What are the domain and range of the logarithmic function f(x) = log7x?

The prices of commodities X,Y,Z are respectively x, y, z, rupees per unit. Mr. A purchases 4 units of Z and sells 3 units of X a

liubo4ka [24]

Answer:

$(x,y,z)=(1477, 1464, 1437)$

Step-by-step explanation:

Consider the selling of the units positive earning and the purchasing of the units negative earning.

Mr. A purchases 4 units of Z and sells 3 units of X and 5 units of Y
Mr.A earns Rs6000

So, the equation would be

$3x + 5y - 4z = 6000$

Mr. B purchases 3 units of Y and sells 2 units of X and 1 units of Z
Mr B neither lose nor gain meaning he has made 0₹

hence,

$2x - 3y + z = 0$

Mr. C purchases 1 units of X and sells 4 units of Y and 6 units of Z
Mr.C earns 13000₹

therefore,

$- x + 4y + 6z = 13000$

Thus our system of equations is

$\begin{cases}3x + 5y - 4z = 6000\\2x - 3y + z = 0\\ - x + 4y + 6z = 13000\end{cases}$

<u>Solving </u><u>the </u><u>system </u><u>of </u><u>equations</u><u>:</u>

we will consider elimination method to solve the system of equations. To do so ,separate the equation in two parts which yields:

$\begin{cases}3x + 5y - 4z = 6000\\2x - 3y + z = 0\end{cases}\\\begin{cases}2x - 3y + z = 0\\ - x + 4y + 6z = 13000\end{cases}$

Now solve the equation accordingly:

$\implies\begin{cases}11x-7y=6000\\-13x+22y=13000\end{cases}$

Solving the equation for x and y yields:

$\implies\begin{cases}x= \dfrac{223000}{151}\\\\y= \dfrac{221000}{151}\end{cases}$

plug in the value of x and y into 2x - 3y + z = 0 and simplify to get z. hence,

$\implies z= \dfrac{217000}{151}$

Therefore,the prices of commodities X,Y,Z are respectively approximately 1477, 1464, 1437

6 0

2 years ago

A dogs weighs 7 pounds and triples each year for two years. How much does the dog weigh?

Tanya [424]

Year 1: 7lbs x 3years= 21lbs
Year 2: 21lbs x 3years = 63lbs

5 0

3 years ago

Read 2 more answers

Adriana baked 42 cookies with 7 scoops of flour. With 8 scoops of flour, how many cookies

mylen [45]

Answer:

she can make 48 cookies.

4 0

3 years ago

Read 2 more answers

Stephen and Bridget win some money and share it in the ratio 1:3. Stephen gets £11. How

pentagon [3]

Answer:

£44

Step-by-step explanation:

We have been given the ratio 1 : 3 , where 1 is stephens value and 3 is bridgets value.

We have told that stephen gets £11.

The relationship between stephens 'value' of 1 and the amount of money that he actually gets (11) is x11.

Therefore we must also x11 to Bridgets value.

11 x 3 = £33

Now, we add the two answers to find how much they won in total.

£33 + £11 = £44

hope this helps :)

4 0

3 years ago

Read 2 more answers

For which values of k does the system of linear equations have zero, one, or an infinite number of solutions? [Note: not all thr

viktelen [127]

Answer:

The system has an infinite solution at k = 6, otherwise for any value of k, it has zero solution.

Step-by-step explanation:

Consider the system of linear equations:

$3x_{1} -x_{2}=2\;\;\;\;\;\;(1)\\ 9x_{1} -3x_{2}=k\;\;\;\;\;(2)$

The system of linear equations can have zero, one, or an infinite number of solutions:

simplify equation (1):

$x_{2}=3x_{1} -2$

substitute in equation (2), we get

$9x_{1} -3(3x_{1}-2)=k\\9x_{1} -9x_{1}+6=k\\0+6=k$

we cannot find the value of $x_{1}$ and $x_{2}$ .

so, there is no solution.

Multiply the equation (1) with 3 and put k is 6,

$3(3x_{1} -x_{2})=3\times2\\9x_{1} -3x_{2})=6$

it means both equations are overlapped. Then, the solution has infinite solutions.

Hence, the system has an infinite solutions at k is 6 otherwise for any value of k it has no solution.

4 0

3 years ago