The length of a rectangle is 9” greater than the width. The area is 36”2. Find the dimensions

Multiply on the right by the transpose of the matrix on the left side:

[tex]X\begin{bmatrix}1&-1&2\\3&0&1\end{bmatrix}=\begin{bmatrix}-5&-1&0\\5&-2&5\end{bmatrix}[/tex]

[tex]X\begin{bmatrix}1&-1&2\\3&0&1\end{bmatrix}\begin{bmatrix}1&-1&2\\3&0&1\end{bmatrix}^\top=\begin{bmatrix}-5&-1&0\\5&-2&5\end{bmatrix}\begin{bmatrix}1&-1&2\\3&0&1\end{bmatrix}^\top[/tex]

The transpose is just the same matrix with the entries reflected along the main diagonal:

[tex]\begin{bmatrix}1&-1&2\\3&0&1\end{bmatrix}^\top=\begin{bmatrix}1&3\\-1&0\\2&1\end{bmatrix}[/tex]

So

[tex]X\begin{bmatrix}1&-1&2\\3&0&1\end{bmatrix}\begin{bmatrix}1&3\\-1&0\\2&1\end{bmatrix}=\begin{bmatrix}-5&-1&0\\5&-2&5\end{bmatrix}\begin{bmatrix}1&3\\-1&0\\2&1\end{bmatrix}[/tex]

[tex]X\begin{bmatrix}6&5\\5&10\end{bmatrix}=\begin{bmatrix}-4&-15\\17&20\end{bmatrix}[/tex]

Now multiply on the right by the inverse of the matrix on the left side:

[tex]X\begin{bmatrix}6&5\\5&10\end{bmatrix}\begin{bmatrix}6&5\\5&10\end{bmatrix}^{-1}=\begin{bmatrix}-4&-15\\17&20\end{bmatrix}\begin{bmatrix}6&5\\5&10\end{bmatrix}^{-1}[/tex]

[tex]X=\begin{bmatrix}-4&-15\\17&20\end{bmatrix}\begin{bmatrix}6&5\\5&10\end{bmatrix}^{-1}[/tex]

The inverse is

[tex]\begin{bmatrix}6&5\\5&10\end{bmatrix}^{-1}=\frac1{60-25}\begin{bmatrix}10&-5\\-5&6\end{bmatrix}=\begin{bmatrix}2/7&-1/7\\-1/7&6/35\end{bmatrix}[/tex]

So

[tex]X=\begin{bmatrix}-4&-15\\17&20\end{bmatrix}\begin{bmatrix}2/7&-1/7\\-1/7&6/35\end{bmatrix}=\boxed{\begin{bmatrix}1&-2\\2&1\end{bmatrix}}[/tex]

Answer:

472 feet

Step-by-step explanation:

The 220 ft is the opposite leg.

The distance from the boat to the base of the lighthouse is the adjacent leg.

tan 25 = 220/x

x = 220/tan 25

x = 472

Answer 472 feet

Answer:

D. In a chemical change, a new substance forms.

Step-by-step explanation:

The chemical reaction produces a new substance with new and different physical and chemical properties.

(hope this helps :P)

Answer:

x < 5/4

Step-by-step explanation:

8x−2<8

Add 2 to each side

8x−2+2<8+1

8x<10

Divide each side by 8

8x/8 < 10/8

x < 10/8

Simplify

x < 5/4

Answer:

Lee earns 2x.

They both earn 3x.

Step-by-step explanation:

If mic earns x, and lee earns 2 times as much, it will be x * 2, or 2x. Then adding mic's salary, x, the number will result in 2x+x. This simplifies into 3x.

Answer: 1,800 pies in total

Step-by-step explanation:

A key detail missing is that there are 378 green tea pies.

Assuming the total number of pies is x.

65% of this is taro pies. This leaves 35% to be red bean pies and green tea pies.

If 40% of this remaining 35% are red bean pies, that means that 60% are green tea pies.

= 35% * 60%

= 21% of the total are green tea pies

There are 378 green tea pies and this is 21% of the total number of pies.

378 = 0.21 * x

x = 378 / 0.21

= 1,800 pies in total

Answer:The fourth function

Step-by-step explanation:

You can never have repeating x-values. You can have repeating y-values though. Whenever determining whether something is a function, just look at whether it has repeating x-values or not. If it does, it is not a function. If it doesn't, it is a function.

Answer:

176

Step-by-step explanation

1/4*320= 80

20%=1/5

1/5*320=64

64+80=144

320-144

Answer:

X is 160 degrees

Step-by-step explanation:

Angles on a straight line add up to 180 degrees.

Answer:

X=160° because straight line =180

180°-20

160°

Answer:

5-6 people needed fieoshshdudhsbsbz

Answer:

40

Step-by-step explanation:

Because if janice getd 20 and kayla also 40 gets Sweets among

Answer:

x² + 10x + 24

Step-by-step explanation:

Use foil to multiply them.

x ( x + 4 ) = x² + 4x

6 ( x + 4) = 6x + 24

Combine like terms: x² + 10x  + 24

Hope this helps :)

Answer:

What I'd do is pick one either decimal, percentage or fraction and convert the rest into that

Answer:

0.36 3.6% 6/17 is from least to greatest

Step-by-step explanation:

Answer:

A, B, D

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

20 + 60 ÷ 5 + (9-4)2

Use PEMDAS to solve this equation, so first solve what is in the parentheses

20 + 60 ÷ 5 + (5)2

Since there are no exponents, next solve the multiplication

20 + 60 ÷ 5 + 10

Next is division

20 + 12 + 10

Finally, addition

42

Answer:

the numbers are 213 and 497

Step-by-step explanation:

First, add the digits of the ratio: 3 + 7 = 10

Then, divide the sums: 710/10 = 71

What this does is find the value of each 'unit' - we don't know what 3 is, or 7, but we know that 1 = 71

Since 1 x 3 = 3 and 1 x 7 = 7, by multiplying 71 with 3 and 7 we can find the numbers:

71 x 3 = 213

71 x 7 = 497

u can check this by adding them together: 213 + 497 = 710

hope this helps!

Answer:

Step-by-step explanation:

There are six sides, in this case they are all equal square faces.

A=6s^2, s, side length is 5.5 so

A=6(5.5)^2

A=6(30.25)

A=181.5 cm^2

Step-by-step explanation:

-26=3v+1

-1 on both sides

-27=3v

divide by 3 both sides

-9=v

answer 143.00 Step-by-step explanation:

Answer:

six and twenty one hundredths

Answer:

6 Students

Step-by-step explanation:

10% of 60 is 6.