What is the quotient of the complex number 4-3i divided by its conjugate?
ANSWERS:
A. 24/25 + 7/25i
B. 24/25 - 7/25i
C. 7/25- 24/25i
D. 7/25 + 25/25i
Need an answer ASAP

Multiplying a complex number by -1 flips it across the origin on the complex plane, changing its direction by 180 degrees but not its magnitude, resulting in a point directly opposite to the initial position.

The question asks about the effect of multiplying a complex number by -1 in the complex plane. Multiplying a complex number by -1 essentially flips the point representing the complex number across the origin. If Point A represents a complex number on the complex plane, multiplying that complex number by -1 will result in a point that lies exactly opposite of Point A with respect to the origin. This operation does not change the magnitude of the complex number but changes its direction by 180 degrees. This is because the complex plane is analogous to a two-dimensional Cartesian coordinate system where complex numbers are represented as vectors. The multiplication by -1 is a reflection across the origin in such a plane.

For example, if a complex number z is represented by the point (a, b) where a is the real part and b is the imaginary part, then multiplying z by -1 gives us the point (-a, -b). This operation is similar to rotating the vector z 180 degrees around the origin or mirroring it across both the x and y axes.

Answer:

[tex]P(x)=12.50x-150.[/tex]

Step-by-step explanation:

Let x be the number of tickets sold. If a theater group charges $12.50 per ticket for its opening play of the season, then x tickets cost $12.50x. Production costs for the play are $150. Then the profit the theater group earns from selling x tickets is

[tex]P(x)=12.50x-150.[/tex]

Joe has 8 green pepper plants and 28 red pepper plants in his garden.

Let's denote the number of green pepper plants as G and the number of red pepper plants as R.

According to the given information, the ratio of green pepper plants to red pepper plants is 2 to 7.

This can be written as G:R = 2:7.

It is also mentioned that there are 20 more red pepper plants than green pepper plants. This can be written as R = G + 20.

Now, we can substitute the value of R from the second equation into the first equation:

G:G+20 = 2:7

By cross-multiplying, we have 7G = 2(G+20).

Simplifying the equation, we get 7G = 2G + 40.

Subtracting 2G from both sides, we have 5G = 40.

Dividing both sides by 5, we get G = 8.

Therefore, there are 8 green pepper plants and 8 + 20 = 28 red pepper plants in Joe's garden.

Answer:

I would say...

C.)x - 5 = 3 (x + 2)

Really really sorry if I'm wrong...

One thing I can say is that when it says 5 less than a #, that means the # is being subtracted from another #...

The correct equation for the situation 'Five less than a number is equal to three times the sum of the number and two' is x - 5 = 3(x + 2).

The correct equation for this situation is C.) x - 5 = 3(x + 2).

Here's how you can decipher the sentence: 'Five less than a number' translates to 'x - 5' in mathematical terms where 'x' stands for the number. 'Is equal to' signifies the equality sign '='. Finally, 'three times the sum of the number and two' corresponds to '3(x + 2)', where 'x' is the number, '2' is the two and '3' the three times mentioned in the equation. So, putting it all together gives you

x - 5 = 3(x + 2).

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Answer:

Perimeter = 32.44 unit

Area of triangle = 30 unit²

Step-by-step explanation:

By distance formula distance between (a,b) and (c,d) is [tex]\sqrt{(c-a)^2+(d-b)^2}[/tex]

So, we have

      [tex]AB=\sqrt{(16-2)^2+(2-8)^2}=15.23\\\\BC=\sqrt{(16-6)^2+(2-2)^2}=10\\\\AC=\sqrt{(2-6)^2+(8-2)^2}=7.21[/tex]

Perimeter = 15.23 + 10 + 7.21 = 32.44 unit

We have [tex]s=\frac{15.23+10+7.21}{2}=16.22[/tex]

Area of triangle[tex]=\sqrt{s(s-AB)(s-BC)(s-AC)}=\sqrt{16.22(16.22-15.23)(16.22-10)(16.22-7.21)}=30[/tex]

Area of triangle = 30 unit²

Answer: 4.5kg = 9.9208lbs

4.5kg = 158.733oz

The watermelon weighs approximately 4.5 kg, which can be converted to pounds and ounces by using the conversion factors. It is approximately 9 pounds and 15 ounces after conversion.

A watermelon at the grocery store weighs 4.5 kg. To convert this weight into pounds and ounces, we can use the fact that 1 kg is equivalent to 2.205 pounds (lb) and 1 pound equals 16 ounces.

First, let's find out how much the watermelon weighs in pounds:

Since we want the weight in pounds and ounces, we'll convert the decimal part of the pounds to ounces:

Therefore, the watermelon weighs approximately 9 pounds and 15 ounces (rounding 14.76 ounces to the nearest whole number).

The total number of observations is

2+9+16+12+8+6+4+2+1=60

The first five counts refer to 0 to four cars:

2+9+16+12+8=47

The probability is the fraction less than five,

p= 47/60 = 0.783333...

