The graph of f(x) is obtained by translating the graph g(x)=|x| five units down.

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

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4 0

3 years ago

In a survey, of the voters support a particular referendum. If 40 voters are chosen at random, find the mean and variance for th

Katyanochek1 [597]

This question is incomplete, the complete question is;

In a survey, 55% of the voters support a particular referendum. If 40 voters are chosen at random,

find the mean and variance for the number of voters who support the referendum.

Answer:

a) The Mean is 22

b) Variance is 9.9

Step-by-step explanation:

Given that;

55% of the voters support a particular referendum p = 0.55

q = 1 - p = 1 - 0.55 = 0.45

sample size n = 40

a)

Mean = sample size n × p

Mean = 40 × 0.55

Mean = 22

Therefore the Mean is 22

b)

Variance = n × p × q

so we substitute

Variance = 40 × 0.55 × 0.45

Variance = 9.9

Therefore the Variance is 9.9

3 0

3 years ago

A pentagon has 5 equivalent sides, if each side is represented by the expression 2k+3, what is the perimeter

Musya8 [376]

Answer:

hy5ju5ju5uj5huj5h5

Step-by-step explanation:

3 0

3 years ago

Students in a science class are divided into 6 equal groups with at least 4 students in each group for a project. write and solv

S_A_V [24]

There are a total of 6 groups.

And each group contains at least 4 students.

So the minimum number of students is:

minimum = 6 * 4 = 24 students

Let us say that x represents the number of students, hence:

x ≥ 24

5 0

3 years ago

BRAINLIEST ANSWER NOW!!! MEDAL, STARS, THANK YOU'S! PLEASE HELP ME ASAP! AND IF YOU CAN, EXPLAIN YOUR ANSWER! THANKS SO MUCH IN

bazaltina [42]

The problem says that Donovan is using similar rectangles, so you can calculate the length of the second rectangle, by using the similarity concept.

We have that the first rectangle is 2 inches wide and 6 inches long, and the second rectangle must has 5 inches wide. Then:

2/5=6/L (L: the length of the second rectangle).
 2L=6x5
2L=30
L=30/2
L=15 inches

How long must the second rectangle be?

The answer is: The second rectangle must be 15 inches long.

7 0

3 years ago