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3 years ago

5

Write the inverse of the conditional statement determine whether the inverse is true or false find a counter example. Independen

ce Day in the United States is July 4

1 answer:

timurjin [86]3 years ago

5 0

Inverse = If it is not independence day, then it is not July 4.

the inverse is true because the statement is true.

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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

1. A is a quadrilateral with exactly one<br> pair of parallel sides.

strojnjashka [21]

Answer:

So what’s the question?

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Hi can anyone help please?! What two products do you get when you cross-multiply the fractions 2/5 and 3/8?

IceJOKER [234]

Answer:

I think C

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Can someone solve this for me (:

mario62 [17]

I have no idea what the answer to that is or how to solve it but i LOVE UR PROFILE PICTURE

5 0

4 years ago

Ben's living room is a rectangular measuring 12 yards x 204" by how many feet does the length of the room exceed the with the le

Firlakuza [10]

Answer:

The length of the room exceeds the width by 19 feet

Step-by-step explanation:

From the question, the room measures 12 yards x 204", that 12 yards x 204 inches. To determine by how many feet the length of the room exceeds the width, we will first convert both units of measurement ( yards and inches) to feet.

To convert 12 yards to feet,

1 yard = 3 feet

∴ 12 yards will be 3 × 12 feet = 36 feet

To convert 204" to feet

12" = 1 foot

∴ 204" will be 204/12 feet = 17 feet

Hence, the room measures 36 feet × 17 feet

That is, Length of the room = 36 feet

and width of the room = 17 feet

Now, to determine by how many feet the length of the room exceeds the width, we will deduct the width of the room from the length of the room, that is,

36 feet - 17 feet = 19 feet

Hence, the length of the room exceeds the width by 19 feet.

6 0

3 years ago