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LenaWriter [7]
3 years ago
11

X-2/3= 6 1/3 what is the answer??????????

Mathematics
1 answer:
vichka [17]3 years ago
4 0

For this case we must find the solution of the following equation:

x- \frac {2} {3} = 6 \frac {1} {3}

Rewriting the mixed number in the form of improper fraction we have:

x- \frac {2} {3} = \frac {3 * 6 + 1} {3}\\x- \frac {2} {3} = \frac {19} {3}

Add \frac {2} {3} to both sides of the equation:

x = \frac {19} {3} + \frac {2} {3}

We add the fractions with the same denominator:

x = \frac {19 + 2} {3}\\x = \frac {21} {3}\\x = 7

So, the solution is x = 7

Answer:

x = 7

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Express z = square root (4 + 3i) in the form p + qi , where p and q and are rational numbers.​
Gwar [14]

Answer:

z = (3/√2) + (1/√2)î = (1/√2) [3 + i] = (2.1213 + 0.7071i)

OR

z = -(3/√2) + i(1/√2) = (1/√2) [-3 + i] = (-2.1213 + 0.7071i)

p = (3/√2) = 2.1213

q = (1/√2) = 0.7071

OR

p = (-3/√2) = -2.1213

q = (1/√2) = 0.7071

Step-by-step explanation:

z = √(4 + 3i)

Let the complex number z be equal to

z = p + qi

So, we can write

z = p + qi = √(4 + 3i)

p + qi = √(4 + 3i)

Square both sides

(p + qi)² = [√(4 + 3i)]²

p² + pqi + pqi + (qi)² = (4 + 3i)

p² + 2pqi + q²i² = 4 + 3i

note that i² = -1

p² + 2pqi - q² = 4 + 3i

(p² - q²) + 2pqi = 4 + 3i

Comparing both sides, and them equating the real parts on both sides to each other and the complex parts to each other

(p² - q²) = 4 (eqn 1)

2pq = 3 (eqn 2)

From eqn 2

p = (3/2q)

p² = (9/4q²)

Substituting this into eqn 1

(9/4q²) - q² = 4

multiplying through by 4q²

9 - 4q⁴ = 16q²

4q⁴ + 16q² - 9 = 0

let q² = x, q⁴ = x²

4x² + 16x - 9 = 0

Solving the quadratic equation

x = 0.5 or -4.5

q² = 4

q² = 0.5 or q² = -4.5

q = √0.5 or √-4.5

q = (1/√2) = (√2)/2 = 0.7071

Or q = i(3/√2) = i(3√2)/2 = 2.1213I

p = (3/2q)

If q = (1/√2) = (√2)/2 = 0.7071

p = (3/√2) = (3√2)/2 = 2.1213

if q = i(3/√2) = i(3√2)/2 = 2.1213I

p = i(1/√2) = i(√2)/2 = 0.7071i

z = p + qi

If q = (1/√2) = (√2)/2 = 0.7071

p = (3/√2) = (3√2)/2 = 2.1213

z = (3/√2) + (1/√2)î = (1/√2) [3 + i]

= 2.1213 + 0.7071i

if q = i(3/√2) = i(3√2)/2 = 2.1213I

p = i(1/√2) = i(√2)/2 = 0.7071i

z = i(1/√2) + [i(3/√2) × i]

z = i(1/√2) - (3/√2)

z = -(3/√2) + i(1/√2)

z = (1/√2) [-3 + i]

z = -2.1213 + 0.7071i

Hope this Helps!!!

8 0
4 years ago
Help please with this lol.
seraphim [82]
<h2>answer:</h2>

the value is $3.02

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Answer:

d=100

Step-by-step explanation:

.99d=10 + .89d

subtract .89d from both sides

.1d=10

divide by .1 on both sides

d=100

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