MATHEMATICS HIGH SCHOOL

The product of (3+2i) and a complex number is (17+7i)

What is the complex number.

Answers

Answer 1
Answer: The question is asking us to find the complex number such that: ( 3 + 2 i ) * x = 17 + 7 i. We know that i^ 2 = - 1. x = ( 17 + 7 i ) / ( 3 + 2 i ) . We have to multiply the numerator and the denominator by ( 3 - 2 i ). Then: x = ( 17 + 7 i ) * ( 3 - 2 i ) / ( 9 - 4 i^2 ) = ( 51 - 34 i + 21 i - 14 i^2 ) / ( 9 + 4 ) = ( 51 + 14 - 13 i ) / 13 = ( 65 - 13 i ) / 13 = 65 / 13 - 13 i / 13 = 5 - i. Answer: The complex number is 5 - i.

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Refrer to the attached picture on which question is written. This question will be done according to Pathagoras theorem. This question answer is √a2-25 . I want step to step explanation.

Answers

i got something different

Identify the GCF of 12a^4b^3 + 8a^3b^2.
4a^3b^2
2a^3b
4a^2b
8a^3b^2

Answers

a is the answer you seek

There are 15 cards, numbered 1 through 15. If you pick a card, what is the probability that you choose an odd number or a two?A)
2
3

B)
3
5


C)
8
15


D)
8
225

Answers

Answer:

Option B

Step-by-step explanation:

Given that the 15 cards are numbered 1 to 15.

A card is picked at random.  We have to find the probability that the card is odd or two

Let A - selected card is odd

B - selected card is 2

A and B are mutually exclusive

Hence P(AUB) = P(A)+P(B)

Since there are 1,3....15 i.e. 8 odd numbered cards

P(A) = 8/15

P(B) = 1/15 (since there is only one two)

Thus required prob = P(AUB) = 8/15+1/15

=9/15

=3/5

Hence option B
There are 8 odd number between 1 and 15 (1,3,5,7,9,11,13,15), so the probability of choosing an odd number is (8)/(15).

The probability of choosing 2 is (1)/(15).

So, the overall probability is equal to (8)/(15)+(1)/(15)=(9)/(15)=(3)/(5)

How do you solve x²-10x+9=0 by completing the square?

Answers

x^2-10x+9=0\n\n\underbrace{x^2-2x\cdot5+5^2}_((*))-5^2+9=0\n\n(x-5)^2-25+9=0\n\n(x-5)^2-16=0\ \ \ /+16\n\n(x-5)^2=16\iff x-5=-√(16)\ \vee\ x-5=√(16)\n\nx-5=-4\ \vee\ x-5=4\n\nx=-4+5\ \vee\ x=4+5\n\nx=1\ \vee\ x=9



(*)\ (a-b)^2=a^2-2ab+b^2
x^2-10x+9=0 \n \nx^2-2\cdot5x+5^2-5^2+9=0\n \n(x-5)^2-25+9=0\n \n(x-5)^2=16\n \nx-5=4\ \ \vee\ \ x-5=-4\n \nx=9\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=1

The Eagles basketball team scored 12 more than 2 times as many points in the last game of the season than in the first game. Which expressions can be used to find the number of points the Eagles scored in the last game? Select all the expressions that apply.

Answers

Answer:

A. 12+2p

G. p+p+12

Step-by-step explanation:

The Eagles basketball team scored 12 more than 2 times as many points in the last game of the season than in the first game

Number of points scored in the last game of the season = 2p + 12

A. 12+2p

Equivalent

B. 2+p+12

= P + 14

Not equivalent

C. 2+12p

Not equivalent

D. p(2+12)

= 2p + 12p

Not equivalent

E. p+2+12

= P + 14

Not equivalent

F. 12p+2p

Not equivalent

G. p+p+12

= 2p + 12

Equivalent

a 5ft ladder is leaning against a 4 ft wall. how far must the bottom of the ladder be from the wall so that the top of the ladder rests on the top of the wall?

Answers

The ladder leaning against the wall forms a right angled triangle with the gound and the wall. So we can use the formula:

a² + b² = c²

The ladder is the hypotenuse c²

The vertical leg is b²

The base or horizontal leg is a²

We need to find the length of the base a²,  so:

a² = c² - b²

a² = 5² - 4²

a² = 25 - 16

a² = 9

a = √9

a = 3

Therefore the bottom of the ladder must be 3 feet  from the wall.

 
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