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2 years ago

Graph each function. state the domain and range f(x)= {-x-2if x>0

Mathematics

1 answer:

nevsk [136]2 years ago

5 0

9514 1404 393

Answer:

Step-by-step explanation:

For values of x less than zero, the graph of the function is a graph of the line

y = -x

Because the function is defined by this expression at x=0, there will be a solid dot at the end of the line there, at (0, 0).

For values of x greater than 0, the graph of the function is a graph of the line

y = -x -2

This line has the same -1 slope as before, but has a y-intercept of -2. The function is not actually defined as (0, -2), so there is an open circle at the end of the line there.

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Solve. The answer must be a fraction. Solve by substituting.

maw [93]

Answer: x = -14/5

Step-by-step explanation: We shall begin by expanding the brackets for both sides of the equation

-2/3 (x + 2) = 1/6 (x + 6)

(-2x/3) -4/3 = (x/6) + 1

By collecting like terms we now have

(-2x/3) - (x/6) = 1 + 4/3

(-4x - x)/6 = 7/3

-5x/6 = 7/3

By cross multiplication we now have

-5x (3) = 7 (6)

-15x = 42

x = -(42/15) {simplify further by dividing the RHS by 3}

x = -14/5

Therefore x equals, minus fourteen over five (-14/5)

4 0

3 years ago

The value of x is negative. What must be true about 10 - x? Explain.

pashok25 [27]

What must be true is the expression will actually be adding 10 + (+ x), because of the two marks you have to make when subtracting by a negative.

The subtraction sign is also the negative sign. So in this case, the expression is also saying -x, which means there is two negative signs.

A double negative is a positive, so in this case the x will be turned to a positive integer.

If this is still too confusing, she can plug in a number to replace x. Let’s try it with -2:

Ex. 10 - (-2)= 12.

The two negative signs turn into one positive sign, AKA an addition sign. So, the above expression can be simplified as 10 + 2, or 12.

3 0

3 years ago

Please answer! These are due tmr and it's 12:53 rn!

SashulF [63]

1.D
2.D
3.C
4.C
5.D
6.2160
7.288

You really shouldn't be waiting untill 1 AM to do your homework!

5 0

3 years ago

The combined area of two squares is 80 square centimeters. Each side of one square is twice as long as a side of the other squar

olganol [36]

Answer:

The length of each side of the larger square is 8 centimeter.

Step-by-step explanation:

Given:

The combined area of two squares is 80 square centimeters. Each side of one square is twice as long as a side of the other square.

Now, to find the length of each side of the larger square.

Let $s$ be the length of the smaller square.

So, the length of the larger square = $2s.$

Now, we find the areas of the square by putting formula:

The area of smaller square = length² $=s^2.$

The area of larger square = (length)² $=(2s)^2=4s^2.$

As, given:

The combined area of two squares is 80 square centimeters.

According to question:

$s^2+4s^2=80\\5s^2=80$

So, dividing both sides by 5 we get:

$s^2=16$

Using square root on both sides we get:

$s=4\ centimeter.$

And, to get the length of each side of the larger square we substitute the value of $s$ :

$2s=2\times 4=8\ centimeter.$

The length of larger square = 8 centimeter

Therefore, the length of each side of the larger square is 8 centimeter.

8 0

3 years ago

A quadrilateral PQRS is translated to the left by 4 units to obtain another quadrilateral P᾿Q᾿R᾿S᾿

IrinaVladis [17]

Answer:

the length of PQ is equal to the length of P'Q'

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.

Translation is the movement of a point either up, down, right or left. Translation is a type of rigid transformation. Rigid transformation is a transformation in which both the image and pre-image have the same shape and size. types of rigid transformation are rotation, reflection and translation.

Quadrilateral PQRS is translated to the left by 4 units to obtain another quadrilateral P᾿Q᾿R᾿S᾿. Since translation is a rigid transformation, the shape and size of PQRS is the same as that of P'Q'R'S. Hence the length of PQ is equal to the length of P'Q'.

8 0

3 years ago