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lubasha [3.4K]
3 years ago
10

Convert the following fraction to a decimal.

Mathematics
1 answer:
Nookie1986 [14]3 years ago
6 0
I think it’s C but I could be wrong but I don’t think I am
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The height of a candle, in centimeters, can be modeled by the linear equation h = 28 - 2t, where t represents the hours that the
Ostrovityanka [42]

The slope is -2. In context to this problem, the candle will burn away 2cm of its length every hour.

5 0
3 years ago
Solve for XX. Assume XX is a 2×22×2 matrix and II denotes the 2×22×2 identity matrix. Do not use decimal numbers in your answer.
sveticcg [70]

The question is incomplete. The complete question is as follows:

Solve for X. Assume X is a 2x2 matrix and I denotes the 2x2 identity matrix. Do not use decimal numbers in your answer. If there are fractions, leave them unevaluated.

\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]· X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right] =<em>I</em>.

First, we have to identify the matrix <em>I. </em>As it was said, the matrix is the identiy matrix, which means

<em>I</em> = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

So, \left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]· X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right] =  \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

Isolating the X, we have

X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]= \left[\begin{array}{cc}2&8\\-6&-9\end{array}\right] -  \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

Resolving:

X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]= \left[\begin{array}{ccc}2-1&8-0\\-6-0&-9-1\end{array}\right]

X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]=\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]

Now, we have a problem similar to A.X=B. To solve it and because we don't divide matrices, we do X=A⁻¹·B. In this case,

X=\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]⁻¹·\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]

Now, a matrix with index -1 is called Inverse Matrix and is calculated as: A . A⁻¹ = I.

So,

\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]·\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

9a - 3b = 1

7a - 6b = 0

9c - 3d = 0

7c - 6d = 1

Resolving these equations, we have a=\frac{2}{11}; b=\frac{7}{33}; c=\frac{-1}{11} and d=\frac{-3}{11}. Substituting:

X= \left[\begin{array}{ccc}\frac{2}{11} &\frac{-1}{11} \\\frac{7}{33}&\frac{-3}{11}  \end{array}\right]·\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]

Multiplying the matrices, we have

X=\left[\begin{array}{ccc}\frac{8}{11} &\frac{26}{11} \\\frac{39}{11}&\frac{198}{11}  \end{array}\right]

6 0
3 years ago
The sum of 3 consecutive even integers is 18<br>​
larisa [96]

Answer:

4,6,8

Step-by-step explanation:

Let x = 1st even integer

x+2 =2nd even integer

x+4 =3nd even integer

x+ x+2 + x+4 = 18

Combine like terms

3x+6 = 18

Subtract 6 from each side

3x+6-6=18-6

3x= 12

Divide by 3

3x/3 =12/3

x = 4

x+2 = 6

x+4 = 8

5 0
3 years ago
Simplly the square root of 75z^18
notsponge [240]

Answer:5√(3)z^9

Step-by-step explanation:

Square root of 75z^18

√(75z^18)

√(75) x √(z^18)

√(25x3) x (z^18)^(1/2)

√(25) x √(3) x z^(18x1/2)

5 x √(3) x z^9

5√(3)z^9

8 0
3 years ago
4.07065 in words or written form?
MAVERICK [17]
Four and seven thousand sixty-five hundred thousandths, I believe
3 0
3 years ago
Read 2 more answers
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