Mathematics High School

If i = sqrt -1 what is the value of i3

A. -1
B. i
C. 1
D. -i

Answers

Answer 1
i^3  = i * i * i  = i^2 * i  = -1 * i = -i Answer

Its D
Answer 2

Answer:

The value of i3 is equal to D. -i

Step-by-step explanation:

We can find the answer by taking the definition of i :

i = sqrt(-1)        (1)

i ^2 = (sqrt(-1)) ^2 = -1             (2) because square root and squaring are inverse operations

so from (2)

i ^3= i ^2* i = -1*i = -i

So -i is the final answer or  – (sqrt(-1))         which is the same

Related Questions

What is the 12th term of the sequence? 3, −9, 27, −81, 243, ...

531441
−531441
177147
−177147

Answers

The answer would be B. -531,441.

There are 2 ways you can find this.

A. You can find this by starting with 3, and multiply -3 then multiply -3 to each product after that 11 times. Or...

B. Simply find 3 to the 12th power. Then add a negative since each even term (term 2, 4, 6, etc) are negative.

I hope this helps!

5/8 ≠ (3/4 + 1/16) because 5/8 < 3/4 EXPLAIN THIS PROBLEM AND WHAT IT MEANS

Answers

5/8 = 3/4+1/16 is false because, the final values compared on each side of equation is not the same

- 5/8 = 0.625
- 3/4+1/16 = 0.8125
 
0.625 = 0.8125, it is not equal but less than



PLLLLLLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Find the value of n.

Answers

The answer to this question is 23. How you get this is by adding all the sides like this: 2n+6+135+151+140+63=540. Then you just solve the equation.

PLS HELP ME ASAP WITH 1!

BRAINLIEST WILL BE GIVEN HOPEFULLY

Do question 2 if u can, if u can’t it’s fine

(Random answers gets moderated)

Answers

All of these make use of the expansion
   (a + b)² = a² + 2ab + b²
You would do well to memorize this "formula." Of course, it also helps to be able to double (or halve) a number, and to know the squares of small integers.

1.
   x² +2x +1
   x² -6x +9
   x² +12x +36
   x² -0.4x +0.04
   4x² +28x +49
   9x² +30x +25

2.
   (x + 4)²
   (x + 3)²
   (x - 9)²
   (x - 5)²

3. (12/2)² = 36

4. ±2√49 = ±14

What value of c makes the trinomial below a perfect square x2 + 7x + c?

Answers

we have that
x² + 7x + c
Group terms that contain the same variable
(x² + 7x )+ c
Complete the square. Remember to balance the equation 
(x² + 7x+3.5² )+ c-3.5²

Rewrite as perfect squares

(x+3.5)²+ c-3.5²
so
c-3.5² must be zero
c-3.5²=0------- c=3.5²------> c=12.25

the answer is
the value of c must be 12.25

Answer:49/4

Step-by-step explanation:

How can you prove a triangle is a right triangle? select one:a. use the distance formula to see if at least two sides are congruent.b. use the slope formula to see if any sides are perpendicular.c. use the distance formula to see if all three sides are congruent.d. use the slope formula to see if any sides are parallel?

Answers

B.
__________________

The point (-1.3, -1.7) is located in which quadrant?

Answers

Hello!

This point would be located in the third quadrant.

Why?

First Quadrant: (2, 2)
Second Quadrant: (-2, 2)
Third Quadrant: (-2, -2)
Fourth Quadrant: (2, -2)

Algebra question ( Matrices and Determinants ) 20 points

Answers

The correct answer is option A
A. -30 
The determinant of B = -18*1 -3*4 = -18-12 = -30

I WILL GIVE BRAINLIEST The area of the surface of the trampoline (square) is equal to twice its perimeter. Find the dimensions. length= 4x ft., width= (x+6) ft.

FACTORING POLYNOMIALS/SOLVE THE EQUATION BY FACTORING HOMEWORK

Answers

Given that the area is equal to twice the perimeter and the dimensions are:
length=4x ft, width=(x+6) ft
the perimeter will be:
P=2(L+W)
P=2(4x+(x+6))
P=2(4x+x+6)
P=2(5x+6)
P=(10x+12)

Area of the rectangle is:
A=4x(x+6)
A=4x²+24x
but:
2P=A
thus
2(10x+12)=4x²+24x
20x+24=4x²+24x
thus
4x²+4x-24=0
x²+x-6=0
x²-2x+3x-6=0
x(x-2)+3(x-2)=0
(x-2)(x+3)=0
thus the answer is:
x=-3 or x=2
thus
length=4x=4*2=8 ft
width=(x+6)=(2+6)=8 ft

What is true about side AB and side AD?

