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3 years ago

Simplify the following expression. (10-4i)(4-5i)+(-15+20i)

Mathematics

1 answer:

Vikki [24]3 years ago

3 0

Answer:

5-46i

Step-by-step explanation:

1. Multiply (10-4i) and (4-5i), I recomnd using foil:

40-50i-16+20i^2 + (-15+20i)

2. Remove the parenthesis around -15+20i

*we can do this since there is a "+":

40-50i-16+20i^2 + (-15)+20

3. Simplify i^2

* i^2 is -1 by textbook defination:

40-50i-16+20(-1) + (-15)+20

4. Simplify

40-50i-16-20 + (-15)+20

6. Combine like terms:

-5-50i-16i+20i

5-46i

And the problem is done

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What is the equation of a circle with center (-3,-5) and radius 4?

kobusy [5.1K]

Answer: D) (x + 3)² + (y + 5)² = 16

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

The equation of a circle is: (x - h)² + (y - k)² = r²

where (h, k) = center and r = radius

Given: (h, k) = (-3, -5) r = 4

Equation: (x - (-3))² + (y - (-5))² = 4²

(x + 3)² + (y + 5)² = 16

8 0

3 years ago

using two of the number cards from the list, fill in the gaps so that the values are in ascending order

Mademuasel [1]

The two gaps of the series are 236 % and 2.41.

The series is 2(32/100) _, _ , 247/100.

We are given that the series is in ascending order.

Let the missing numbers be x and y respectively.

We know that 2(32/100) = 2.32 in decimal form and 247/100 is 2.47 in decimal form.

Hence, we can write,

2.32 < x < y < 2.47

The given options are:-

231 % = 231/100 = 2.31 < 2.32

Hence, it is not the answer.

0.42 < 2.31

Hence, it is not the answer.

236 % = 236/100 = 2.36 > 2.31

Hence, this is one of the answers.

34 % = 0.34

0.34 < 2.31

Hence, it is not the answer.

0.237 < 2.31

Hence, it is not the answer.

2.41 > 2.32

Hence, this is one of the answers.

24.2 % = 24.2/100 = 0.242 < 2.31

Hence, it is not the answer.

0.36 < 2.31

Hence, it is not the answer.

As, 2.36 < 2.41, hence,

x = 2.36 or 236 % and,

y = 2.41

To learn more about series, here:-

brainly.com/question/15415793

#SPJ1

6 0

1 year ago

Jack mails 10 packages that each weigh the same amount. If the combined weigh of all 10 package is 67 1/2 pounds, how much does

kykrilka [37]

The answer is 6.75, I hope this helped

7 0

3 years ago

Suppose that a college determines the following distribution for X = number of courses taken by a full-time student this semeste

lidiya [134]

Answer:

$E(X) = \sum_{i=1}^n X_i P(X_i) = 3*0.07 +4*0.4 +5*0.25 +6*0.28= 4.74$ In order to find the variance we need to calculate first the second moment given by:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i) = 3^2*0.07 +4^2*0.4 +5^2*0.25 +6^2*0.28= 23.36$ And the variance is given by:

$Var(X) = E(X^2) +[E(X)]^2 = 23.36 -[4.74]^2 = 0.8924$

And the deviation would be:

$Sd(X) =\sqrt{0.8924} =0.9447$

Step-by-step explanation:

Previous concepts

The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.

The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).

Solution to the problem

For this case we have the following distribution given:

X 3 4 5 6

P(X) 0.07 0.4 0.25 0.28

We can calculate the mean with the following formula:

$E(X) = \sum_{i=1}^n X_i P(X_i) = 3*0.07 +4*0.4 +5*0.25 +6*0.28= 4.74$

In order to find the variance we need to calculate first the second moment given by:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i) = 3^2*0.07 +4^2*0.4 +5^2*0.25 +6^2*0.28= 23.36$

And the variance is given by:

$Var(X) = E(X^2) +[E(X)]^2 = 23.36 -[4.74]^2 = 0.8924$

And the deviation would be:

$Sd(X) =\sqrt{0.8924} =0.9447$

3 0

3 years ago

A cargo elevator has a maximum carrying capacity of 400 pounds. If each cargo box weighs 25 pounds, what is the maximum number o

daser333 [38]

Answer:

Step-by-step explanation:

400÷25

=16

25×16

=400

5 0

3 years ago