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3 years ago

Find (f-g)(x). What is the domain of f/g f(x)=2x-5 g(x)=2-x

1 answer:

6 0

$f(x)=2x-5 , \ \ \ \ g(x)=2-x \\\\(f-g)(x)=f(x)-g(x) = 2x-5 -(2-x)=2x-5-2+x = 3x+5 \\\\\\
 domain : \frac{f}{g}=\frac{2x-5}{2-x}\\\\2-x\neq 0 \\ \\x\neq 2 \\ \\D=R\setminus \left \{ 2 \right \}$

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Jada has some pennies and dimes. The ratio of Jada's pennies to dimes is 2 to 3. From the information given, can you determine h

Anuta_ua [19.1K]

Answer:

No, we can't determine how many coins Jada has.

She will have 22 pennies and 33 dimes.

4 0

3 years ago

Graph these equations: x+2y=6, y=-1/2x+4 How many solutions does the system of equations have?

inysia [295]

Answer:

The system has no solution

Step-by-step explanation:

we have

$x+2y=6$

Isolate the variable y

$2y=-x+6$

Divide by 2 both sides

$y=-\frac{x}{2}+3$ ---> equation A

$y=-\frac{x}{2}+4$ ---> equation B

Compare the equations

Equation A and equation B have the same slope and different y-intercept

Remember that

If two lines have the same slope, then the lines are parallel

The solution of the system is the intersection point both graphs

In this problem, the lines don't intersect, therefore, the system has no solution

using a graphing tool

The graph in the attached figure

7 0

3 years ago

Look at the system of equations below.

Annette [7]

Answer:

Substitution and graphing are less efficient methods than elimination for this system as there is extra amount of steps we have to take to solve the same system of equations - hence time consuming and a margin or error may happen. Therefore, elimination is the suitable method for solving this system.

Step-by-step explanation:

Let us consider the system of equation below.

$4x-5y=3$

$3x+5y=13$

Elimination method sounds the most appropriate option to solve the given system of equations as we can easily sort out an equation in one variable x in minimal steps by just adding the both equations as the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation, and we can determine an equation in one variable x.

Adding both equations will eliminate the y-variable and we can easily sort out the value of x from the resulting equation.

As the given system of equation

$4x-5y=3$ $......[1]$

$3x+5y=13$ $......[2]$

Adding Equation 1 and Equation 2

$4x-5y+3x+5y=3+13$

$7x=16$

$x=$ $\frac{16}{7}$

Putting $x=$ $\frac{16}{7}$ in Equation [1]

$4x-5y=3$ $......[1]$

$y=$ $\frac{43}{35}$

Although substitution or graphing methods can also be used to bring the solution of the given system of equations, but using substitution or graphing method can be sometimes cumbersome or time-consuming as it would have to take some additional steps to solve the system.

For example, if we would have to use the substitution methods to solve the given system of equations, first we would have to solve one of the equations by choosing one of the equation for one of the chosen variables and then putting this back into the other equation, and solve for the other, and then back-solving for the first variable.

As the given system of equation

$4x-5y=3$ $......[1]$

$3x+5y=13$ $......[2]$

Solving the equation 2 for x variable

$3x=13-5y$

$x=\frac{13-5y}{3}$

Plugging $x=\frac{13-5y}{3}$ in equation [1]

$4(\frac{13-5y}{3}) -5y=3$

$y = \frac{43}{35}$

Putting $y = \frac{43}{35}$ in Equation 2

$3x+5y=13$ $......[2]$

$x = \frac{16}{7}$

So, you can figure out, we have to make additional steps when we use substitution method to solve this system of equations.

Similarly, using graphing method, it would take a certain time before we identify the solution of the system.

Hence, from all the discussion and analysis we did, we can safely say that substitution and graphing are less efficient methods than elimination for this system as there is extra amount of steps we have to take to solve the same system of equations - hence time consuming and a margin or error may happen.

Therefore, we agree with the student argument that Elimination is the best method for solving this system because the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation.

Keywords: substitution method, system of equations, elimination method

Lear more about elimination method of solving the system of equation from brainly.com/question/12938655

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4 0

3 years ago

If anyone can i help me

natulia [17]

Answer:

x=9.4

x=9.43

Step-by-step explanation:

I used the Pythagorean theorem.

Have a nice day!

and can I maybe have brainliest? Thanks!

3 0

2 years ago

Read 2 more answers

Try to prove the hypothesis from part B that the sum of a rational and an irrational number is an irrational number.

Maurinko [17]

The next step of your proof is to subtract (a/b) from both sides.

Then you get, x = (m/n) - (a/b)

Since rationals are closed over addition, (m/n) + (-a/b) is a rational number.

Therefore, x (an irrational number) = a rational number <em>This is a false statement which is a contradiction. So, the assumption was incorrect.</em>

Thus, the sum of a rational and irrational number is an irrational number. QED

8 0

3 years ago