Answers

Side AB and side AD are perpendicular because they cross at a ninety degree angle, and the sides are also the same length. 

Haley sings for $1,000 an hour. Her rate increases by 50% after midnight. If she sings one
night from 8:30 pm until 1:00 am, how much should she be paid?
a) $4500 b) $5000 c) $5500 d) $6000

Answers

The Answer is B) 5000$

How much of a 14% iodine solution should be added to 89 ounces of a 47% iodine solution to get a 29% solution

Answers

whatever% of anything is just (whatever/100) * anything.

x = ounces of 14% iodine.

y = ounces of 29% iodine.

we know that in a 14% iodine solution, 14% is iodine and the rest is something else, we also know that "x" ounces of the solution have 14% of iodine, how much is that?  (14/100) * x, or 0.14x.

likewise, in the 89 ounces of 47% solution there is (47/100) * 89 of iodine.

and likewise as well, in "y" ounces of 29% iodine there is (29/100) * y, or 0.29y of iodine.

bearing in mind that, whatever "x" and "y" may be, x + 89 = y, and that the sum of the iodine amounts also will equate 0.29y.

[tex]\bf \begin{array}{lccclll} &\stackrel{ounces}{amount}&\stackrel{\%~of~iodine}{quantity}&\stackrel{iodine~oz}{amount}\\ &------&------&------\\ \textit{14\% solution}&x&0.14&0.14x\\ \textit{47\% solution}&89&0.47&41.83\\ ------&------&------&------\\ mixture&y&0.29&0.29y \end{array} \\\\\\ \begin{cases} x+89=\boxed{y}\\ 0.14x+41.83=0.29y\\ --------------\\ 0.14x+41.83=0.29\left( \boxed{x+89} \right) \end{cases} \\\\\\ 0.14x+41.83=0.29x+25.81\implies 16.02=0.15x \\\\\\ \cfrac{16.02}{0.15}=x\implies 106.8=x[/tex]

WILL VOTE BRAINIEST IF CORRECT(must be next few minutes): The formula for the area of circle A is Area=πr2 . Sector CAB is a fraction of circle A. In degrees, the fraction is θ/360∘ . In radians, the fraction is _____. Inserting this fraction into the formula for the area of a circle, and then simplifying, results in the formula _____.

(image attached)
choices: 2pi0, 0pi, 0/2pi, area=0r^2, area= 2pi0r^2, area= 0/2r^2

Answers

Final answer:

The fraction of the sector of a circle in radians is (θπ/180). Substituting this fraction into the formula for the area of a circle, and simplifying, results in the formula for the area of the sector being A = (θπ/360) * r^2.

Explanation:

In a circle, the angle in degrees is often converted to radians for calculations. A full circle is equivalent to 360 degrees or 2π radians. Therefore, if the sector angle is θ degrees, then in radians, the equivalent is (θ/360) * 2π = θπ/180.

Inserting this into the formula for the area of a circle, which is A = πr2, the area A of the sector becomes a fraction of the full circle's area, which is calculated as follows: (θ/360) * A = (θ/360) * πr2 = (θπ/180) * r2. Simplifying this results in the formula A = (θπ/360) * r2.

Learn more about Circle Sector Area here:

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Final answer:

For a sector in a circle, the fraction is θ/2π in radians. After substituting this into the formula for circle's area, we get the area of sector as Area = (θr²)/2.

Explanation:

The fraction in radians for a sector in a circle is θ/2π, because there are 2π radians in a whole circle. As the formula for the area of circle A is Area=πr², when we insert this fraction, which represents the proportion of the circle that Sector CAB occupies, we get the formula for the area of a sector: Area= (θ/2π) * πr². This simplifies to Area= (θr²)/2, as the π's cancel out. This formula says that the area of a sector is proportionate to its central angle and the square of the radius of the circle.

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Divide 2y2 + 8 by 2y + 4. Which expression represents the quotient and remainder?



Answers

Final answer:

To divide 2y² + 8 by 2y + 4, use long division to find the quotient and remainder.

Explanation:

To divide 2y² + 8 by 2y + 4, we can use long division. Here are the steps:

Divide the first term of the dividend by the first term of the divisor, which gives us y.

Multiply the entire divisor by y to get 2y² + 4y.

Subtract 2y² + 4y from the dividend 2y² + 8 to get 4.

