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3 years ago

What is the standard form of (1-3i)(2+5i)

Mathematics

1 answer:

artcher [175]3 years ago

3 0

Answer:

17 - i

Step-by-step explanation:

Step 1: FOIL out

(1 - 3i)(2 + 5i)

(2) + (1 * 5i) + (-3i * 2) + (-3i * 5i)

2 + 5i - 6i - 15i^2

2 - i + 15

17 - i

Answer: 17 - i

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What is the image of (1,0) after a counterclockwise rotation of 60 degrees?

Anestetic [448]

Answer:

$\vec s = \left(\frac{1}{2},\frac{\sqrt{3}}{2} \right)$

Step-by-step explanation:

The coordinate has the following polar form:

$\vec r = (1, 0^{\circ})$

The image of the coordinate rotated counterclockwise 60° is:

$\vec s = (1, 60^{\circ})$

Its equivalent form in rectangular coordinates is:

$\vec s = (1\cdot \cos 60^{\circ}, 1 \cdot \sin 60^{\circ})$

$\vec s = \left(\frac{1}{2},\frac{\sqrt{3}}{2} \right)$

3 0

2 years ago

Expand the following: 1/5 (10x-25)

mario62 [17]

This must be your answer:
Expanded: 1/5 x 10x + 1/5 x -25

3 0

3 years ago

The volume of this cylinder is 20,403.72 cubic yards. What is the radius? Use ≈ 3.14 and round your answer to the nearest hund

MakcuM [25]

The formula for the volume of a cylinder is V=3.14r^2(h).
So substituting the volume: 20,403.72=3.14r^2(h).

To solve for ‘r’, divide both sides by 3.14h
r^2=6,498/h
Then find square root of both sides
r= sqrt(6,498/h)
Since ‘h’ is not specified here, it cannot be solved further.

4 0

1 year ago

The number of employees per department are normally distributed with a population standard deviation of 198 employees and an unk

cricket20 [7]

Answer:

EBM = +-54.126

Step-by-step explanation:

In this question we have confidence interval to be 80%

The formula to solve this is in the attachment.

Bar X = 1460

Z-alpha/2 = 1.282

Sd = standard deviation = 198 employees

n = 22 departments

After we have inserted all values in to the formula we have:

1460 +-(1.282*198/√22)

= 1460+-(54.12604)

= (1405.87, 1514.126)

The error bounded mean EBM

= +-z-alpha/2 x (sd/√n)

= 1.282 x 198/√22

= 1.282 x 42.22

EBM = +-54.126

6 0

2 years ago

Cameron makes a quilt design using four congruent triangles as shown below. What is the perimeter of the entire design?

Lunna [17]

Answer: 64cm

Step-by-step explanation:

7 0

3 years ago