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3 years ago

What is the solution to the equation 1 over 21 multiplied by x is equal to 1 over 7?

Mathematics

1 answer:

Ulleksa [173]3 years ago

6 0

It would be X=3 because 3 multiplied by 1 equals 3 and you get 3 over 21. that simplifies to 1 over 7.

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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

There are 10 roller coasters at 6 flags, and you only have time to ride 3 before the park closes. How many different ways can yo

Charra [1.4K]

Answer:

120

Step-by-step explanation:

If order doesn't matter, there are 10 ways to chose the first ride, 9 ways to choose the second, and 8 ways to choose the third. This product (720) has you riding the same 3 coasters in 6 different orders. Dividing by 6 gives ...

720/6 = 120 different combinations of roller coasters

_____

This number might be written as 10C3 (choose 3 from 10). The meaning of that notation is ...

nCk = n!/(k!(n-k)!)

10C3 = 10!/(3!·7!) = 10·9·8/(3·2·1) = 120

4 0

3 years ago

Read 2 more answers

Isabel’s car gets 33.5 miles per gallon. Her gas tank holds 15.1 gallons of gas how many miles can Isabel drive on a full tank o

bagirrra123 [75]

Isabel can drive 505.85 miles with a gas tank that holds 15.1 gallons of gas

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

Given that, Isabel’s car gets 33.5 miles per gallon

Her gas tank holds 15.1 gallons of gas

To find: Number of miles can Isabel drive on a full tank of gas

Let "x" be the miles drive with 15.1 gallons of gas

From given,

1 gallon = 33.5 miles

15.1 gallon = x miles

This forms a proportion and we can solve the sum by cross multiplying

$1 \times x = 15.1 \times 33.5\\\\x = 505.85$

Thus Isabel can drive 505.85 miles on a full tank of gas

6 0

3 years ago

Help A.S.A.P please thank you and please :D

Lina20 [59]

Answer:

Emma was right to say that both packages are close to 2 pounds.

If we round-off the weights of both to the nearest whole number we would get 2 pounds on both. We look at the the difference of both from 2 pounds we get the following:

2.36 - 2.0 = 0.36

2.09 - 2.0 = 0.09

The smaller the difference the closer it is to the base value. So we can say that the closest one is 2.0 pounds is the package that weighs 2.09 pounds.

8 0

3 years ago

What is 144 divided by 960?Working out is needed.

Ipatiy [6.2K]

Answer:

The answer is 0.15

Step-by-step explanation:

Hope this helps!

7 0

2 years ago

Read 2 more answers