Next, divide 4 by 2y + 4, which gives us 2.

Finally, we have a remainder of 0.

Therefore, the quotient is y + 2 and the remainder is 0.

Multiply. 0.35 × 0.003 =

Answers

0.00105. or 21/20000,1.05x10^-3

Answer:

0.00105

Step-by-step explanation:

What is the length of an arc cut off by an angle of 3 radians on a circle of radius 8 inches?

Answers

A formula for arc length, s, given the radius, r and central angle, Ф (in radians) is s = r × Ф.

s = 8 × 3 = 24 inches

How does the volume of an oblique cylinder change if the radius is reduced to 2/9 of its original size and the height is quadrupled?

A. V=2/81pir^2h
B. V=16/81pir^2h
C. V=4/9pir^2h
D. V=16/9pir^2h

Answers

New volume is given by:
New volume=(old volume)×(4×2/9×2/9)
simplifying the above we get:
New volume=(old volume)×16/81
Thus the new volume is 16/81 times the old volume
old volume=πr²h
Hence:
Answer:16/81πr²h



3(−4x) + 3(5) = 12

−12x + 15 = 12

−12x + 15 − 15 = 12 − 15

−12x = −3

x =

Answers

x = -3 / -12 = 1/4 Answer

Answer:   1/4

don't forget to rate and thank plz.

A line has a slope of -5 and passes through (1,-1). Which is the equation of the line in point-slope form?

Answers

The general form for point slope is y-y1=m(x-x1). Just substitute the information. y+1=-5(x-1).

How many times larger is 4 x 1016 than 5 x 108?

Answers

4 × 1,016 = 4,064

5 × 108 = 540

4,064 ÷ 540 = 7.5

Answer = 7.5

~Aamira~

Hope this helped☺☺

They traveled 200 kilometers in total, and they biked 40 kilometers more than they were bussed. how many kilometers did they travele by bike

Answers

Let the distance travelled by bus be x and the distance travelled by bike be (x+40)

So...

x + (x+40) = 200

2 x = 160 

1 x = 80            

200 - 80 = 120km by bike. 

Choose an example of a fixed expense and an example of a variable expense, and explain why they are classified that way.

Answers

Fixed costs are those that do not depend on the level of production of a company and whose only way to avoid them is to close the company. For example, the cost of renting the plant or machinery.
 Variable costs are those that depend on the level of production of the company. For example, the cost of raw material. In a company that produces juices, the bottles will be part of the cost of raw material, and the amount of bottles to use depends on the amount of juice to produce, if this amount increases the cost of raw material will also increase. On the other hand, the rental cost of the place where the juices are produced will be the same regardless of the amount of juices that are produced, for this reason it is considered a fixed cost.
Final answer:

Fixed costs, such as rent, remain constant regardless of production levels, while variable costs, like raw material expenses, will fluctuate based on the level of production.

Explanation:

Firms classify their costs into two categories: fixed costs and variable costs. Fixed costs are expenses that do not change regardless of the level of production. For instance, a lease on a retail space would be considered a fixed cost as it remains the same whether you sell a lot or a little. On the other hand, variable costs are directly tied to the level of production. For example, the cost of buying materials to produce a product tends to rise as the level of production increases. It's variable because the more you produce, the more materials you would need, and therefore the cost varies with the level of output.

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Given that f(x) = x2 − 4x − 3 and g(x) = the quantity of x plus three, over four, solve for f(g(x)) when x = 9. 



−6

3

6

9

Answers

Hello! To find the composition of functions we want to take all the x values in f(x) and replace them with g(x). Then to solve for a specific value, we plug in that value for x. Let's look at the steps below
[tex] f(x)=x^{2} -4x-3[/tex]
[tex]g(x)=\frac{x+3}{4}[/tex]

So we find
[tex]f(g(x))=f(g(9))=(\frac{9+3}{4})^2 - 4(\frac{9+3}{4})-3[/tex]
[tex] =3^2 - 4(3)-3 [/tex]
[tex]= 9-12-3=-6[/tex]
Now we want to find the solution when x is 9 so we plug in a 9 whenever we see an x




Final answer:

The solution to f(g(x)) when x = 9 is -6.

Explanation:

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the codomain), where each input is related to exactly one output.

