Which explains how you round 212.809 to the nearest hundredth?

I know you want to answer this question.

Alik [6]

Answer:

D. x = 3

Step-by-step explanation:

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

First, convert $4^{x-3}$ to base 2:

$4^{x-3}$ = $(2^{2})^{x-3}$

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

Next, convert $\frac{1}{2} ^{x-4}$ to base 2:

$\frac{1}{2} ^{x-4}$ = $(2^{-1})^{x-4}$

$(2^{-1})^{x-4}$ - 3 = $(2^{2})^{x-3}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$(2^{-1})^{x-4}$ = $2^{-1*(x-4)}$

$2^{-1*(x-4)}$ - 3 = $(2^{2})^{x-3}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$(2^{2})^{x-3}$ = $2^{2(x-3)}$

$2^{-1*(x-4)}$ - 3 = $2^{2(x-3)}$ - 2

Apply exponent rule: $a^{b+c}$ = $a^{b}$ $a^{c}$ :

$2^{-1(x-4)}$ = $2^{-1x}$ * $2^{4}$ , $2^{2(x-3)}$ = $2^{2x}$ * $2^{-6}$

$2^{-1 * x}$ * $2^{4}$ - 3 = $2^{2x}$ * $2^{-6}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

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

$(2^{x})^{-1}$ * $2^{4}$ - 3 = $(2^{x})^{2}$ * $2^{-6}$ - 2

Rewrite the equation with $2^{x} = u$ :

$(u)^{-1}$ * $2^{4}$ - 3 = $(u)^{2}$ * $2^{-6}$ - 2

Solve $u^{-1}$ * $2^{4}$ - 3 = $u^{2}$ * $2^{-6}$ - 2:

$u^{-1}$ * $2^{4}$ - 3 = $u^{2}$ * $2^{-6}$ - 2

Refine:

$\frac{16}{u}$ - 3 = $\frac{1}{64}$ $u^{2}$ - 2

Add 3 to both sides:

$\frac{16}{u}$ - 3 + 3 = $\frac{1}{64}$ $u^{2}$ - 2 + 3

Simplify:

$\frac{16}{u}$ = $\frac{1}{64}$ $u^{2}$ + 1

Multiply by the Least Common Multiplier (64u):

$\frac{16}{u}$ * 64u = $\frac{1}{64}$ $u^{2}$ + 1 * 64u

Simplify:

$\frac{16}{u}$ * 64u = $\frac{1}{64}$ $u^{2}$ + 1 * 64u

Simplify $\frac{16}{u}$ * 64u:

1024

Simplify $\frac{1}{64}$ $u^{2}$ * 64u:

$u^{3}$

Substitute:

1024 = $u^{3}$ + 64u

Solve for u:

u = 8

Substitute back u = $2^{x}$ :

8 = $2^{x}$

Solve for x:

x = 3

4 0

3 years ago

Find the difference (20m+3)-(7m-5)

xz_007 [3.2K]

Answer:

Simplifying

(20m + 3) + -1(7m + -5) = 0

Reorder the terms:

(3 + 20m) + -1(7m + -5) = 0

Remove parenthesis around (3 + 20m)

3 + 20m + -1(7m + -5) = 0

Reorder the terms:

3 + 20m + -1(-5 + 7m) = 0

3 + 20m + (-5 * -1 + 7m * -1) = 0

3 + 20m + (5 + -7m) = 0

Reorder the terms:

3 + 5 + 20m + -7m = 0

Combine like terms: 3 + 5 = 8

8 + 20m + -7m = 0

Combine like terms: 20m + -7m = 13m

8 + 13m = 0

Solving

8 + 13m = 0

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '-8' to each side of the equation.

8 + -8 + 13m = 0 + -8

Combine like terms: 8 + -8 = 0

0 + 13m = 0 + -8

13m = 0 + -8

Combine like terms: 0 + -8 = -8

13m = -8

Divide each side by '13'.

m = -0.6153846154

Simplifying

m = -0.6153846154Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Pen are shipped to the office supply store in boxes of 12 each. Write a function rule to calculate the total number of pens when

Tom [10]

p = 12x is the function rule to calculate the total number of pens when you know the number of boxes

<em><u>Solution:</u></em>

Given that,

Pen are shipped to the office supply store in boxes of 12 each

To find: Write a function rule to calculate the total number of pens when you know the number of boxes

Let "p" be the total number of pens

Let "x" be the number of boxes

Number of pens in each box = 12

Then from given information,

Total number of pens = Number of boxes multiplied by number of pens in each box

$p = x \times 12\\\\p = 12x$

Thus the function rule is found

6 0

3 years ago

Write the word sentence as an inequality. A number m multiplied by 4 is than 12

kow [346]

Answer:

m x 4 = 12?

Answer is this is right, then m is 3.

3 0

2 years ago

Read 2 more answers

You are out bottle caps, and decide to use Popsicle sticks instead. You measure them, and they are 15.2 cm tall. How many Popsic

satela [25.4K]

It depends on how many Popsicle sticks you are going to use.So, for example, say that you are using 5 Popsicle sticks for the model. What you do is 15.2 x 5, 15.2 being the height of the sticks and 5 for the number of sticks you are using. The answer will be 76 cm tall. 21 15.2 x 5 --------- 76.0

3 0

2 years ago