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3 years ago

Which definitions or properties would you use to simplify the expression

1 answer:

N76 [4]3 years ago

7 0

Exponent multiplication and addition will simplify this expression.
Exponent Addition: a^b * a^c = a^(b + c)
Exponent Multiplication: (a^ d) ^ e = a ^ (d * e)

Multiplication of 4^8 * 4^(-4) is the same as adding exponents together:
4^(8 - 4)

Which makes the expression simplify to (4^4). This expression is now to another exponent which is equivalent to multiplying exponents together:

(4^4)^-2 = 4^ (4 * -2) = 4 ^ -8

The expression has been reduced to its simplest form.

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Solve the simultaneous equation 3x²-xy=0, 2y-5x=1

White raven [17]

Answer:

exact Form:(0,),(1,3)

Equation Form: ( 0, )

x=1 y=3

Step-by-step explanation:

6 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· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ =I.

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

I = $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

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

George and Maria decided to create a garden in their backyard. George Works on the garden every third day and Maria works on the

mario62 [17]

The LCM of 3 and 4 is 12

8 0

3 years ago

Read 2 more answers

Solve the equation by completing the square. -9n^2+79+=-18n

poizon [28]

Hello,
-9n²+79=-18n
==>9n²-18n-79=0
==>9(n²-2n+1-1)-79=0
==>9(n-1)²-88=0
==>[3(n-1)-2√22][3(n-1)+2√22]=0
==>3(n-1)=2√22 or 3(n-1)=-2√22
==>n-1=2/3*√22 or n-1=-2/3*√22
==>n=1+2/3*√22 or n=1-2/3*√22

6 0

3 years ago

A bag contains counters that are red, black , or green . 1/3 of the counters are red 1/6 of the counters are black There are 15

Nadya [2.5K]

Answer:

There are 5 black counters in the bag.

Step-by-step explanation:

15 green counters in the bag

The proportion of green counters is given by:

$p = 1 - (\frac{1}{3} + \frac{1}{6}) = 1 - (\frac{2}{6}+\frac{1}{6}) = 1 - \frac{3}{6} = 1 - \frac{1}{2} = \frac{2}{2} - \frac{1}{2} = \frac{1}{2}$