Given:

f(x) = x2 - 4x - 3, g(x) = (x + 3) / 4

To find f(g(x)) when x = 9:

Calculate g(9): Substitute x = 9 into g(x) to get (9 + 3) / 4 = 12 / 4 = 3Substitute g(9) into f(x): Substitute g(9) = 3 into f(x) to get f(3) = 32 - 4(3) - 3 = 9 - 12 - 3 = -6

Therefore, f(g(x)) when x = 9 is -6.

For which angle is secant undefined?
30°
45°
180°
270°

Answers

180
The secant is undefined at angle values that represent 1/4 and 3/4 of a full circle. At these angles, the triangle geometrically vanishes into a simple line segment on the Y axis. The value of the triangle's adjacent side is zero and division by zero is undefined.

Answer:

the answer is 180 degrees

Step-by-step explanation:

i used my head and my google maths

katy buys ‘x’ cakes.
Gugu buys 3 times as many cakes as katy.
Deanna buys 2 more cakes than Katy.

Each cake costs 85p
The total of the cakes is £52.70

How many cakes did each girl buy?

Answers

Answers:
Katy bought 12 cakes
Gugu bought 36 cakes
Deanna bought 14 cakes

Explanation:
We are given that:
Katy bought x cakes 
Gugu bought 3 times as many as Katy. This means that Gugu bought 3x cakes
Deanna bought 2 cakes more than Katy. This means that Deanna bought x+2 cakes

Total number of cakes bought = x + 3x + x + 2 = 5x + 2 cakes

We know that the price of each cake is 85 p = £0.85 and that the total amount paid is £52.7
This means that:
(5x+2)(0.85) = 52.7
4.25x + 1.7 = 52.7
4.25x = 52.7 - 1.7
4.25x = 51
x = 51 / 4.25
x = 12

Now, we will get the number of cakes that each bought as follows:
Katy bought x cakes = 12 cakes
Gugu bought 3x cakes = 3(12) = 36 cakes
Deanna bought x+2 cakes = 12 + 2 = 14 cakes

Hope this helps :)

Answer:

Katy bought 12 cakes

Gugu bought 36 cakes

Deanna bought 14 cakes

Step-by-step explanation:

Rewrite the expression log(3x) as an equivalent logarithmic expression using only addition.

Answers

[tex]\log 3 + \log x[/tex]

Which is the correct form of the quadratic formula? A) x = b ± b2 - 4ac a B) x = b ± b2 - 4ac 2a C) x = - b ± b2 - 4ac a D) x = - b ± b2 - 4ac 2a

Answers

Hello!

The quadratic formula is 

[tex]x = \frac{-b +- \sqrt{ b^{2}-4ac } }{2a} [/tex]

So the answer is D

Hope this helps!

The correct form of the quadratic formula is x = (-b±√(b² - 4ac)) / (2a).

Hence, option D) is the correct answer.

What is a Quadratic Equation?

Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;

ax² + bx + c = 0

Where x is the unknown

To solve for x using the quadratic formula;

x = (-b±√(b² - 4ac)) / (2a)

The correct form of the quadratic formula is x = (-b±√(b² - 4ac)) / (2a).

Hence, option D) is the correct answer.

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Make a box ­and ­whisker plot of the data.

24, 18, 29, 21, 16, 23, 13, 11

Answers

To make a box and whisker plot you must first order the data:

11, 13, 16, 18, 21, 23, 24, 29

Then find the median:

19.5

Then split the data into two sections by the median:

11, 13, 16, 18 and 21, 23, 24, 29

Now find the medians of those sets

14.5 and 23.5

With this information we can conclude Option C is the correct plot

Hope this helps!
none of those are correct.
minimum-11
lower quartile-17
median-23.5
upper quartile-26.5
maximum-29

A company spent 32% of its annual budget developing a new machine. What fraction of the company's budget was spent developing the new machine?

Answers

The answer is 8/25! This is because 32% is equal to 32/100, when you simplify this it equals 8/25.

We have been given that the company spent 32% of its annual budget developing a new machine.

Let us convert the percentage to fraction.

[tex]32 \%=\frac{32}{100} \\ \\ 32 \%=\frac{4\times 8}{4\times 25}\\ \\ \text{Cancel 4 from numerator and denominator}\\ \\ 32 \%=\frac{8}{25}[/tex]

Thus, when we convert 32% to fraction that will be equal to 8/25.

Hence, [tex]\frac{8}{25}[/tex] company's budget was spent developing the new machine.

Sharon wants to know the difference between the average amount she stacked and the average amount Diane stacked. Which operation would she use to find the difference?

Answers

Sharon would subtract the amount that she stacked from Diane to figure out the difference.

Hope this helped :D
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