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3 years ago

Sadika fell asleep at 9:30 p.m. She slept for 4 hours and 45 minutes. What time did she awake?

Mathematics

1 answer:

Novosadov [1.4K]3 years ago

4 0

Answer:

She woke up at 2:25am

Step-by-step explanation:

Hope this helps and have a good day!

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andrey2020 [161]

First observe that if $a+b>0$ ,

$(a + b)^2 = a^2 + 2ab + b^2 \\\\ \implies a + b = \sqrt{a^2 + 2ab + b^2} = \sqrt{a^2 + ab + b(a + b)} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}$

Let $a=0$ and $b=x$ . It follows that

$a+b = x = \sqrt{x \sqrt{x \sqrt{x \sqrt{\cdots}}}}$

Now let $b=1$ , so $a^2+a=4x$ . Solving for $a$ ,

$a^2 + a - 4x = 0 \implies a = \dfrac{-1 + \sqrt{1+16x}}2$

which means

$a+b = \dfrac{1 + \sqrt{1+16x}}2 = \sqrt{4x + \sqrt{4x + \sqrt{4x + \sqrt{\cdots}}}}$

Now solve for $x$ .

$x = \dfrac{1 + \sqrt{1 + 16x}}2 \\\\ 2x = 1 + \sqrt{1 + 16x} \\\\ 2x - 1 = \sqrt{1 + 16x} \\\\ (2x-1)^2 = \left(\sqrt{1 + 16x}\right)^2$

(note that we assume $2x-1\ge0$ )

$4x^2 - 4x + 1 = 1 + 16x \\\\ 4x^2 - 20x = 0 \\\\ 4x (x - 5) = 0 \\\\ 4x = 0 \text{ or } x - 5 = 0 \\\\ \implies x = 0 \text{ or } \boxed{x = 5}$

(we omit $x=0$ since $2\cdot0-1=-1\ge0$ is not true)

3 0

1 year ago

What is 1x1x1x1x1x1x1x1x1x1x1x1x1x1x1x1x1x1x1x1x1x1x1x1x1x1

Reptile [31]

Answer:

Step-by-step explanation:

Because each is just being multiplied by the same number.

7 0

3 years ago

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The town of Passaic had 58,753 people in 1990 and 71,509 people in 2014.

OLEGan [10]

Answer:

21.71% increase

Step-by-step explanation:

increase = Increase ÷ Original Number × 100

12756/58753*100

0.217112318*100

21.71% increase.

MARK ME BRAINLIEST

7 0

2 years ago

If pencils sell at 6 for 59 cents how many pencils can be bought for 2.95

Olegator [25]

We already know from the given data that 6 pencils can be bought for 59 cents. We have to determine the number of pencils that can be bought for $2.95.
So
Price of 6 pencils = 59 cents.
Price of 1 pencil = (59/6) cents
   = 9.83 cents
Now total amount in hand for buying pencils = $2.95
   = 295 cents
Then the number of pencils that can be bought for 295 cents = (295/9.83)
   = 30.01
So the maximum number of pencils that can be bought for $2.95 is 30 pencils.

4 0

3 years ago

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Need help on my math work here is a pic of the question

faltersainse [42]

Answer:

-3

Step-by-step explanation:

A = midpoint

-17 + 5 = -12

-12/2 = -6 = A

-6 + 0 = -6

-6/2 = -3 = B

8 0

2 years ago

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