Given g(x) = 3x + 3 , find g(k)

-5(x + 1) = -3(2x - 2)

kicyunya [14]

Answer:

x=11

Step-by-step explanation:

hope this helps

3 0

2 years ago

Read 2 more answers

HELP PLEASE! Can you please explain so I can understand how it was completed?

nlexa [21]

Answer:

(3 square root of 2 , 135°), (-3 square root of 2 , 315°)

Step-by-step explanation:

Hello!

We need to determine two pairs of polar coordinates for the point (3, -3) with 0°≤ θ < 360°.

We know that the polar coordinate system is a two-dimensional coordinate. The two dimensions are:

The radial coordinate which is often denoted by r.

The angular coordinate by θ.

So we need to find r and θ. So we know that:

$r=\sqrt{x^{2}+y^{2}}$ (1)

x = rcos(θ) (2)

x = rsin(θ) (3)

From the statement we know that (x, y) = (3, -3).

Using the equation (1) we find that:

$r=\sqrt{x^{2}+y^{2}}=\sqrt{3^{2}+(-3)^{2}} = 3\sqrt{2}$

Using the equations (2) and (3) we find that:

3 = rcos(θ)

-3 = rsin(θ)

Solving the system of equations:

θ= -45

Then:

r = 3\sqrt{2}[/tex]

θ= -45 or 315

Notice that there are two feasible angles, they both have a tangent of -1. The X will take the positive value, and Y the negative one.

So, the solution is:

(3 square root of 2 , 135°), (-3 square root of 2 , 315°)

4 0

2 years ago

Identify all number sets to which the square root of 25 belongs to.

const2013 [10]

Answer:

SOLUTION: Explain why the square root of 25 belongs to 4 subsets of the real numbers , but the square root of 5 only belongs to 1 . tell which subsets each belong to and why .

Step-by-step explanation:

The square root of 25 is 5, which

1. A rational number, since 5 is the ratio of the two integers 5 and 1.

2. An integer since 5 is an element of {...,-3,-2,-1,0,1,2,3,.}

3. A whole number, since 5 is an element of {0,1,2,3.}

4. A counting number, since 5 is an element of {1,2,3,}

The square root of 5 is only

1. An irrational number, since it is not the ratio of any two integers.

[It can only be approximated by

this nonrepeating infinite decimal, it goes on forever:

2.2360679774997896964091736687312762354406183596115257...]

4 0

2 years ago

the ordered pairs (0,-1),(1,0),(2,3),(3,8),(4,15) represent a function what is a rule that represents this function? Please help

yarga [219]

Answer:

The function rule is

$f: x\to \: {x}^{2} - 1$

Step-by-step explanation:

The given ordered pairs are (0,-1), (1,0),(2,3),(3,8),(4,15)

We can observe the following pattern.

$f(0) = {0}^{2} - 1 = - 1$

$f(1) = {1}^{2} - 1 = 0$

$f(2) = {2}^{2} - 1 = 3$

$f(3) = {3}^{2} - 1 = 8$

$f(4) = {4}^{2} - 1 = 15$

When we generalize this pattern, we obtain:

$f(x) = {x}^{2} - 1$

This is the function equation.

The function rule is

$f: x\to \: {x}^{2} - 1$

8 0

2 years ago

Find an equation of the line passing through the pair of points. Write the equation in the form Ax +By = C.

Alexxandr [17]

9514 1404 393

Answer:

5x -y = -37

Step-by-step explanation:

One way to find the coefficients A and B is to use the differences of the x- and y-coordinates:

A = Δy = y2 -y1 = 2 -(-3) = 5

B = -Δx = -(x2 -x1) = -(-7 -(-8)) = -1

Then the constant C can be found using either point.

5x -y = 5(-7) -2 = -37

The equation of the line is ...

5x -y = -37

_____

<em>Additional comment</em>

This approach comes from the fact that the slope of a line is the same everywhere.

$\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{\Delta y}{\Delta x}\\\\\Delta x(y-y_1)=\Delta y(x-x_1)\qquad\text{cross multiply}\\\\\Delta y(x-x_1)-\Delta x(y-y_1)=0\qquad\text{subtract y term}\\\\\Delta y(x) -\Delta x(y) = \Delta y(x_1)-\Delta x(y_1)\qquad\text{Ax+By=C form}$

The "standard form" requires that A be positive, so we chose point 1 and point 2 to make sure that was the case.

5 0

2 years ago