MATHEMATICS HIGH SCHOOL

Simplify $(1-3i)(1-i)(1+i)(1+3i)$

Answers

Answer 1
Answer:

(1-3i)(1-i)(1+i)(1+3i)=\n(1^2-(3i)^2)(1^2-i^2)=\n(1+9)(1+1)=\n10\cdot2=20
Answer 2
Answer:

Answer:

\huge\boxed{(1-3i)(1-i)(1+i)(1+3i)=20}

Step-by-step explanation:

(1-3i)(1-i)(1+i)(1+3i)\n\n\text{use the commutative property}\n\n=(1-3i)(1+3i)(1-i)(1+i)\n\n\text{use the associative property}\n\n=\bigg[(1-3i)(1+3i)\bigg]\bigg[(1-i)(1+i)\bigg]\n\n\text{use}\ (a-b)(a+b)=a^2-b^2\n\n=\bigg[1^2-(3i)^2\bigg]\bigg[1^2-i^2\bigg]\n\n=\bigg(1-9i^2\bigg)\bigg(1-i^2\bigg)\n\n\text{use}\ i=√(-1)\to i^2=-1\n\n=\bigg(1-9(-1)\bigg)\bigg(1-(-1)\bigg)\n\n=\bigg(1+9\bigg)\bigg(1+1\bigg)\n\n=(10)(2)\n\n=20

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Which expressions are equivalent to the one below. Check all that apply. Log9 1 * log9 81

Answers

The expression Log9 1 * log9 81 is equivalent to 0.

Given
Log9 1 * log9 81

What is simplification?

In mathematics to operate and interpret the function to make function simple or more understandable known as simplify and the phenomenon is called simplification.

Here,


=log_(9) 1 *log_(9)81\n=0* log_(9)9^2\n=0*2log_(9)9\n=0

Thus, the expression Log9 1 * log9 81 is equivalent to 0.

Learn more about simplification here:
brainly.com/question/12501526

#SPJ2
Log9 1 = 0
Log9 81 = 2
0 * 2 = 0

20 is 12.5$ of what number?

Answers

Asumming you mean "20 is 12.5% of what number?", the answer is 160.

HELP PLEASEEEE!!The math team decided to sell customized pocket protectors as a
fundraiser. These were truly a hot item in our school, and $240 was
raised. Cecily had originally suggested a price that was $2 lower
for each item, but if the team had agreed to that price they would have
had to sell 20 more pocket protectors to get the $240.
How many pocket protectors did they actually sell? What was the price of
each?

Answers

Answer:

40

Step-by-step explanation:

6×40⇒240

future value = P × (1+ i)t Kate wants to have $25,000 in 16 years. How much does she need to invest if the interest rate is 6 percent per year?

Answers

If Kate wants $25,000, then that's the future value.
i is the rate of change, which is 6% in this case, which is rewritten as 0.06.
P is the starting value, or what she has to originally put in, which is what we need to find.
You put times t but it's actually to the power of t, which is time.
The time in this problem is 16 years, so t is 16.
Let's rewrite the equation with the plugged in values.
25,000 = P(1 + 0.06)^16
Now simplify:
25,000 = P(1.06)^16
25,000 = P(1.06^16)
25,000 = P(2.54)
How do you find P?
Isolate the variable!
To do this, divide both sides by 2.54.
25,000 / 2.54 = 9842.52
So that means she needs to invest an original amount of $9,842.52 if she wants to have $25,000 in 16 years with a 6% interest rate per year.

Now just check your work:
25,000 = 9842.52(1 + 0.06)^16
25,000 = 9842.52(1.06^16)
25,000 = 9842.52(2.54)
25,000 = 25,000
It works!
So $9,842.52 is the correct answer.

If 3 1/2 pounds of bananas cost $1.96 how much would one pound cost

Answers

It would simply be 1.96 divided by 3.5. It would be 56 cents per pound.
3 1/2 ib = $1,96  
(7)/(2) * (2)/(7) ib = (196)/(100) * (2)/(7) \n \n 1ib = (28)/(100) * (2)/(1) \n \n 1ib = (56)/(100) = 0,56

Answer 1 pound of bananas costs $0.56 

From a survey, a reporter determined that the true estimate for the proportion of citizens who plan to sign a petition is between 68% and 74%. What is the survey’s margin of error?

Answers

Answer:

Therefore, the survey's margin of error is ±3%

Step-by-step explanation:

From a survey, a reporter determined that true estimate for the proportion of citizens who plan to sign a petition is between 68% and 74%.

given estimate range = 68% to 74%

Margin of error = (74% - 68%) ÷ 2

6 ÷ 2 = 3%

Therefore, the survey's margin of error is ±3%
±3% this was the answer from my test 
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