Which function shows the combined cost in dollars, y, for three shipments with x number of chargers and tablets?

Does anyone know how to do this?? Help please!!!!

Doss [256]

Answer:

When we have a rational function like:

$r(x) = \frac{x + 1}{x^2 + 3}$

The domain will be the set of all real numbers, such that the denominator is different than zero.

So the first step is to find the values of x such that the denominator (x^2 + 3) is equal to zero.

Then we need to solve:

x^2 + 3 = 0

x^2 = -3

x = √(-3)

This is the square root of a negative number, then this is a complex number.

This means that there is no real number such that x^2 + 3 is equal to zero, then if x can only be a real number, we will never have the denominator equal to zero, so the domain will be the set of all real numbers.

D: x ∈ R.

b) we want to find two different numbers x such that:

r(x) = 1/4

Then we need to solve:

$\frac{1}{4} = \frac{x + 1}{x^2 + 3}$

We can multiply both sides by (x^2 + 3)

$\frac{1}{4}*(x^2 + 3) = \frac{x + 1}{x^2 + 3}*(x^2 + 3)$

$\frac{x^2 + 3}{4} = x + 1$

Now we can multiply both sides by 4:

$\frac{x^2 + 3}{4}*4 = (x + 1)*4$

$x^2 + 3 = 4*x + 4$

Now we only need to solve the quadratic equation:

x^2 + 3 - 4*x - 4 = 0

x^2 - 4*x - 1 = 0

We can use the Bhaskara's formula to solve this, remember that for an equation like:

a*x^2 + b*x + c = 0

the solutions are:

$x = \frac{-b +- \sqrt{b^2 - 4*a*c} }{2*a}$

here we have:

a = 1

b = -4

c = -1

Then in this case the solutions are:

$x = \frac{-(-4) +- \sqrt{(-4)^2 - 4*1*(-1)} }{2*(1)} = \frac{4 +- 4.47}{2}$

x = (4 + 4.47)/2 = 4.235

x = (4 - 4.47)/2 = -0.235

5 0

2 years ago

Given the preimage and image,find the dilation scale factor.

Oliga [24]

Answer:

The dilation scale factor is $\frac{1}{2}$ .

Step-by-step explanation:

The image is the dilated form of its preimage if and only if the following conditions are observed:

1) $K' = \alpha_{1} \cdot K$

2) $T' = \alpha_{2} \cdot T$

3) $P' = \alpha_{3} \cdot P$

4) $J' = \alpha_{4} \cdot J$

5) $\alpha_{1} = \alpha_{2} = \alpha_{3} = \alpha_{4}$

If we know that $K = (2, 0)$ , $K' = (1, 0)$ , $T = (3, 0)$ , $T' = (1.5,0)$ , $P = (1, 5)$ , $P' = (0.5, 2.5)$ , $J = (0, 3)$ and $J' = (0, 1.5)$ , then the coefficients are, respectively:

$\alpha_{1} = \frac{1}{2}$ , $\alpha_{2} = \frac{1}{2}$ , $\alpha_{3} = \frac{1}{2}$ , $\alpha_{4} = \frac{1}{2}$

As $\alpha_{1} = \alpha_{2} = \alpha_{3} = \alpha_{4}$ , we conclude that the dilation scale factor applied in the preimage is equal to $\frac{1}{2}$ .

7 0

2 years ago

Solve for w. 7(-2w + 3) = 1 - 4w <br>what is the value of w?

blondinia [14]

Answer:

w=2

Step-by-step explanation:

-14w + 21 = 1 - 4w

-10w + 21 = 1

-10w = -20

w = -20/-10

w=2

5 0

2 years ago

Read 2 more answers

Arrow 1 is rotated by 45° , 90° , 180° respectively as shown below , Based on this we can say – “Any object when rotated by ____

Free_Kalibri [48]

Any object when rotated by 360°, will look exactly the same

7 0

2 years ago

Describe the rotation of J

Serga [27]

Answer:

The coordinates of J' when rotating by 90° counterclockwise will be: J'(3, 1)

The coordinates of J' when rotating by 90° clockwise will be: J'(-3, -1)

Step-by-step explanation:

Square JKLM with vertices

J(1, -3)

K(5, 0)

L(8, -4)

M(4, -7)

We have to determine the answer for the image J' of the point (1, -3) when we rotate the point by 90° counterclockwise, we need to switch x and y, make y negative.

In other words, the rule to rotate a point by 90° counterclockwise.

P(x, y) → P'(-y, x)

As we are given that J(1, -3), so the coordinates of J' will be:

J(1, -3) → J'(3, 1)

Therefore, the coordinates of J' when rotating by 90° counterclockwise will be: J'(3, 1).

When the point is rotated by 90° clockwise, we need to switch x and y, make x negative.

In other words, the rule to rotate a point by 90° clockwise.

P(x, y) → P'(y, -x)

As we are given that J(1, -3), so the coordinates of J' will be:

J(1, -3) → J'(-3, -1)

Therefore, the coordinates of J' when rotating by 90° clockwise will be: J'(-3, -1)

3 0

2 years ago