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3 years ago

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If the points at (-4, 3) and (2, 3) are reflected over the x-axis to create two new points, what shape can be formed by the four

points? Select the most precise description of the shape.

1 answer:

Svetllana [295]3 years ago

3 0

Answer:

Step-by-step explanation:

Let $(a,b)\in \mathbb{R}^{2}$ , a reflection over the x-axis consists in the following operation:

$(a,b) \rightarrow (a,-b)$

If we know that $X = (-4,3)$ and $Y = (2, 3)$ , then the points translated over the x-axis are $X' = (-4, -3)$ and $Y' = (2,-3)$ , respectively. The most precise description of the shape is a rectangle for the following facts:

1) $XX' = YY' = 8$ and $XY = X'Y' = 6$ .

2) $X$ and $X'$ have the same x-component.

3) $Y$ and $Y'$ have the same x-component.

4) $X$ and $Y$ have the same y-component.

5) $X'$ and $Y'$ have the same y-component.

A representation of the shape is included below as attachment.

You might be interested in

A cylindrical container has a radius of 3 centimeters and a height of 12 centimeters. The container is filled with water up to t

evablogger [386]

Answer:

volume of empty space = 141.3 cm³

Step-by-step explanation:

volume of empty space = volume of the cylinder - volume of water

First, we need to calculate the volume of the container

volume of a cylinder = πr²h

where r = radius of the container and h is the height of the container

r = 3cm and h = 12 cm π is a constant which is ≈ 3.14

volume of a cylinder = πr²h

=3.14 × 3²×12

=3.14×9×12

=339.12 cm³

We will proceed to find the volume of water

since liquid will take the shape of its container,

then volume of water = πr²h

r is the radius of the container and h is the height of the water

r = 3cm and h = 7cm

volume of water = πr²h

= 3.14 ×3²×7

=3.14×9×7

=197.82 cm³

volume of empty space = volume of the cylinder - volume of water

=339.12 cm³ - 197.82 cm³

= 141.3 cm³

OR

WE CAN SOLVE DIRECTLY

height of empty space = height of container - height of water

= 12 - 7

=5 cm

volume of empty space = πr²h

=3.14×3²×5

=3.14×9×5

=141.3 cm³

volume of empty space = 141.3 cm³

4 0

3 years ago

Joanie runs the concession stand for the school's baseball games. At each game, the best selling items are pretzels and hot dogs

Elenna [48]

X is pretzels and y is hot dogs
3x + 2y=195
x +15 =y

3x + 2(x+15)=195
5x=165
x=33
D

4 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

#learnwithBrainly

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3 years ago

A survey asked the question, “Do you think a vaccination should be mandatory to enter shopping areas?!” to a random sample of 10

Sergio [31]

Answer: no it shouldn’t

Step-by-step explanation:

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2 years ago

the percent of sales tax is 10%. what is the actual price of a pair of basketball shoes that cost $98?

larisa [96]

Answer:

(98/100)*110 = $107.8

Step-by-step explanation:

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3 years ago