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3 years ago

Evaluate the expression when x = 9.x + 5(x + 2)

Mathematics

2 answers:

jasenka [17]3 years ago

8 0

Answer:

Step-by-step explanation:

x + 5(x + 2)

Distribute

x + 5x+10

Combine like terms

6x+10

Let x = 9

6(9) +10

54+10

prisoha [69]3 years ago

4 0

Answer:-10/13

Step-by-step explanation:

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Step-by-step explanation:

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2 years ago

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3 years ago

Which classification best describes the following system of equations?

wolverine [178]

The given system of equations is consistent and independent so, $\fbox{\begin\\\ \bf option (3)\\\end{minispace}}$ is correct.

Further explanation:

A system of equations is said to be a consistent system if the solution exists and if the solution does not exist then it is an inconsistent system.

If a consistent system has a unique solution then it is an independent system of equations but if the number of solutions is infinite then it is a dependent system of equations.

Label the given equations as shown below:

$\boxed{x-2y+4z=3}$ …… (1)

$\boxed{12x+5y-3z=36}$ …… (2)

$\boxed{9x-10y+5z=27}$ …… (3)

The augmented matrix for the above equations is, as follows:

$\left[\begin{array}{ccc}1&-2&4\\12&5&-3\\9&-10&5\end{array}\Biggm\vert\begin{array}{c}3\\26\\27\end{array}\right]$

Apply row transformation $R_{2}\rightarrow R_{2}-12R_{1}$ and $R_{3}\rightarrow R_{3}-9R_{1}$ as,

$\left[\begin{array}{ccc}1&-2&4\\0&29&-51\\0&8&-31\end{array}\Biggm\vert\begin{array}{c}3\\0\\0\end{array}\right]$

Now, apply row transformation $R_{2}\rightarrow R_{2}-4R_{3}$ and $R_{3}\rightarrow R_{3}-3R_{2}$ as,

$\left[\begin{array}{ccc}1&-2&4\\0&-3&73\\0&-1&188\end{array}\Biggm\vert\begin{array}{c}3\\0\\0\end{array}\right]$

Now, apply row transformations $R_{2}\rightarrow -R_{2}+2R_{3}$ and $R_{3}\rightarrow R_{3}+R_{2}$ as,

$\left[\begin{array}{ccc}1&-2&4\\0&1&303\\0&0&491\end{array}\Biggm\vert\begin{array}{c}3\\0\\0\end{array}\right]$

The equations obtained from the above augmented matrix are,

$\begin{aligned}x-2y+4z&=3\\y+303z&=0\\491z&=0\end{aligned}$

The first equation is simplified to obtain the value of z as,

$\begin{aligned}491z&=0\\z&=0\end{aligned}$

Substitute $0$ for $z$ in the equation $y+303z=0$ to obtain the value of $y$ as,

$\begin{aligned}y+(303\cdot0)&=0\\y&=0\end{aligned}$

Now, substitute $0$ for $z$ and $0$ for $y$ in the equation $x-2y+4z=3$ to obtain the value of $x$ as,

$\begin{aligned}x-(2\cdot0)+(4\cdot0)&=3\\x&=3\end{aligned}$

Therefore, the value of $x$ is $3$ , the value of $y$ is $0$ and the value of $z$ is $0$ and the system has a unique solution.

Thus, the given system of equations is consistent and independent.

Option (1)

Here, the first option is inconsistent and dependent.

There exists a solution of the given system of equations so it is consistent.

Therefore, option (1) is incorrect.

Option (2)

Here, the second option is consistent and dependent.

There exists a solution of the given system of equations so it is consistent.

Also, the solution is unique therefore the system of equations is independent.

Therefore, option (2) is incorrect.

Option (3)

Here, the third option is consistent and independent.

There exists a solution of the given system of equations so it is consistent.

Also, the solution is unique therefore the system of equations is independent.

Therefore, option (3) is correct.

Option (4)

Here, the fourth option is inconsistent and independent.

There exists a solution of the given system of equations so it is consistent.

Therefore, option (4) is incorrect.

Learn more:

1. A problem on circle brainly.com/question/9510228.

2. A problem on general equation of a circle brainly.com/question/1506955.

Answer details

Grade: High school

Subject: Mathematics

Chapter: System of linear equations

Keywords: Equations, unique solution, independent, dependent, consistent, inconsistent, infinite solutions, homogeneous equation, non- homogeneous equation, determinant.

5 0

3 years ago

Read 2 more answers

A speedboat's top speed is 3 times faster than a sailboat's top speed. If the sailboat's top speed is 20 knots, what is the spee

alexandr402 [8]

Answer: 60 knots

Step-by-step explanation: if its 3x as fast. You will take the 20 knots and multiply it by 3. Getting the answer 60.

7 0

3 years ago

Evaluate the expression when x = 9.x + 5(x + 2)​

Evaluate the expression when x = 9.x + 5(x + 2)