All categories

3 years ago

In the figure shown, lines 1 and 2 are parallel.

Mathematics

1 answer:

Sav [38]3 years ago

7 0

Answer:

Step-by-step explanation:

8=09

You might be interested in

Solve the matrix and prove that it is equal 0

Art [367]

Step-by-step explanation:

$\underline{ \underline{ \text{Given}}} :$

$\tt{ {A}^{T} = \begin{bmatrix} 2 & - 4 \\ 4 & 3 \\ \end{bmatrix}}$

$\underline{ \underline { \text{To \: Find}}} :$

$\sf{ {A}^{2} - 5A+ 22I= 0}$

$\underline{ \underline{ \text{Solution}}} :$

The new matrix obtained from a given matrix by interchanging it's rows and columns is called the transposition of matrix. It is denoted by $\sf{ {A}^{T}}$ . Again , Interchange it's rows and columns in order to find ' A '.

$\tt{A = \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix}}$

Now , LEFT HAND SIDE ( L.H.S )

$\tt{ {A}^{2} - 5A+ 22I}$

Here, I refers to identity matrix. A diagonal matrix in which all the elements of leading diagonal are 1 ( unit ) is called unit or identity matrix.

⟼ $\begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} \times \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} - 5 \times \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} + 22 \times \begin{bmatrix} 1 & 0 \\ 0 & 1\\ \end{bmatrix}$

⟼ $\begin{bmatrix} 2 \times 2 + 4 \times ( - 4)& 2 \times 4 + 4 \times 3 \\ - 4 \times 2 + 3 \times ( - 4) & - 4 \times 4 + 3 \times 3 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20& 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}$

⟼ $\begin{bmatrix} 4 + ( - 16) & 8 + 12 \\ - 8 + ( - 12) & - 16 + 9 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}$

⟼ $\begin{bmatrix} - 12 & 20\\ - 20& - 7 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}$

⟼ $\begin{bmatrix} - 22 & 0 \\ 0& - 22 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}$

⟼ $\begin{bmatrix} - 22 + 22 & 0 + 0 \\ 0 + 0 & - 22 + 22 \\ \end{bmatrix}$

⟼ $\begin{bmatrix} 0 & 0\\ 0 & 0 \\ \end{bmatrix}$

⟼ $\sf{0}$

RIGHT HAND SIDE ( R.H.S ) : 0

L.H.S = R.H.S [ Hence , proved ! ]

Hope I helped ! ♡

Have a wonderful day / night ! ツ

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

4 0

3 years ago

a box of granola contains 13.6 ounces. It costs $3.40. what is the average cost, to the nearest cent, of granola per ounce?

Airida [17]

Answer:hey

Step-by-step explanation:

so ii was wondering like what kind of math are uu working on for me to figure this question out

6 0

4 years ago

If the first chapter of a certain book is 16 pages long and makes up 4% of the book, how many pages does the entire book have?

galina1969 [7]

If 16 pages equal to 4%, how many pages will equal to 100%?

4/100 = 16/x
4x=1600
X= 400

So total pages should be 400.

5 0

2 years ago

Un asked six friends how many different foreign countries they'd been to. He recorded 0, 1, 1, 2,

saveliy_v [14]

Answer:

MAD = Σ|x - mean|/n

mean = (0 + 1 + 1 + 2 + 5 + 9)/6 = 18/6 = 3

MAD = (|0 - 3| + |1 - 3| + |1 - 3| + |2 - 3| + |5 - 3| + |9 - 3|)/6 = (3 + 2 + 2 + 1 + 2 + 6)/6 = 16/6 = 2.7 countries.

Step-by-step explanation:

6 0

4 years ago

The Alden Middle School girls' soccer team won 80% of its games this season.If the team won 12 games,how many games did it play?

Alenkasestr [34]

0.8g=12

g=12/0.8

Where 0.8 is 80% in fraction form (80/100), g is the number of games played and 12 is the games won.

0.8g=12
----- ---
0.8 0.8
g=15

g=12/0.8
g=15

They played a total of 15 games.

Check:
<span>0.8(15)
=12</span>

7 0

4 years ago