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jeyben [28]
3 years ago
6

29. Which of the following expressions will result in a real answer after being simplified? Select all that apply.

Mathematics
1 answer:
nexus9112 [7]3 years ago
5 0

Answer: A, B, C, and E

Step-by-step explanation:

If both sides are real numbers, then the product will be a real number.

If in at least one of the sides we have a complex number, then the product will be real if:

The other number is zero.

The other number is the conjugate of the first.

This is when:

Suppose we have a number:

z = a + b*i

The conjugate will be:

w = a - b*i

And the product between them is:

(a + b*i)*(a - b*i) = a^2 + a*b*i - a*b*i + b^2 = a^2 + b^2

Then the options that will have a real answer are:

A. (4+5i)(4-5i) = 4^2 + 5^2 = 16 + 25 = 41

B. (4 + 91)*(41 - 9) = 3040

C. (3 + 2*i)*(3 -2*i) = 3^2 + 2^2 = 9 + 4 = 13

E. (312 + 7i)*(312 - 7i) = 312^2 + 7^2 = 97,393

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Derek was 4 years 2 months old when he joined school. Today he is 11 years 1 month old. For how long has he been in school?
lora16 [44]

Answer:

hi

Step-by-step explanation:

first of all,we should do this:

1 year is 12 month

amd 4 year is 48 month(12×4)

then we must add 2 months (wich is given) to 48

He was 50 months old when he started school

and we should find how old is he now

11 ×12=132months

132+1=133months

133-50=83 ( he has been 83 months in school)

let's turn it to years 6 years 11 months

( for finding years you should divide 83 to 12)

hope it helps

6 0
2 years ago
Anna saved $20 in a jar each month for 2/1/2 years. She spent 75% of her savings on a computer. How much money did Anna have lef
strojnjashka [21]
2 and 1/2 years = 30 months

20 \times 30 = 600
100\% - 75\% = 25\%
600 \times 25\% = 150
The answer is A. $150

Hope this helps.
6 0
3 years ago
Arlo invested $4000 in an account that earns 5.5% interest, compounded annually. The formula for compound interest is A(t)=P(1+i
USPshnik [31]

\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A=4000\left(1+\frac{0.055}{1}\right)^{1\cdot 4}\implies A=4000(1.055)^4\implies A\approx 4955.2986

4 0
3 years ago
Read 2 more answers
Claire jogs around an oval track and is able to complete one lap in 5 minutes. If she jogs at the same pace for 42 minutes, how
Maslowich
I would say about 8 whole laps
7 0
3 years ago
A floor tile is shaped like a regular hexagon. The side lengths are 4 cm and the apothem 23‾√ cm.
Nata [24]

Answer:

<h2>41.57 cm²</h2>

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>
  • geometry
  • PEMDAS
<h3>tips and formulas:</h3>
  • area of a regular hexagon when apothem is given:½×P×A
<h3>let's solve:</h3>

parimeter of a regular hexagon:6a

therefore

=½×[4×6]×2√3 cm²

simplify parentheses:

=½×24×2√3 cm²

simplify fraction:

=24×√3 cm²

=41.57cm²

8 0
3 years ago
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