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2 years ago

What is the correct ratio?

Mathematics

1 answer:

damaskus [11]2 years ago

5 0

Answer:

A: 9/40

Step-by-step explanation:

Hopefully this helps!

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Please help asap. Thank you! :)

Kruka [31]

When he cubed ,

Result is x³

On further squaring x³, he got = (x³)²

${x}^{6}$

<h3>Therefore, k = 6</h3>

7 0

2 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

Which triangle is a right triangle?

iren [92.7K]

Answer:

A right triangle is always 90 degrees.

Step-by-step explanation:

4 0

3 years ago

12.2z + 19.4 = -2.7z + 93.9

Digiron [165]

Answer:

z=5

Step-by-step explanation:

12.2z+ 19.4 = -2.7z + 93.9

14.9z=74.5

z=5

3 0

3 years ago

Read 2 more answers

Calculați aplicând distributivitatea înmulțirii fata de adunare și de scădere

solmaris [256]

Răspuns:

7/5;

2 întreg 5/12

Explicație pas cu pas:

6/7 × (2 numere întregi și 5 / 6-1 numere întregi și 1/5)

6/7 * (2 5/6 - 1 1/5)

6/7 * (17/6 - 6/5)

6/7 * (85 - 36) / 30

7/7 * 49/30

1/1 * 7/5

= 7/5

2.)

5/8 × 1 întreg și 2/3 + 11/5

5/8 * (1 2/3 + 11/5)

5/8 * (5/3 + 11/5)

5/8 * (25 + 33) / 15

5/8 * 58/15

1/8 * 58/3

= 58/24

= 2 întreg 10/24

= 2 întreg 5/12

4 0

2 years ago