1. -6x + 3y = 6 -4x + 2y = -10 Solve by substitution method

HELP ASAP!! please show work!!! what is the value of x in the matrix equation below?

son4ous [18]

Answer:

$x=2$

Step-by-step explanation:

The given matrix equation is ;

$\frac{3}{2}\left[\begin{array}{cc}x&6\\8&4\end{array}\right] +y \left[\begin{array}{cc}1&4\\3&2\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right]$

We multiply the scalars to get;

$\left[\begin{array}{cc}\frac{3}{2}x&9\\12&6\end{array}\right] +\left[\begin{array}{cc}y&4y\\3y&2y\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right]$

We simplify to get;

$\left[\begin{array}{cc}\frac{3}{2}x+y&9+4y\\12+3y&6+2y\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right]$

By the equality property of matrices, we can write the following equations;

$\frac{3}{2}x+y=z...(1)$

$6+2y=2$

$2y=2-6$

$2y=-4$

$y=-2$

Also;

$12+3y=6z$

$\Rightarrow 12+3(-2)=6z$

$\Rightarrow 12-6=6z$

$\Rightarrow 6=6z$

$\Rightarrow z=1$

We substitute these values into equation (1) to find x.

$\frac{3}{2}x-2=1$

$\frac{3}{2}x=1+2$

$\frac{3}{2}x=3$

$\frac{1}{2}x=1$

$x=2$

6 0

3 years ago

Find the domain and range

atroni [7]

Answer:To find the domain and range, we simply solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain. To calculate the range of the function, we simply express x as x=g(y) and then find the domain of g(y).

Step-by-step explanation:sorry if i'm wrong

6 0

3 years ago

Use the drawing tool(s) to form the correct answer on the provided graph. The function f(x) is shown on the provided graph. Grap

MariettaO [177]

Answer:

$f(x)=x+6 \\$

Step-by-step explanation:

The transformation is a translation 6 units up.

$f(x)=x+6 \\$

We can use the parent function f(x)=x, which is a linear function to graph this function.

Then just translate the function 6 units up.

6 0

4 years ago

A ticket service is selling tickets to a concert. An order of 4 tickets has a price of $63 and an order of 6 tickets has a price

Valentin [98]

Answer:

x = Number of tickets for the concert

y = Price of the order of x tickets

y = 14.5x + 5

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Order of 4 tickets has a price of $63

Order of 6 tickets has a price of $92

2. Write an equation to find the price of any amount of tickets.

Let's find out the price of a ticket to understand if there's a service fee and how much is it, this way:

Price of a ticket = (Order of 6 tickets - Order of 4 tickets)/2

Price of a ticket = (92 - 63)/2

Price of a ticket = 29/2 = 14.50

If a ticket costs $ 14.50, 4 tickets will cost $ 58 and 6 tickets will cost $ 87, therefore there is a service or delivery fee of $ 5.

Order of 4 tickets - Price of 4 tickets = Service or delivery fee

Replacing, we have:

63 - 58 = 5

Order of 6 tickets - Price of 6 tickets = Service or delivery fee

Replacing, we have:

92 - 87 = 5

Now, we can write the equation to find the price of an order of any amount of tickets, this way:

x = Number of tickets for the concert

y = Price of the order of x tickets

y = 14.5x + 5

6 0

3 years ago

If the rate , in gallons per minute , continues , approximately how many gallons of water from the hose in 45 minutes ?

navik [9.2K]

Every 5 minutes, you gain 4 gallons. 45/5 = 9, 9x4 equals 36, there would be 36 gallons of water in 45 minutes

3 0

3 years ago