Evaluate i^15 i^12
Show work

Answers

Answer 1

Answer:  15 = -i & 12=1

use the pattern : i, -1, -i, 1

Step-by-step explanation:

i = [tex]\sqrt{-1}[/tex]

[tex]i^{2}[/tex] = [tex]\sqrt{-1}[/tex]

[tex]i^{3}[/tex] = [tex]\sqrt{-1}[/tex]

[tex]i^{4}[/tex] = [tex]\sqrt{-1}[/tex]

the pattern just repeats from here

5 = i

6 = -1

7 = -i

8  = 1

9 = i

10 = -1

11 = -i

12  = 1

13 = i

14 = -1

15 = -i

16  = 1


Related Questions

helpppppppppppppppppp

Answers

Answer:

Dude

sheesh i only seeing 5 and 18
The answer is 5 it is the only number that can be multiplied by another number to get 10

Express -2.456 x 10 to the power of six in standard form

Answers

Answer:

-2,456,000

Step-by-step explanation:

-2.456 x  [tex]10^{6}[/tex] = -2,456,000

find second derivation for function f(x)=x²-(2/x)​

Answers

Hi there!

[tex]\large\boxed{f''(x) = 2 - \frac{4}{x^{3}}}[/tex]

[tex]f(x) = x^2 - \frac{2}{x}[/tex]

Recall the power rule:

[tex]\frac{dy}{dx} x^n = nx^{n-1}[/tex]

Rewrite the function for ease of differentiation:

[tex]f(x) =x^2 - 2x^{-1}[/tex]

Use the power rule:

[tex]f'(x) = 2x + 2x^{-2}[/tex]

Take the derivative once more:

[tex]f''(x) = 2 - 4x^{-3}[/tex]

Rewrite:

[tex]f''(x) = 2 - \frac{4}{x^{3}}[/tex]

Describe fully the single
transformation which maps
triangle T to triangle U.
-2-
-1
U
-5
-4
-3
-2
-1
0
1
2
3
4
-1

Answers

Answer:

Rotation 90⁰ clockwise about point (-1,-1)

Solve for x. Round to the nearest tenth, if necessary.

Answers

Answer:

x = 2.1

Step-by-step explanation:

We have:

[tex]\frac{x}{sin90}[/tex] = [tex]\frac{1.3}{sin38}[/tex]

=> sin38 × x = sin90 × 1.3

=> x = 1.3 ÷ sin38

=> x = 2.11155001... = 2.1

<3 Have a nice day!!

The value of x for the given triangle will be, x = 2.1.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It is used to solve problems involving angles and distances and is applied in a wide range of fields such as engineering, physics, architecture, and navigation, among others.

The value of x will be calculated as,

x / sin(90) = 1.3/ sin(38)

sin38 × x = sin90 × 1.3

x = 1.3 ÷ sin38

x = 2.11155001...

x = 2.1

The value of x will bed x =2.1.

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Someone pls help me ill give out brainliest pls don’t answer if you don’t know

Answers

Hello!

(1/3)^2x = (1/3)^x+14 <=>

<=> 2x = x + 14 <=>

<=> 2x - x = 14 <=>

<=> x = 14

Good luck! :)

which choice is the explicit formula for the following geometric sequence 0.5,-0.1, 0.02, -0.004, 0.0008

Answers

Hello,

Answer is C

[tex]a_1=0.5=\dfrac{1}{2} \\\\a_2=-0.1=-\dfrac{1}{10} =a_1*(-\dfrac{2}{10} )=a_1*(-\dfrac{1}{5} )\\\\a_3=0.02=\dfrac{2}{10^2} =a_2*(-\dfrac{2}{10} )=a_2*(-\dfrac{1}{5} )=a_1*(-\dfrac{1}{5} )^2\\...\\a_n=a_1*(-\dfrac{1}{5} )^{n-1}\\\\\boxed{a_n=0.5*(-0.2)^{n-1}}\\[/tex]

[tex]\frac{a^{3}b^{5}}{a^{4}b}[/tex]

Answers

Answer:

b^4 / a

Step-by-step explanation:

I have attached the explanation above. hopefully this will help

MNPQ is a rectangle. Find the measure of <1 and <2

Answers

Answer: ∠1 = 48°, ∠2 = 42°

Step-by-step explanation:

Because it's a rectangle, NP and MQ are parallel lines. ∠2 and (3x)° are alternate interior angles and are therefore equal. NM and PQ are also parallel lines. ∠1 is equal to (2x + 20)° because they're also alternate interior angles.

