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3 years ago

Helpppp help helppppppp

Mathematics

2 answers:

Gnoma [55]3 years ago

8 0

Answer:

They are a linear pair so m<B is 56 degrees

Step-by-step explanation:

Yuri [45]3 years ago

4 0

Answer:

56 degrees

Step-by-step explanation:

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The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the ge

Leno4ka [110]

Answer:

Infinite number of solutions.

Step-by-step explanation:

We are given system of equations

$5x+4y+5z=-1$

$x+y+2z=1$

$2x+y-z=-3$

Firs we find determinant of system of equations

Let a matrix A= $\left[\begin{array}{ccc}5&4&5\\1&1&2\\2&1&-1\end{array}\right]$ and B= $\left[\begin{array}{ccc}-1\\1\\-3\end{array}\right]$

$\mid A\mid=\begin{vmatrix}5&4&5\\1&1&2\\2&1&-1\end{vmatrix}$

$\mid A\mid=5(-1-2)-4(-1-4)+5(1-2)=-15+20-5=0$

Determinant of given system of equation is zero therefore, the general solution of system of equation is many solution or no solution.

We are finding rank of matrix

Apply $R_1\rightarrow R_1-4R_2$ and $R_3\rightarrow R_3-2R_2$

$\left[\begin{array}{ccc}1&0&1\\1&1&2\\0&-1&-3\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\1\\-5\end{array}\right]$

Apply $R_2\rightarrow R_2-R_1$

$\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&-1&-3\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\6\\-5\end{array}\right]$

Apply $R_3\rightarrow R_3+R_2$

$\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&0&-2\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\6\\1\end{array}\right]$

Apply $R_3\rightarrow- \frac{1}{2}$ and $R_2\rightarrow R_2-R_3$

$\left[\begin{array}{ccc}1&0&1\\0&1&0\\0&0&1\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]$

Apply $R_1\rightarrow R_1-R_3$

$\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$ : $\left[\begin{array}{ccc}-\frac{9}{2}\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]$

Rank of matrix A and B are equal.Therefore, matrix A has infinite number of solutions.

Therefore, rank of matrix is equal to rank of B.

4 0

4 years ago

HELP ME PLEASE!!!!

navik [9.2K]

$24=4\cdot6\\96=16\cdot6\\\\2\sqrt6-4\sqrt{24}+\sqrt{96}=2\sqrt6-4\sqrt{4\cdot6}+\sqrt{16\cdot6}\\\\=2\sqrt6-4\cdot\sqrt4\cdot\sqrt6+\sqrt{16}\cdot\sqrt6=2\sqrt6-4\cdot2\cdot\sqrt6+4\cdot\sqrt6\\\\=2\sqrt6-8\sqrt6+4\sqrt6=(2-8+4)\sqrt6=-2\sqrt6\\\\\text{Answer:}\ -2\sqrt6\\\\\text{Used:}\ \sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}$

5 0

4 years ago

Which statement is true?

pantera1 [17]

The first one is all squares are rectangles and the second one is not all parallelograms are rectangles.

4 0

3 years ago

Skylar and Wyatt both play soccer. Wyatt scored 2 times as many goals as Skylar. Together they scored 15 goals. Could Skyler hav

Mekhanik [1.2K]

Answer:

No, because 3(2)+3 not equal to 15

Step-by-step explanation:

let the goals of Skylar be x

goals of wyatt be y

y=2x

x+y=15

3x=15

x=5

y=10

8 0

3 years ago

Help please and thanks

12345 [234]

Answer:

Step-by-step explanation:

6/9 simplified is 2/3 they're equal to each other so they're proportional

Hope this helps :)

6 0

3 years ago