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3 years ago

12

The distance between two cities is 1900 km. How long will it take, in h, to drive from one city to the other if your average spe

ed is 84 mi/h?

1 answer:

OLEGan [10]3 years ago

3 0

Answer: 14 hours

Step-by-step explanation:

from the formular;

speed = distance / time

time = distance / speed

distance = 1900km

speed = 84 mi/h

we have to change this to km/h since our distance is in km

1 mile = 1. 609km

84mile = x

cross multiply

x = 84 × 1. 609

x = 135. 156km

speed = 135. 156km/h

Time = distance / speed

time= 1900 / 135. 166

time = 14. 058

time = 14 hours approximately

Therefore it takes 14 hours to drive from one city to the other.

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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

Maureen went on a 3 day 50 mile trip. the first day she biked 17 7/8 miles . the second day she biked 18 5/7 miles. How many mil

Inessa [10]

To find the miles for 3rd day, we take away the miles she biked for the first two day from the total.

$50 - 17 \dfrac{7}{8} - 18\dfrac{5}{7}$

$=50 - 17 \dfrac{7 \times 7}{8 \times 7} - 18\dfrac{5 \times 8}{7 \times 8}$

$= 48 \dfrac{112}{56} - 17 \dfrac{49}{56} - 18\dfrac{40}{56}$

$= 13 \dfrac{23}{56} \text { miles }$

-----------------------------------------------------------------------------------
Answer: She traveled 13 23/56 miles on the third day.
-----------------------------------------------------------------------------------

7 0

3 years ago

24 - c/12 = -89 what is x

VLD [36.1K]

Answer:

24

−

c

12

=

−

89

=

c

=

−

1356

x

=

c

=

−

1356

Step-by-step explanation:

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2 years ago

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gregori [183]

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3 years ago

Select all equations that have the same solution as 3x - 12=24

Evgen [1.6K]

Answer:

4

Step-by-step explanation:

3x-12=24

-12 to both sides

3x-12-12=24-12

3x=12

3x/3=12/3x

x=4

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3 years ago