∠M = 90° = ∠1 + (3x)° = (2x + 20)° + (3x)°

2x + 20 + 3x = 90

2x + 3x = 90 - 20

5x = 70

x = 14

Because ∠1 = (2x + 20)°,

∠1 = 2x + 20 = 2(14) + 20 = 28 + 20 = 48°

Because ∠2 = (3x)°,

∠2 = 3x = 3(14) = 42°

(I hope this is right :\)

The x- intercepts of a parabola are (0,-6) and (0,4). The parabola crosses the y- axis at -120. Lucas said that an equation for the parabola is y=5x^2+10x-120 and that the coordinates of the vertex are (-1, -125). Do you agree or disagree? List why?

Answers

Given:

The x- intercepts of a parabola are (0,-6) and (0,4).

The parabola crosses the y- axis at -120.

Lucas said that an equation for the parabola is [tex]y=5x^2+10x-120[/tex] and that the coordinates of the vertex are (-1, -125).

To find:

Whether Lucas is correct or not.

Solution:

The x- intercepts of a parabola are (0,-6) and (0,4). It means (x+6) and (x-4) are the factors of the equation of the parabola.

[tex]y=a(x+6)(x-4)[/tex]             ...(i)

The parabola crosses the y- axis at -120. It means the equation of the parabola must be true for (0,-120).

[tex]-120=a(0+6)(0-4)[/tex]

[tex]-120=a(6)(-4)[/tex]

[tex]-120=-24a[/tex]

Divide both sides by -24.

[tex]\dfrac{-120}{-24}=a[/tex]

[tex]5=a[/tex]

Substituting [tex]a=5[/tex] in (i), we get

[tex]y=5(x+6)(x-4)[/tex]

[tex]y=5(x^2+6x-4x-24)[/tex]

[tex]y=5(x^2+2x-24)[/tex]

[tex]y=5x^2+10x-120[/tex]

So, the equation of the parabola is [tex]y=5x^2+10x-120[/tex].

The vertex of a parabola [tex]f(x)=ax^2+bx+c[/tex] is:

[tex]Vertex=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]

In the equation of the parabola, [tex]a=5,b=10,c=-120[/tex].

[tex]-\dfrac{b}{2a}=-\dfrac{10}{2(5)}[/tex]

[tex]-\dfrac{b}{2a}=-\dfrac{10}{10}[/tex]

[tex]-\dfrac{b}{2a}=-1[/tex]

Putting [tex]x=-1[/tex] in the equation of the parabola, we get

[tex]y=5(-1)^2+10(-1)-120[/tex]

[tex]y=5-10-120[/tex]

[tex]y=-125[/tex]

So, the vertex of the parabola is at point (-1,-125).

Therefore, Lucas is correct.

OMG HELP NOW PLZZ <3

Answers

Answer:

I think it would be Maxine's, since they did more tests.

Who is sometimes referred to as the Columbus of statistics because his book made a fundamental contribution by attempting to demonstrate the quantitative characteristics of birth and death data

Answers

Answer: John Graunt

Step-by-step explanation:

John Graunt is referred to as the Columbus of statistics because his book made a fundamental contribution by attempting to demonstrate the quantitative characteristics of birth and death data.

He's regarded as the founder of demography which is the statistical study of the population of human beings.

you've run 250 ft of cable that has a loss rate of 3.6 dB per 100 ft. what is your total loss?

Answers

Answer:

2.5 dB/100 ft

Explanation:

If 5 dB was lost after 200 ft of cable and 100 ft is half of 200 ft, then the rate of loss should be 2.5 dB per 100 ft.

Step-by-step explanation:

The total loss is 9 dB

Since we have 250 ft of cable that has a loss rate of 3.6 dB per 100 ft, we need to find the total loss of the 250 ft of cable.

To find this total loss, we multiply the loss rate by the total length of cable.

So, the total loss for the 250 ft of cable, L = loss rate × length of cable.

Since loss rate = 3.6 dB per 100 ft and the length of cable = 250 ft, substituting the values of the variables into the equation, we have

L = loss rate × length of cable.

L =  3.6 dB/100 ft × 250 ft.

L = 3.6 dB/10  × 25.

L = 3.6 × 25/10 dB

L = 3.6 × 2.5 dB

L = 9 dB

So, the total loss is 9 dB

Learn more about dB loss here:

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Solve the following system of equations algebraically.

y=2x-12
y=x+22+3

Answers

Answer:

x=37

Step-by-step explanation:

because

y=y

or as, 2x-12=x+22+3

or as, 2x-x=12+22+3

or as, x = 37

____________ was designed to tabulate the 1890 census and used cards with designated areas representing data fields.

Answers

Answer:

Hollerith tabulating machine

Step-by-step explanation:

The Hollerith tabulating machine was invented by Herman Hollerith in other to assist in the data processing of the United States 1890 election. This machine was used to read and summarize the information stored on punchcards. This machine paved the way for the development of enhanced models which were employed for accounting and some other aspects related to business management.