Answer: 78%

Answer:

59%

Step-by-step explanation:

First let us work out the total number of cars waiting in the  given period.

= 0 *2 + 1*9 + 2*16 + 3*12 + 4*8 + 5*6 + 6*4+7*2+8*1

= 185

Now the number when there are less than 5 cars in line ( that is when there are 0 - 4 cars in line) =

0*2 + 1*9 + 2*16 +3*12+4*8

= 109

Thus the required probability = 109/185

= 0.589

= 59%  (answer)

B - Brandon's age

4B - Michael's age

B + 27 - Michael's age

The equation:

4B = B + 27       subtract B from both sides

3B = 27      divide both sides by 3

B = 9

4B = 4(9) = 36

Answer:

There are 272 students going on the field trip.

Step-by-step explanation:

68 students on each bus. 4 busses. 68 x 4 = 272

Answer:

The answer is 272 students.

Step-by-step explanation:

1. First, I looked at how many students and buses are there.

2. I looked at the question, "How many students are going on the field trip?"

3. Next, I will multiply the number of students on each bus by the number of buses on there.

4.   68

   x  4

   272

-----------------------------------------------------------------------------------------------------------------

Hope this helped! Your answer is 272 students. ❤️

[tex]f(x)=4\cdot2^x\\\\y-intercept\ for\ x=0:\\\\f(0)=4\cdot2^0=4\cdot1=4[/tex]

Answer: Third option (bottom left)

Step-by-step explanation: We want to find which one of the graphs is the graph of the function f(x) = 4*2^x

Let's analyze some interesting points.

f(0) = 4*2^0 = 4*1 = 4

So we need to find the graph that passes through the point (0,4) (this means that intercepts the y-axis in the 4)

The graph that passes through the point (0,4) is the third option (bottom left one)

Answer:

length of each plan A work out: 1 hour

length of plan B work out: [tex]\frac{1}{2}[/tex] hours

Step-by-step explanation:

Let x represents the time taken to do plan A

y represents the time taken to do plan B

On Monday there were 5 clients who did Plan A and 2 who did Plan B.

Miguel trained his Monday clients for a total of 6 hours

5x + 2y = 6 -----------> equation 1

On Tuesday there were 3 clients who did Plan A and 8 who did Plan B. .He trained his Tuesday clients for a total of 7 hours

3x + 8y = 7  -------------------> equation 2

Now we solve for  x  and y

Let multiply the first equation by -4 to eliminate y

-20x -8y = -24

  3x + 8y = 7

------------------------ (add both equations)

-17x    = -17

Divide both sides by -17

So x= 1

Plug in 1 for x  in first equation and  solve for y

5x + 2y = 6

5(1) + 2y = 6

5 + 2y =6

Subtract 5 on both sides

2y = 1

y = 1/2

length of each plan A work out: 1 hour

length of plan B work out: [tex]\frac{1}{2}[/tex] hours

To find the number of answers that are not choice B, subtract the number of answers that are choice B from the total number of questions.

To find the number of answers that are not choice B, we first need to calculate the number of answers that are choice B. Since 25% of the answers are choice B, we can multiply the total number of questions (20) by 0.25 to find that there are 5 answers that are choice B. To find the number of answers that are not choice B, we subtract the number of answers that are choice B from the total number of questions. So, the number of answers that are not choice B is 20 - 5 = 15.

Answer:

50

Step-by-step explanation:

if x years past  she is twice her daughter's age,

so  we get:

28+x=2(3+x)

x=22,    22+28=50

Answer:

Step-by-step explanation:

Thank you that helped me with mine

eg:

L is 26, C is 4, how many years until L is 2 times as old as C?

26+x=2(4+x)

26+x=8+2X

-8 -8

18+x=2x

-x -x

18=1x

in 18 years L will be 2 times as old as C

[tex]\frac{y-307,650}{x-9} = 850\\\\y-307,650 =850(x-9)\\\\multiply\\\\y =307,650 +850(x -9)\\\\y =307,650+850(16-9)\\\\y= 313,600[/tex]

The linear equation can be formed as P = P0 + rt. Replacing each variable with the values from the problem, we find that the population of Beth's town on her 16th birthday will be approximately 319,600.

The question refers to a situation of linear growth. It states that the population of Beth's town grows at a constant rate of 850 people per year. If on Beth's 9th birthday the population was 307,650, we can create a linear equation to find the population when she turns 16. This linear equation can be represented as follows: P = P0 + rt, where P is the future population, P0 is the initial population, r is the rate of growth, and t is the time elapsed.

In Beth's situation, we will let her 9th birthday be the starting point (time zero). So, P0 is 307,650, r is 850, and t is 7 (the years from her 9th birthday to her 16th birthday). Plugging these values into our equation gives us P = 307,650 + 850 * 7. Solving the equation gives us P = 313,650 + 5,950 = 319,600. Therefore, the estimated population of Beth's town on her 16th birthday is 319,600.

