Question

Simplify (3-2i)(1-6i)

Answer 1

Evaluate 5-3|3•(-6)|

Answer 2

Solve 1/4-2/x=3/x

Answer 3

How many degrees is 11pi/18

Answer 4

Solve x^2-6x+13=0

Answer 5

given g=《3,-5》and h=《-4,6》, find 4g+3h

Answer 6

To simplify the expression (3-2i)(1-6i), we can use the distributive property or FOIL method:

(3-2i)(1-6i) = 3(1) + 3(-6i) - 2i(1) - 2i(-6i)

Simplifying further:

= 3 - 18i - 2i + 12i^2

Since i^2 = -1, we can substitute this value:

= 3 - 18i - 2i + 12(-1)

Simplifying further:

= 3 - 18i - 2i - 12

= -9 - 20i

So, (3-2i)(1-6i) simplifies to -9-20i.

Answer 7

First, we evaluate the absolute value: |3•(-6)| = |-18| = 18.

Then, we substitute this value into the expression: 5-3•18.

Next, we perform the multiplication: 3•18 = 54.

Substituting this value back into the expression: 5-54.

Finally, we compute the subtraction: 5-54 = -49.

Therefore, 5-3|3•(-6)| simplifies to -49.

Answer 8

To solve the equation (1/4) - (2/x) = (3/x), we can first find a common denominator. The common denominator for the fractions is 4x.

Multiplying every term by 4x:

(4x)(1/4) - (4x)(2/x) = (4x)(3/x)

This simplifies to:

x - 8 = 12

Next, we isolate the variable x by adding 8 to both sides of the equation:

x - 8 + 8 = 12 + 8

This simplifies to:

x = 20

Therefore, the solution to the equation is x = 20.

Answer 9

To convert radians to degrees, we use the formula:

Degrees = (Radians * 180) / π

In this case, we want to convert 11π/18 to degrees.

Degrees = (11π/18) * (180/π)

Simplifying:

Degrees = (11 * 180) / 18

Degrees = 1980 / 18

Degrees = 110

Therefore, 11π/18 is equal to 110 degrees.

Answer 10

To solve the quadratic equation x^2 - 6x + 13 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 1, b = -6, and c = 13.

Substituting the values into the quadratic formula:

x = (6 ± √((-6)^2 - 4(1)(13))) / (2 * 1)

Simplifying:

x = (6 ± √(36 - 52)) / 2

x = (6 ± √(-16)) / 2

Since we have a negative value inside the square root, the equation does not have any real solutions. However, we can still find the solutions in terms of complex numbers by using the imaginary unit i, where i^2 = -1.

x = (6 ± √(-16)) / 2

x = (6 ± 4i) / 2

Simplifying further:

x = 3 ± 2i

Therefore, the solutions to the equation x^2 - 6x + 13 = 0 are x = 3 + 2i and x = 3 - 2i.

Answer 11

To find 4g + 3h, we first calculate 4g and 3h separately.

4g = 4 * ⟨3, -5⟩ = ⟨4*3, 4*(-5)⟩ = ⟨12, -20⟩
3h = 3 * ⟨-4, 6⟩ = ⟨3*(-4), 3*6⟩ = ⟨-12, 18⟩

Now, we add the corresponding components together:

4g + 3h = ⟨12, -20⟩ + ⟨-12, 18⟩ = ⟨12 + (-12), -20 + 18⟩ = ⟨0, -2⟩

Therefore, 4g + 3h = ⟨0, -2⟩.