Given that g(x) = 2x ^ 2 - 2x + 8 , find each of the following. a) g(0) b) g(- 2) C) g(3) d) g(- x) e) g(1 - t)

Answers

Answer:

[tex]g(-2)=20[/tex]

Step-by-step explanation:

Given [tex]g(x)=2x^2-2x+8[/tex], substitute what is in the parentheses for [tex]x[/tex] to find an output.

For [tex]g(-2)[/tex], the term [tex]-2[/tex] is in the parentheses. Thus, substitute [tex]x=-2[/tex] into [tex]2x^2-2x+8[/tex] to find [tex]g(-2)[/tex]:

[tex]g(-2)=2(-2)^2-2(-2)+8,\\g(-2)=2\cdot 4+4+8,\\g(-2)=8+4+8,\\g(-2)=\boxed{20}[/tex]

Answer:

a) 8

b) 20

c) 20

Step-by-step explanation:

a) Insert X=0 from g(0) to the equation: 2(0) power of 2 - 2x0 +8.

b) Insert X=(-2) from g(-2) to the equation: 2(-2) power of 2 - 2x(-2) +8.

c) Insert X=3 from g(3) to the question 2(3) power of 2 - 2x3 +8.

Parallelogram A B C D is shown. Line segment X Y goes from point X on side A B to point Y on side C D to form 2 trapezoids.
Figure ABCD is a parallelogram. Two trapezoids are created using line segment XY such that AX ≅ CY.

What is true about the areas of the trapezoids?

Each area is equal to half of the area of ABCD.
The area of AXYD is less than the area of BXYC.
The area of AXYD is greater than the area of BXYC.
Each area is equal to the area of ABCD.

Answers

Answer:

Each area is equal to half the area of ABCD

Step-by-step explanation:

AX ≅ CY    

In parallelogram, opposite sides are equal.

AB = CD

AX + XB = CY + YD

 CY + XB = CY + YD

          XB = CY + YD - CY

XB  = CY

Both trapezoids have equal area

Area of AXYD + area of BXYC =  area of ABCD        

Answer:

A. )  Each area to equal to half of the area of ABCD

Step-by-step explanation:

Edge 2021

A casserole is removed from a 375oF oven and cools to 190oF after 25 minutes in a room at 68oF. How long (from the time it is a removed from the oven) will it take the casserole to cool to 105oF

Answers

Answer:

57.3 minutes

Step-by-step explanation:

We know that the temperature as a function of time of an object is described by the equation:

[tex]T(t) = T_a + (T_0 - Ta)*e^{-k*t}[/tex]

Where:

k is a constant

Tₐ =  room temperature = 68°F

T₀ =  initial temperature of the object = 375°F

Replacing these in our equation we will get

T(t) = 68°F + (375°F - 68°F)*e^{-k*t} = 68°F + (307°F)*e^{-k*t}

And we know that after 25 minutes, at t = 25min, the temperature of the casserole is 190°F

then:

T(25min) = 190°F = 68°F + (307°F)*e^{-k*25 min}

Now we can solve this for k:

190°F = 68°F + (307°F)*e^{-k*25 min}

190°F - 68°F = (307°F)*e^{-k*25 min}

(122°F)/(307°F) = e^{-k*25 min}

Now we can apply the natural logarithm in both sides:

Ln( 122/307) = Ln(e^{-k*25 min}) = -k*25min

Ln( 122/307)/(-25 min) = k = 0.0369 min^-1

Then the temperature equation is:

T(t) = 68°F + (307°F)*e^{-0.0369 min^-1*t}

Now we want to find the value of t such that:

T(t) = 105°F = 68°F + (307°F)*e^{-0.0369 min^-1*t}

We can solve this in the same way:

105°F - 68°F =  (307°F)*e^{-0.0369 min^-1*t}

37°F =  (307°F)*e^{-0.0369 min^-1*t}

(37°F)/(307°F) = e^{-0.0369 min^-1*t}

Ln( 37/307) = -0.0369 min^-1*t

Ln( 37/307)/( -0.0369 min^-1 ) = 57.3 min

So after 57.3 minutes, the temperature of the casserrole will be 105°F

if you know the value of X and Y.. please let me know.​

Answers

Answer: X= 35° and y= 20°
Hopefully, this was helpful
if i’m not wrong the shape is trapezium, the side should be the same which mean it’ll be 65 ay the y side and 125 at x side. so we all can see the first triangle is 90 which we can get x with 125-90=35 so the answer for x=35 then to find x we just need minus the whole sec triangle which is 180-125-35=20 so y=20

hope you understand what i’m trying ti explain for you

a salesperson earns a monthly salary of $500 and an 8% commission on all sales for that month. write an equation to model this relation

Answers

Answer:

pay = $500 + (.08*Sales)

Step-by-step explanation:

Nissa is going to plant 485 485485 trees this year. If Nissa plants 5 55 orchards of trees, how many trees will be in each orchard?

