All categories

1 year ago

What is the value of the shown expression? 33 x 3-2 A) -54 B) -243 C) 243 D) 3

Mathematics

1 answer:

alex41 [277]1 year ago

4 0

We have the following general rule for exponents:

$a^n\cdot a^m=a^{n+m}$

then, in this case we have the following:

$3^3\cdot3^{-2}=3^{3+(-2)}=3^{3-2}=3^1=3$

therefore, the answer is 3

You might be interested in

Question 5 (5 points)

Tpy6a [65]

Answer:

The solution of the system of equations is, (1,-1,2)

Step-by-step explanation:

Given system equation;

x + 5y - 3z = -10

-5x + 6y – 5z = -21

-x + 8y - 8z = -25

Matrix form is written as;

$\left[\begin{array}{ccc}1&5&-3\\-5&6&-5\\-1&8&-8\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}-10\\-21\\-25\end{array}\right] \\\\\\det. = 1\left[\begin{array}{cc}\\6&-5\\8&-8\end{array}\right] -5\left[\begin{array}{cc}\\-5&-5\\-1&-8\end{array}\right] -3\left[\begin{array}{cc}\\-5&6\\-1&8\end{array}\right] \\\\\\det. = 1(-8) -5(35)-3(-34)= -8 - 175+ 102 = -81$

Cofactor;

$First \ row \left[\begin{array}{cc}+\\ 6&-5\\\ 8&-8\end{array}\right \left\begin{array}{cc}-\\ -5&-5\\-1&-8\end{array}\right \left\begin{array}{cc}+\\-5&6\\-1&8\end{array}\right] = [-8 \ \ -35 \ \ -34]\\\\\\\ Second \ row \left[\begin{array}{cc}-\\ 5&-3\\\ 8&-8\end{array}\right \left\begin{array}{cc}+\\ 1&-3\\-1&-8\end{array}\right \left\begin{array}{cc}-\\1&5\\-1&8\end{array}\right] = [16\ \ -11 \ \ -13]\\\\\\$

$Third \ row \left[\begin{array}{cc}+\\ 5&-3\\\ 6&-5\end{array}\right \left\begin{array}{cc}-\\ 1&-3\\-5&-5\end{array}\right \left\begin{array}{cc}+\\1&5\\-5&6\end{array}\right]= [-7 \ \ 20\ \ 31]$

$Cofactor =$ $\left[\begin{array}{ccc}-8&-35&-34\\16&-11&-13\\-7&20&31\end{array}\right]$

$inverse \ matrix =-\frac{1}{81} \left[\begin{array}{ccc}-8&16&-7\\-35&-11&20\\-34&-13&31\end{array}\right] \\\\\\$

Solution of the matrix:

$\left[\begin{array}{c}x\\y\\z\end{array}\right] = -\frac{1}{81} \left[\begin{array}{ccc}-8&16&-7\\-35&-11&20\\-34&-13&31\end{array}\right] X \left[\begin{array}{c}-10\\-21\\-25\end{array}\right] = \left[\begin{array}{c}\frac{-8*-10 }{-81 } +\frac{16*-21 }{-81 } + \frac{-7*-25 }{-81 }\\\\\frac{-35*-10 }{-81 } +\frac{-11*-21 }{-81 }+ \frac{20*-25 }{-81 }\\\\\frac{-34*-10 }{-81 }+ \frac{-13*-21 }{-81 }+ \frac{31*-25 }{-81 }\end{array}\right] \\\\\$

$\left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}\frac{-81}{-81} \\\\\frac{81}{-81} \\\\\frac{-162}{-81} \end{array}\right] = \left[\begin{array}{c}1\\-1\\2\end{array}\right]$

Therefore, the correct option is (1,-1,2)

5 0

3 years ago

Alex is thinking of a number. He multiplies it by 1,000 then divided it by 10.

sergeinik [125]

Solutions

1) Lets use n as alex's number
⇒ n x 1000
⇒ n ÷ 10
⇒ = 475

To solve the problem do the opposite steps

475 ÷ 1000 = n
n = 0.475

0.475 x 10 = n
n = 4.75

CHECK YOUR WORK

4.75 x 1000 = 4750
4750 ÷ 10 = 475

The answer is correct

⇒ The answer Alex is thinking of is 4.75

6 0

3 years ago

Read 2 more answers

Will the product of3/7 and 3 be greater or less than 3

Marianna [84]

Answer:

Step-by-step explanation:

333212121212121

5 0

4 years ago

Write 750 g as a fraction of 5 kg. Give your answer in its simplest form.

Valentin [98]

Answer:

3/20 is the answer.......

8 0

2 years ago

There are 4 gear wheels on fixed axles next to each other, as shown. The first one has 30 gears, the second one 15, the third on

rjkz [21]

Answer:

The last gearwheel would make 3 revolutions.

Step-by-step explanation:

The measure of the revolution of a gear per minute is referred to as the speed ratio. The speed ratio is the ratio of the speed of the driver gear to that of the driven gear, or ratio of the number of teeth of the driven gear to the number of teeth of the driver gear.

In the given question, the second and third gears are idlers. while the first is the driver and the fourth the driven.

The revolution of the last gearwheel can be determined by;

Speed ratio = $\frac{number of teeth of the driven gear}{number of teeth of the driver gear}$

= $\frac{10}{30}$

= $\frac{1}{3}$

Speed ratio = 1 : 3

The last gear would make 3 revolutions.

7 0

3 years ago