MATHEMATICS MIDDLE SCHOOL

Which expressions are equal to a real number?

Answers

Answer 1

Answer:

Answer:

Option B

Option C

Step-by-step explanation:

$i = √(-1)$

⇒ $i^2 = (√(-1))^2 = -1$ , which is a real number.

Similarly, $i^3 = i^2.i = -1 * i = -i$

And we also know that $i^4 = 1$

So, we see that odd powers of $i$ is a complex number and even powers renders us a real number.

Using this we solve the problem.

Option A: $(-4i)^(11)$ 11 is an odd power. This would be a complex number and not a real number.

Option B: $(-3i)^(12)$ Even power of i. So, this should give us a real number.

Option C: $(2 + 3i)^2$

(a + bi)² = a² - b² + 2abi

So, (2 + 3i)² would be a complex number because of the 2bi term.

Option D: (4 + 5i)(4 - 5i)

(a + ib)(a - ib) = a² + b²

So, (4 + 5i)(4 - 5i) = 4² + 5² = 41, a real number.

Option E: (6 + 8i)(8 + 6i)

(a + ib)(c + id) = ac - bd + (ad + bc)i

This would be a complex number because of the (ad + bc) term.

So, Options B and D are real numbers.

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Hi everyone!! Could someone write a real-world problem in which you could graph function? Thanks!! The best ne will win the title of the most brainliest!!

Answers

Madeline is on a diet. She exercises every day in order to lose some weight. she currently has 210 pounds. Make a graph with a number of pounds she loses and with the amount of time she takes (in months) to lose that weight.

Well,

The example I will use will be the relationship between the Celsius scale and the Fahrenheit scale.

The formula for the conversion between Fahrenheit and Celsius:

$F= (9)/(5) C+32$

We can immediately see that this is a linear equation if we substitute y for F and x for C.

$y= (9)/(5) x+32$

or

$f(x)= (9)/(5) x+32$

It is a line that has a y-intercept of (0,32), and has a slope of 9/5.

I have attached the line below.

Please show work thank you

Answers

∠D = 90°
∠E = x
∠F = 2x - 12

Angles in a triangle = 180°
  90 + x + 2x - 12 = 180
  78 + 3x = 180
-78 -78
3x = 102

   $(3x)/(3) = (102)/(3)$
3 and 3 cancels out

34 = x

∠E = 34°

∠F = 2x -12
= 2 × 34 - 12
= 56°

320 girls, 180 boys what percent are girls

Answers

if we have 320 girls and 180 boys so the total number is 320 + 180 = 500 so the percent of girls will be:
320/500 = ?/100
so ? is your answer:
320 * 100 /500 = 64% :)))
i hope this is helpful
have a nice day

First add them up to to find the total. 320+180=500. 320 out of 500 is 320/500, which is 0.64, which is 64%.

30 inches increased by 30%

Answers

30 x .3 = 9
30 + 9 = 39

Answer:

thh

Step-by-step explanation:

Rupert drove home at an average rate of 58 miles per hour. Find his rate in feet per second.

Answers

To find this, you must first multiply 58 by the number of feet in a mile, 5280, to get a total number of feet. This comes out to 306,240 feet per hour. Next, you divide this by 60, since there are 60 minutes per hour, to find the rate of feet per minute, which comes out to 5,104 feet per minute. Finally, you divide this number by 60 again, since there are 60 seconds per minute, to get the final answer of a rate of about 85.0666... feet per second.

I am a fraction > 3/11 but < 4/11.
My numerator is 7. ________

Answers

First, we need to create a higher denominator.
3/11 = 6/22
4/11 = 8/22
Thus the only fraction between them is 7/22 which is the answer.

7 over 22 or 7\22 randomrandom

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