Answers

Answer:

There will be 97 trees in each orchard.

Step-by-step explanation:

Given that,

Nissa is going to plant 485 trees this year.

Nissa plants 5 orchards of trees.

We need to find the number of trees in each orchard. Let it is n. So, we can find it as follows :

[tex]n=\dfrac{485}{5}\\\\n=97[/tex]

So, there will be 97 trees in each orchard.

can i get a little help on this one please? asap.

Answers

³√5 / ⁴√5 = ¹²√5 = 5^1/12

5^1/12

Answer:

the answer is  5/|1 5

Step-by-step explanation:

1. make r the subject of the relation. 2. Find the value of r when s=117, m = 2 and n=-3. m=r-s ÷2nr​

Answers

Answer:

Hence, the required answers are (i) r= -s/(2nm-1) and r=g.

Step-by-step explanation:

solution: m= r-s/2nr

i) m= r-s/2nr  2)  m(2nr) = r-s (i) s=117 ,m=2, n=-3

2) 2xnxmxr= r-s        2) r= -s/(2nm-1)

3) move the "r" on the right to the 2)   r=  -117/(2x(-3)x2)-16

-2nrm-r= -s

- r(r-2nm-1)= -s                     2)  r= (-117/-13)=)r=g

- r= -s/(2nm-1)

Hence, the required answers are (i) r= -s/(2nm-1) and r=g.

[tex]\text{Solve the system of equations:}\\\\\left \{ {{y=3x+5} \atop {y=-4x+7}} \right.\\\\\text{Thank you.}[/tex]

Answers

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

(0.286, 5.587)

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

I have graphed the two equations in a program. When graphed, the lines intersect at point (0.286, 5.587). See the graph attached.

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

The number of clicks for a search text ad is 50 and the number of impressions is 5000. The CTR would be Group of answer choices 1% 2% 5% 10%

Answers

Given:

Clicks = 50

Impressions = 5000

To find:

The CTR percentage.

Solution:

We know that,

[tex]CTR=\dfrac{\text{Clicks}}{\text{Impressions}}\times 100[/tex]

Substituting the given values, we get

[tex]CTR=\dfrac{50}{5000}\times 100[/tex]

[tex]CTR=\dfrac{1}{100}\times 100[/tex]

[tex]CTR=1\%[/tex]

Therefore, the correct option is A.

The arrow on the spinner will be spun one more time. Based on these results, what is the probability that the arrow will land on the purple section?

Answers

The answer would be B. 12/60 is simplified down to 1/5

If
5
3 cosα = in the first quadrant, what does cot α
equal?

Answers

Answer:

5/4

Step-by-step explanation:

To Find :-

cot a .

Solution :-

By question ,

=> cos a = 5/3 = b/h

=> p = √ 5² - 3² = √ 25 -9 = 4

Therefore ,

=> cot a = b/p = 5/4

I need help plsss, check all that apply

Answers

they lie in the same plane is the answer ;)

There are 120 teachers in a ABC school. Determine the value of k using the systematic sampling technique to select a sample of 40 teachers.

Answers

Answer:

K=30

Step-by-step explanation:

120÷4 = 30

k=30

The value of k for selecting 40 teachers out of 120 is 1 / 3.

What is probability?

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Given that there are 120 teachers in an ABC school and 40 teachers need to be selected,

The value of k will be calculated by the concept of probability as below,

k =  Number of favourable outcomes / Number of sample

k = 40 / 120

k = 1/3

Therefore, the value of k for selecting 40 teachers out of 120 is 1 / 3.

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PLEASE ANSWER QUICK!!! 30 POINTS

The figure has angle measures as shown.
A
19x - 15
26x + 20
D
9x + 25
C
B
What is the measure of ZABD?
O 150°
O 120°
O 70°
O 30°

Answers

Answer is 150°. Work is attached

Answer:

Solution given;

<ABD=<BAC+<ACB

Since exterior angle of a triangle is equal to the sum of two opposite interior angle

26x+20=19x-15+9x+25

solve like terms

26x+20=28x+10

subtracting both by 10

26x+20-10=28x+10-10

Subtracting both side by 26x

10=28x-26x

2x=10

dividing both side by 2

2x/2=10/2

x=5

Now

<ABD=26*5+20=l50°

The value of <ABD is 150°

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