All categories

3 years ago

Which equation could be used to find the dimensions of the rectangle?

Mathematics

1 answer:

Nikolay [14]3 years ago

7 0

The second answer i believe

You might be interested in

Nikos finds a toy train set on sale for 20% off at a toy store. The original price was $35. Nikos must also pay 6.5 sales tax. W

Anvisha [2.4K]

Answer:$29.82

First find the discount, then find the tax

5 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx....%7D%20%7D%20%7D%20%7D%20%20%3D%20%

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

2 years ago

A submarine cuts through the water at an elevation of 203 meters under the sea. The sub rises, and the elevation changes by 4.3

Natalija [7]

It should be 76.1m under water. First multiple 15x4.3=64.5, and 5.2x12=62.4. Add those together to get 126.9. Subtract that from the initial elevation of 203 and get your answer.

4 0

3 years ago

A restaurant sells burritos for $8.00 each. To buy supplies, the restaurant pays $1.50 for the meat and $1.00 for the other ingr

3241004551 [841]

Answer:

isnt it just 2.50$ ?

Step-by-step explanation:

1$ + 1.5$ = 2.5$ ?

meat + everything else = total

6 0

3 years ago

Read 2 more answers

PLZ ANSWER THESE U DONT HAVE TO PUT A EXPLANATION

Natasha2012 [34]

Answer:

I believe it is the last choice.

Step-by-step explanation:

3 0

3 years ago