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SX is equal to UX

US and Rt are the lines which make the center of the parallelogram. Hence the center of both lines is X so both the lines must be present at the same distance from the mid point. US is divided in two equal parts on point X and we know that center point is always equidistant from the end points. X must be equidistant from both UX and SX so we can say that SX = UX.

Answer:

Both A and D are false

Step-by-step explanation:

We expect lower academic performance when unemployment is high, so a lower graduation rate. Dropouts—those who don't graduate—tend to have a higher unemployment rate, so there is cause/effect working in both directions. Thus graduation rate and unemployment would be negatively correlated. (One study showed the correlation coefficient to be about -0.11.)

Because D is false, A is also false.

Answer:

x) =g(x) -1  shifts the graph g(x) down 1 unit

Step-by-step explanation:

g(x) = 3x

When we add  to g(x) and make it g(x) +c, we shift the graph vertically,

+c shifts the graph up

-c shifts the graph down

h(x) =g(x) -1  shifts the graph g(x) down 1 unit

Final answer:

The blanks are filled with 'straight line' as angles on a straight line sum to 180°, which is a key concept in geometry related to the properties of angles and triangles.

Explanation:

The sum of the measures of angle 5 and angle 6 is equal to 180° and the sum of the measures of angle 2 and angle 3 is equal to 180° because angles on a straight line measure 180°. This concept is related to the geometric property that when two angles lie on the same line and add up to form a straight angle, their measures sum up to 180°.

In geometry, specifically the study of polygons and angles, we learn that a triangle is a three-sided figure lying on a plane with three angles adding up to 180°. This is called the Triangle Sum Theorem, which is fundamental to understanding the properties of triangles and other polygons.

Answer:

A quadrilateral has 4 right angles

Step-by-step explanation:

In a conditional statement

If hypothesis, then conclusion

OR

Conclusion, if hypothesis.

The hypothesis goes with the if part.

f(x) = 4x - 18

f(-3) - put x = -3 to the equation of the function

f(-3) = 4(-3) - 18 = -12 - 18 = -30

f(x) = -46

We have the equation:

4x - 18 = -46       add 18 to both sides

4x = -28    divide both sides by 4

x = -7

Answer:

617.5

Step-by-step explanation:

If you expand the series by putting in [tex]n=1,n=2,n=3...[/tex] values, you will see:

68.7, 66.4, 64.1, ....

To find common difference (d) (difference in a term and its previous term) we take any term and subtract from it the term before it:

[tex]66.4-68.7=-2.3[/tex]

The sum of arithmetic series formula is:

[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex]

Where,

Substituting these values, we get:

[tex]S_{50}=\frac{50}{2}[2(68.7)+(50-1)(-2.3)]\\S_{50}=25[137.4+(49)(-2.3)]\\S_{50}=25[24.7]\\S_{50}=617.5[/tex]

Last answer choice is right.

Answer: D. 617.5 hope that helps !

Answer:

1. 29/4

2. 5

3. 6

4. 14/3

5. 29/27

Step-by-step explanation:

Answer: You the answer

Step-by-step explanation: cause your fine

Final answer:

By converting the total amount of pizza into an improper fraction and dividing it by the portion each student ate, it's determined that 13 students were fed.

Explanation:

To find out how many students were fed, we first need to convert the total amount of pizza available into a form that can be easily divided by the portion each student eats. The total pizza available is 3 1/4 small pizzas. Since each student ate 1/4 of a pizza, we can see how many times 1/4 fits into 3 1/4 to determine the number of students.

We convert 3 1/4 into an improper fraction to make the calculation easier. 3 1/4 is equivalent to 13/4. Now, we divide 13/4 by 1/4 to find out how many students were fed. This is equivalent to multiplying 13/4 by the reciprocal of 1/4, which is 4/1.

13/4 × 4/1 = 13, meaning that 13 students were fed.

Answer:

$12.60

Step-by-step explanation:

To find this, you need to remember this equation:

Starting amount x [tex]\frac{100 - percent}{100}[/tex]

Plug these values in:

18 x [tex]\frac{70}{100}[/tex] = 12.6

So the clearance price was $12.60!

Answer:

see below

Step-by-step explanation:

The "fundamental theorem of algebra" tells you the number of roots of a polynomial is equal to its degree. This includes real and complex roots and counts repeated roots the number of times they are repeated. (Real numbers are a subset of Complex numbers, so the choice of "complex" for this problem is appropriate.)

_____

The given quadratic can be solved using the quadratic formula:

for ax²+bx+c=0, the solutions are

... x = (-b±√(b²-4ac))/(2a)

Here, a=2, b=-4, c=-1, so ...

... x = (4 ±√(16 -4·2·(-1)))/(2·2)

... x = (2±√6)/2

Answer:

1. complex    2. 2+6      3. 2-6

Step-by-step explanation:

i took the test :)

Answer:

$8779.52

Step-by-step explanation:

24% = 0.24.

Each year the value of the car = 1 - 0.24 = 0.76 of the previous year.

Value after 3 years = 20,000 * (0.76)^3

=  $8779.52

Answer:  10

Step-by-step explanation: