value as follows:

$\chi^{2}_{\alpha, (n-1)}=\chi^{2}_{0.05, 54}=72.153$

Decision rule:

If the test statistic value is more than the critical value then the null hypothesis will be rejected and vice-versa.

(3)

Compute the test statistic as follows:

$\chi^{2}=\frac{(n-1)\times s^{2}}{\sigma^{2}}$

$=\frac{(55-1)\times 94.7}{75}\\\\=68.184$

The test statistic value is, 68.184.

Decision:

$cal.\chi^{2}=68.184$

The null hypothesis will not be rejected at 5% level of significance.

Conclusion:

The variance of speeds does not exceeds 75 (mph)². Thus, concluding that driving conditions are not dangerous on this highway.

7 0

3 years ago

The length of a square is 10 cm. Calculate the perimeter of the square A. 40cm² B. 400cm² C. 4ocm D. 414cm² I will mark you as b

noname [10]

Answer:

C. 40 cm

Step-by-step explanation:

length of side of square = s

perimeter = s + s + s + s = 4s

We use the formula P = 4s

P = 4 * 10 cm

P = 40 cm

Answer: The perimeter is 40 cm.

Notice that the perimeter is a sum of lengths, so its units are linear units such as cm, inches, feet, a unit of length.

An area has square units such as cm^2, in.^2, ft^2, etc.

3 0

3 years ago

Read 2 more answers

If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per pe

Sonja [21]

Answer:

$Z= 75*6 -250=200$

So then the correct answer is B. $200.

Step-by-step explanation:

Notation

Let X be the average contribution size before John makes his contribution.

Let Y be the total contribution size before John makes his contribution.

Let Z be John's contribution.

We know that for this case $ 75 represent the original average amount before the contribution with 50% increase so we can set up the following equation in order to find the original average amount

$1.5 X = 75$