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andrezito [222]
2 years ago
8

Figure b is a scaled copy of figure a

Mathematics
1 answer:
Romashka [77]2 years ago
6 0

Step-by-step explanation:

Im trying to get pts

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If a = √3-√11 and b = 1 /a, then find a² - b²​
Serga [27]

If b=\frac1a, then by rationalizing the denominator we can rewrite

b = \dfrac1{\sqrt3-\sqrt{11}} \times \dfrac{\sqrt3+\sqrt{11}}{\sqrt3+\sqrt{11}} = \dfrac{\sqrt3+\sqrt{11}}{\left(\sqrt3\right)^2-\left(\sqrt{11}\right)^2} = -\dfrac{\sqrt3+\sqrt{11}}8

Now,

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

and

a - b = \sqrt3 - \sqrt{11} + \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{9\sqrt3 - 7\sqrt{11}}8

a + b = \sqrt3 - \sqrt{11} - \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{7\sqrt3 - 9\sqrt{11}}8

\implies a^2 - b^2 = \dfrac{\left(9\sqrt3 - 7\sqrt{11}\right) \left(7\sqrt3 - 9\sqrt{11}\right)}{64} = \boxed{\dfrac{441 - 65\sqrt{33}}{32}}

5 0
2 years ago
81 is 37.5% of what number?
laila [671]

Hi,

81 is 37.5% of 216.

"1. We assume, that the number 37.5 is 100% - because it's the output value of the task.  

2. We assume, that x is the value we are looking for.  

3. If 100% equals 37.5, so we can write it down as 100%=37.5.  

4. We know, that x% equals 81 of the output value, so we can write it down as x%=81.  

5. Now we have two simple equations:

1) 100%=37.5

2) x%=81

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

100%/x%=37.5/81

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 81 is what percent of 37.5

100%/x%=37.5/81

(100/x)*x=(37.5/81)*x       - we multiply both sides of the equation by x

100=0.46296296296296*x       - we divide both sides of the equation by (0.46296296296296) to get x

100/0.46296296296296=x  

216=x  

x=216                          "

Have a great day!

3 0
3 years ago
What number is needed to complete the pattern. 66 73 13 21 52 __ 10 20
svetoff [14.1K]
Please try 43 I'm not sure
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3 years ago
What is the LCD for the fractions 5/6 and 3/8 PLZ HURRY
stealth61 [152]
The least common denominator for the fractions 5/6 and 3/8 is 24. 6 x 4 = 24, 8 x 3 = 24.
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3 years ago
the number of boys who solved a tough math problem is the same as the number of girls who did not solve it. Are there more girls
Harrizon [31]

Answer:

I want to say the answer is No, I'm sorry if I am wrong.

6 0
3 years ago
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