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3 years ago

15

The temperature in New Jersey is 85 degrees and climbing to 2 degrees per hour the temperature in Florida is a hundred and falli

ng 3 degrees per hour how many hours will it take for their temperature to be the same?

1 answer:

kompoz [17]3 years ago

4 0

Answer:

3

Step-by-step explanation:

i do maths lol

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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

Last year, James earned £1,300 per month.

mrs_skeptik [129]

Answer:

1300/100 X 105 = 1365

1365/4 = 341.25 per week

341.25/40= 8.53125

$8.53

6 0

3 years ago

12 x (3 + 4) ÷2 - 10=

Serga [27]

Answer:

32

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

(1/2)^2 - 6 (2 - 2/3)<br><br> Note: 1/2 and 2/3 is a fraction

shusha [124]

$\bf \left( \cfrac{1}{2} \right)^2-6\left(2-\cfrac{2}{3} \right)\impliedby recall~~\mathbb{PEMDAS}
\\\\\\
\cfrac{1^2}{2^2}-6\left( \cfrac{6-2}{3} \right)\implies \cfrac{1}{4}-6\left( \cfrac{4}{3}\right)\implies \cfrac{1}{4}-\cfrac{6\cdot 4}{3}\implies \cfrac{1}{4}-\cfrac{24}{3}
\\\\\\
\cfrac{1}{4}-8\impliedby LCD~~4\implies \cfrac{1-32}{4}\implies \cfrac{-31}{4}\implies -7\frac{3}{4}$

5 0

3 years ago

Help I need to know this ASAP

Tanzania [10]

The correct answer is b

4 0

2 years ago