Round 411 to the nearest hundred

Lily ran 100 meters in 15 seconds. How long did she take to run 2 meters

denis23 [38]

.15 seconds because I said

7 0

2 years ago

Read 2 more answers

Graph the linear function.<br> f(x) = -2<br> HELP PLEASE!!

Oliga [24]

Need a picture to answer

5 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

10. Melissa has $20 to buy bagels and juice for her class. box of bagels bottle of juice 56.13, including tax $2.08, including t

adelina 88 [10]

The inequality for the maximum number of bottles of juice she can buy

6.13+ 2.08b <20.00

Option B

Given

Melissa has $20 to buy bagels and juice for her class

Box of bagels : 6.13 including tax

Bottle of juice: 2.08 including tax

She will buy only one box of bagels that is for 6.13

Let 'b' be the number of bottles of juice she can buy

Total cost should be less than 20 dollars

6.13(one bagels) +2.08(bottles of juices)<20

So the inequality becomes

$6.13+2.08b$

Learn more : brainly.com/question/1836165

4 0

2 years ago

A 3cm×10cm rectangle sits inside a circle with radius of 12. Find the area of the shaded region

kolezko [41]

Answer:

422.4cm²

Step-by-step explanation:

area of circle is pi x 12² which is 144 pi

144pi subtract 30 is 422.4

6 0

2 years ago

Round 411 to the nearest hundred​

Round 411 to the nearest hundred