3.

<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B2%7D%5E%7Bx%20%2B%202%7D%20-%20%20%7B2%7D%5E%7B%20x%20%2B%203%7D%20%7D%7B%2

weeeeeb [17]

I suppose you just have to simplify this expression.

(2ˣ⁺² - 2ˣ⁺³) / (2ˣ⁺¹ - 2ˣ⁺²)

Divide through every term by the lowest power of 2, which would be x + 1 :

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

Recall that nª / nᵇ = nª⁻ᵇ, so that we have

… = (2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾ - 2⁽ˣ⁺³⁾ ⁻ ⁽ˣ⁺¹⁾) / (2⁽ˣ⁺¹⁾ ⁻ ⁽ˣ⁺¹⁾ - 2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾)

… = (2¹ - 2²) / (2⁰ - 2¹)

… = (2 - 4) / (1 - 2)

… = (-2) / (-1)

… = 2

Another way to get the same result: rewrite every term as a multiple of y = 2ˣ :

… = (2²×2ˣ - 2³×2ˣ) / (2×2ˣ - 2²×2ˣ)

… = (4×2ˣ - 8×2ˣ) / (2×2ˣ - 4×2ˣ)

… = (4y - 8y) / (2y - 4y)

… = (-4y) / (-2y)

… = 2

8 0

3 years ago

One photoshop charges $0.36 per print. Another photoshop charges $2.52 plus $0.08 per print. Juan finds that the cost of printin

Rufina [12.5K]

He would have to print 9

7 0

3 years ago

Read 2 more answers

Engineers and architects often use transformed shapes to design objects or structures. Analyze a building or structure around yo

Crank

Answer:

A two story home might use translation to have both floors identical and most homes have windows of the same size and shape so they might also use translation. Sometimes buildings use reflection to make rooms opposite each other the same.

Step-by-step explanation:

4 0

2 years ago

Prove that if r is any rational number, then 3r2 − 2r + 4 is rational. The following properties may be used in your proof. Prope

ziro4ka [17]

Given:

Expression is

$3r^2-2r+4$

To prove:

If r is any rational number, then $3r^2-2r+4$ is rational.

Step-by-step explanation:

Property 1: Every integer is a rational number. It is Theorem 4.3.1.

Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.

Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.

Let r be any rational number.

We have,

$3r^2-2r+4$

It can be written as

$3(r\times r)-2r+4$

Now,

3, -2 and 4 are rational numbers by property 1.

$r^2=r\times r$ is rational by Property 3.

$3r^2\text{ and }-2r$ are rational by Property 3.

$3r^2+(-2r)+4$ is rational by property 2.

So, $3r^2-2r+4$ is rational.

Hence proved.

6 0

2 years ago

In the equation y=ab^(x-h) +k how does the value of k affect the graph

Ainat [17]

Answer:

if k > 0 then the graph of the given equation will get shifted upward by k units.

if k< 0 then the graph of the given equation will get shifted downward by k units.

Step-by-step explanation:

We have been given the equation y=ab^(x-h) +k and we have to state that how the value of k affect the graph.

We know that if we add/subtract some constant in the function value then the translation of the parent graph occurs in the vertical direction.

In other words, the parent graph either get shifted upward or downward depends on the value of the constant.

Therefore, we have

if k > 0 then the graph of the given equation will get shifted upward by k units.

if k< 0 then the graph of the given equation will get shifted downward by k units.

3 0

3 years ago

Read 2 more answers