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KIM [24]
3 years ago
14

Which of the following matrices is the solution matrix for the given system of equations? x + 5y = 11 x - y = 5

Mathematics
1 answer:
givi [52]3 years ago
7 0
<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

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Given the sequence 2, 5, 8, 11, 14, ..., which term is 59? (Hint: find n.)
____ [38]
N = 3  ( the next number is 3 plus the previous number
 sequence formula = an = 3(n-1) +2

so for term the term that =59

59 = 3(n-1) +2

distribute:
59 = 3n -3+2

59 = 3n -1

60 = 3n
n = 60/3
n = 20

59 is the 20th term



8 0
3 years ago
Which of these shows the result of using the first equation to substitute for y in the second equation, then combining like term
AURORKA [14]

11x=55 just took the test

5 0
3 years ago
Read 2 more answers
I need help with the bottom section b
d1i1m1o1n [39]

Answer:

Interior Angle Theorem

x=5

measure of angles: 46, 46, 134

Step-by-step explanation:

Interior angle theorem

12x-14=5x+21

7x=35

x=5

12x-14=12(5)-14=46

5x+21=5(5)+21=46

20x+34=20(5)+34=134

4 0
3 years ago
In a scale model of a table, 1 centimeter represents 8 inches.
Trava [24]

Answer:

(a): 6 centimeters

(b): 72 inches

Step-by-step explanation:

Rule: From centimeters to inches, multiply centimeters × 8

so from inches to centimeters, divide inches by 8

Scale:

1 cm : 8 in

? cm : 48 in

6 cm : 48 in

Scale:

? in : 9 cm

72 in : 9 cm

8 0
3 years ago
PLEASE HELP!!! GEOMETRY QUESTION
maria [59]

Answer:

Step-by-step explanation:

2y + 100 +6x-10=180(in a cyclic quadrilateral opposite angles are supplementary)

2y+6x+90 =180

2y + 6x = 90

dividing each side by 2

y+3x = 45   ........1

7x+1+2y+74 =180 ( same reason)

7x + 2y =105  ............2

multiplying 1 by 2

2y +6x =90........ 3

subtracting 3 from 2

7x+2y-2y-6x = 105-90

x = 15

substituting x=15 in 1

y+45 =45

y= 0

please mark me as the brainliest

7 0
2 years ago
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