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zepelin [54]
2 years ago
7

Seth took 30 inches of wire and cut it into

Mathematics
1 answer:
svetlana [45]2 years ago
6 0

Answer:

he go 2 full 13 in pecies 2.30

Step-by-step explanation:

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How do you simplify <img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%20%2B%5Csqrt%7B6%7D%20%7D%7B%5Csqrt%7B8%7D%20%2B%
blondinia [14]

The trick is to exploit the difference of squares formula,

a^2-b^2=(a-b)(a+b)

Set a = √8 and b = √6, so that a + b is the expression in the denominator. Multiply by its conjugate a - b:

(\sqrt8+\sqrt6)(\sqrt8-\sqrt6)=(\sqrt8)^2-(\sqrt6)^2=8-6=2

Whatever you do to the denominator, you have to do to the numerator too. So

\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}{(\sqrt8+\sqrt6)(\sqrt8-\sqrt6)}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}2

Expand the numerator:

(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{2\cdot8}+\sqrt{6\cdot8}-\sqrt{2\cdot6}-(\sqrt6)^2

(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{16}+\sqrt{48}-\sqrt{12}-6

(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=4+\sqrt{48}-\sqrt{12}-6

(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(\sqrt4-1)

(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(2-1)

(\sqrt2+\sqrt6)(\sqrt8-\sqrt6}=-2-\sqrt{12}

So we have

\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+\sqrt{12}}2

But √12 = √(3•4) = 2√3, so

\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+2\sqrt3}2=\boxed{-1-\sqrt3}

7 0
3 years ago
The formula for the area of a trapezoid is A = {h(bi + b2), where h is the height
Rina8888 [55]

Answer:h = 2((A)/(b1+b2))

Step-by-step explanation:

7 0
3 years ago
The expression below is scientific notation for what number?<br> 6.1 x 10^6
arlik [135]

Scientific notation is a way to write compactly numbers with lots of digits, either because they're very large (like 2393490000000000000000000), or very small (like 0.0000000000356).

We use powers of ten to describe all those leading/trailing zeros, so that we con concentrate on the significat digits alone.

In your case, the "important" part of the number is composed by the digits 6 and 1, all the other digits are zero. But how many zeroes? Well, let's do the computation.

Every power of 10, 10^n is written as one zero followed by n zeroes, so we have

10^6 = 1000000 \implies 6.1 \times 10^6 =6.1 \times 1000000

Multiplying a number by 10^n means to shift the decimal point to the right and/or add trailing zeroes n times. So, we have to repeat this process six times. We shift the decimal point to the right one position, and then add the five remaning zeroes. The result is thus

6.1 \times 1000000 = 6100000

4 0
3 years ago
The difference of two numbers is 3. Their sum is - 24. Find the numbers.
Katarina [22]

Answer:

y = -13.5

x = -10.5

Step-by-step explanation:

Hi there!

Let the two numbers be equal to <em>x</em> and <em>y</em>.

The difference of two numbers is 3 ⇒ x - y = 3

Their sum is - 24 ⇒ x + y = -24

Solve using elimination:

x - y = 3

x + y = -24

Add the two equations:

x + x - y + y = 3 - 24

2x = -21

x = -10.5

Solve for y:

-10.5 - y = 3

- y = 3 + 10.5

y = -13.5

I hope this helps!

4 0
3 years ago
BRAINLIEST ANSWER GETS 55 POINTS.
REY [17]

Answer:

What are the directions?

4 0
3 years ago
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