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3 years ago

Solve the following equation using the methods learned in this section. 3a2 = 54

Mathematics

1 answer:

MrRissso [65]3 years ago

7 0

The answer is a = 3√2. The explanation and steps of how I got the answer is in the image below.

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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

A rectangle made of square tiles measures 7 tiles long and 3 tiles wide. what is the length of a similar rectangle whose width i

Norma-Jean [14]

The length of the rectangle would be 21

Proportion to set it up would be 7/3 x X/9 cross multiply and solve for x which is 21

6 0

3 years ago

Is the figure a rectangle? Explain.

luda_lava [24]

The correct option is b. No, it is not a rectangle because the sides of the parallelogram do not meet at right angles.

<h3>How to explain the information?</h3>

The figure is a parallelogram and one diagonal measure 28 units.

In this case, it is not a rectangle because the sides of the parallelogram do not meet at right angles.

Therefore, the correct option is B.

Learn more about rectangles on:

brainly.com/question/25292087

#SPJ1

5 0

2 years ago

Solve for x<br> Зx = 6x - 2

allsm [11]

Answer: The answer is x=2/3

Step-by-step explanation: This is the linear equation to solve it we have to take 6x to the other the sign will change to be negative then divide both sides by 3

3x=6x-2

3x-6x=-2

3x=-2

x=2/3

4 0

3 years ago

Read 2 more answers

If a and b are both integers and b does not equal 0, then -(a/b) = (-a)/b = a/(-b) Choose two values for a and b. see if those v

kkurt [141]

a=4 , b=3 These values make the equation true .

<u>Step-by-step explanation:</u>

Here we have , If a and b are both integers and b does not equal 0, then -(a/b) = (-a)/b = a/(-b) Choose two values for a and b. We need to find if those values make the equation true . Let's find out:

We have the following equation:

-(a/b) = (-a)/b = a/(-b) , Let a=4 , b=3 , So

⇒ $-(a/b) = (-a)/b = a/(-b)$