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zhuklara [117]
4 years ago
11

Simplify the following expression

Mathematics
2 answers:
saveliy_v [14]4 years ago
6 0
Answer:
2√6

Explanation:
Before we begin, remember the following:
√a * √b = √ab
√a * √a = a

Now, for the given:
\frac{6 \sqrt{2} }{ \sqrt{3} }

Multiply both the numerator and the denominator by √3:
\frac{6 \sqrt{2} }{ \sqrt{3} } * \frac{ \sqrt{3}}{ \sqrt{3} }

= \frac{6  \sqrt{2}   \sqrt{3} }{ \sqrt{3}   \sqrt{3} }

= \frac{6 \sqrt{6} }{3}

This can be rewritten as:
\frac{6}{3}  \sqrt{6} = 2√6

Hope this helps :)
LenKa [72]4 years ago
3 0
We have the following expression:
 (6root (2)) / (root (3))
 Rationalizing we have:
 (6root (2)) / (root (3)) * (root (3) / root (3))
 Rewriting we have:
 (6root (6)) / (3)
 2root (6)
 Answer:
 The simplified expression for this case is given by:
 2root (6)
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(X+2)(4x-3) multiply place in descending powers
VMariaS [17]

Multiplying out the equation (x + 2)(4x - 3) and arranging in descending powers order gives us the quadratic form as; 4x² + 5x - 6

<h3>How to expand quadratic equations?</h3>

We want to expand the quadratic equation given as;

(x + 2)(4x - 3)

Multiplying out gives us;

4x² + 8x - 3x - 6

⇒ 4x² + 5x - 6

Thus, we can conclude that multiplying out the equation (x + 2)(4x - 3) and arranging in descending powers order gives us the quadratic form as; 4x² + 5x - 6

Read more about Quadratic equations at; brainly.com/question/1214333

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7 0
2 years ago
What are the lengths of SV and QT? no links.
maxonik [38]

ok so we see that TR is 17 units, so RV is the same amount

3x+2 so 3x=15 so divide both sides by 3 we get x=5

now we know x=5 4x+1=21 and 9x-4=41

*drops microphone*

4 0
2 years ago
Read 2 more answers
Can someone help me do part two please? It’s very important send a picture or something. I don’t even care if you tell me the st
Nataly_w [17]
<h3>Explanation:</h3>

1. "Create your own circle on a complex plane."

The equation of a circle in the complex plane can be written a number of ways. For center c (a complex number) and radius r (a positive real number), one formula is ...

  |z-c| = r

If we let c = 2+i and r = 5, the equation becomes ...

  |z -(2+i)| = 5

For z = x + yi and |z| = √(x² +y²), this equation is equivalent to the Cartesian coordinate equation ...

  (x -2)² +(y -1)² = 5²

__

2. "Choose two end points of a diameter to prove the diameter and radius of the circle."

We don't know what "prove the diameter and radius" means. We can show that the chosen end points z₁ and z₂ are 10 units apart, and their midpoint is the center of the circle c.

For the end points of a diameter, we choose ...

  • z₁ = 5 +5i
  • z₂ = -1 -3i

The distance between these is ...

  |z₂ -z₁| = |(-1-5) +(-3-5)i| = |-6 -8i|

  = √((-6)² +(-8)²) = √100

  |z₂ -z₁| = 10 . . . . . . the diameter of a circle of radius 5

The midpoint of these two point should be the center of the circle.

  (z₁ +z₂)/2 = ((5 -1) +(5 -3)i)/2 = (4 +2i)/2 = 2 +i

  (z₁ +z₂)/2 = c . . . . . the center of the circle is the midpoint of the diameter

__₁₂₃₄

3. "Show how to determine the center of the circle."

As with any circle, the center is the <em>midpoint of any diameter</em> (demonstrated in question 2). It is also the point of intersection of the perpendicular bisectors of any chords, and it is equidistant from any points on the circle.

Any of these relations can be used to find the circle center, depending on the information you start with.

As an example. we can choose another point we know to be on the circle:

  z₄ = 6-2i

Using this point and the z₁ and z₂ above, we can write three equations in the "unknown" circle center (a +bi):

  • |z₁ - (a+bi)| = r
  • |z₂ - (a+bi)| = r
  • |z₄ - (a+bi)| = r

Using the formula for the square of the magnitude of a complex number, this becomes ...

  (5-a)² +(5-b)² = r² = 25 -10a +a² +25 -10b +b²

  (-1-a)² +(-3-b)² = r² = 1 +2a +a² +9 +6b +b²

  (6-a)² +(-2-b)² = r² = 36 -12a +a² +4 +4b +b²

Subtracting the first two equations from the third gives two linear equations in a and b:

  11 -2a -21 +14b = 0

  35 -14a -5 -2b = 0

Rearranging these to standard form, we get

  a -7b = -5

  7a +b = 15

Solving these by your favorite method gives ...

  a +bi = 2 +i = c . . . . the center of the circle

__

4. "Choose two points, one on the circle and the other not on the circle. Show, mathematically, how to determine whether or not the point is on the circle."

The points we choose are ...

  • z₃ = 3 -2i
  • z₄ = 6 -2i

We can show whether or not these are on the circle by seeing if they satisfy the equation of the circle.

  |z -c| = 5

For z₃: |(3 -2i) -(2 +i)| = √((3-2)² +(-2-i)²) = √(1+9) = √10 ≠ 5 . . . NOT on circle

For z₄: |(6 -2i) -(2 +i)| = √((6 -2)² +(2 -i)²) = √(16 +9) = √25 = 5 . . . IS on circle

4 0
3 years ago
Find the y-intercept and x-intercept of the following linear equation.<br> 6x+3y=−18
Gnoma [55]

y-intercept is -6 (0,-6) and the x-intercept is -3 (-3,0)

6 0
3 years ago
Read 2 more answers
What is the remainder of 10^2017 divided by 1001?
pashok25 [27]
Note: When I use the double equal sign, I mean the triple bar used with modular arithmetic

10^3 = 1000 == -1 (mod 1001)
10^3 == -1 (mod 1001)
(10^3)^672 == (-1)^672 (mod 1001)
(10^(3*672) == 1 (mod 1001)
10^2016 == 1 (mod 1001)
10*10^2016 == 10*1 (mod 1001)
10^2017 == 10 (mod 1001)

Final Answer: 10


5 0
3 years ago
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