Use a model to divide 8 by 2/3 and find the quotient

A door opening is 2 meters high. If there is a 39 centimeter gap between the top of Casey's head and the top of the door opening

sammy [17]

You should find that Casey is 161 cm tall.

8 0

3 years ago

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

3 years ago

If 3 inches equals 20 miles on map,<br> how<br> many inches is 72 miles?

Vsevolod [243]

Answer:

10.8 inches

Step-by-step explanation:

72/20=3.6

3.6*3=10.8

5 0

3 years ago

A 2-column table with 5 rows. Column 1 is labeled Days with entries 1, 2, 3, 4, 5. Column 2 is labeled miles with entries 6, 12,

ZanzabumX [31]

I believe that it is “Sakura walks 6 miles every day”

3 0

2 years ago

Read 2 more answers

What is the area, in square feet, of the shape below?

grin007 [14]

Answer:

17.4 ft²

Step-by-step explanation:

The formula to find the area of a triangle:

1/2 x b x h, where b is the base and h is the height.

1) Substitute the given values into the formula and solve it.

= 1/2 x 6 x 5.8

= 1/2 x 34.8

= 17.4

7 0

2 years ago

Read 2 more answers