What is the value of i^97 - i

Answers

Answer 1

Answer: $if\ i\ is\ the\ imaginary\ unit\ (i=√(-1)\Rightarrow i^2=-1):\n\ni^(97)-i=i(i^(96)-1)=i(i^(48\cdot2)-1)=i[(i^2)^(48)-1]=i[(-1)^(48)-1]\n\n=i(1-1)=i\cdot0=0\n\ntherefore\ \boxed{i^(97)-i=0}$

Answer 2

Answer:

this can also be explained as b on edg

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Can someone help me plz I'm confused

Answers

9.

2x+3+x+9 = 180 => 3x = 168 => x = 56;
m(<ABD) = 2*56 + 3 = 115.

. Lisa spent $67 for a skateboard and $25 for a protective helmet.. . . . What percent of the total amount that Lisa spent was the price of the skateboard? A. . . 62.7%. . . . . . . . .
B. . . 72.8%. . . . . . . . .
C. . . 75%. . . . . . . . .
D. . . 81.7%. .

Answers

Total amount: $67 + $25 = $92
p = ( 67 x 100 ) : 92 = 72.826 ≈ 72.8 %
Answer: 72.8 %

Divide 7/24 by 35/48 and reduce the quotient to the lowest fraction.A. 4/10
B. 2/5
C. 42/48
D. 245/1152

Answers

the answer is B.2/5
flip 35/48 so it looks like this 48/35 then chance the divide symbol and put the multiply symbol 7*48=336, and 24*35=840. your answer is 336/840 then simply reduce to get 2/5.

  7 35
------ ÷ -------- = ?
24 48

48
------
35

  7   48
------- × --------
24 35

7 × 48 = 336

24 × 35 = 840

336 2
-------- = -------
840 5

SO, Your answer would be B. 2/5.

  7 35 2
------ ÷ ------- = ------- (Simplest Form)
24 48 5

Hope I helped:P

what is the solution to the system of equations? y =1/3 x – 10 2x y = 4 (–8, 6) (–6, 16) (6, –8) (16, –6)

Answers

Answer:

Option C is correct.

Solution to the given system of equation is (6 , -8)

Step-by-step explanation:

Given the system of equation:

$y= (1)/(3) x-10$ ......[1]

$2x+y =4$ .....[2]

Substitute the equation [1] in [2] we get;

$2x +(1)/(3)x -10 =4$

Combine like terms;

$(7)/(3)x -10 =4$

Add 10 to both side of an equation:

$(7)/(3)x -10 +10=4+10$

Simplify:

$(7)/(3)x =14$

Divide both sides by $(3)/(7)$ we get;

$(3)/(7) * (7)/(3)x = 14 * (3)/(7)$

Simplify:

x = 6

Substitute the value of x =6 in equation [1] we get;

$y= (1)/(3)(6)-10$

$y= 2-10$

Simplify:

y = - 8

therefore, the solution to the given system of equation is; (6 , -8)

You can also see in the graph as shown below:

y = 1/3 x - 10
2x + y = 4
2x + 1/3 x - 10 = 4
7/3 x = 14
x = 6
y = 1/3(6) - 10 = 2 - 10 = -8
Therefore solution is (6, -8)

If the vertices of triangle bcd are b(-3,3), c(3,5), and d(-1,0), what is the perimeter

Answers

distance formlula
D= $\sqrt{(x2-x1)^(2)+(y2-y1)^(2)}$

when you want to find the distance between points (x1,y1) and (x2,y2)

we nee
distace from
b to c
c to d
d to b

b to c is (-3,3) to (3,5)
D= $\sqrt{(3-(-3))^(2)+(5-3)^(2)}$ =2√10

c to d is (3,5) to (-1,0)
D= $\sqrt{(-1-3)^(2)+(0-5)^(2)}$ =√41

d to b is (-1,0) to (-3,3)
D= $\sqrt{(-3-(-1))^(2)+(3-0)^(2)}$ =√13

add

b to c+c to d+d to b=2√10+√41+√13

perimiter=2√10+√41+√13 units

One third of a number is 12 less than the number itself

Answers

Answer:

Step-by-step explanation:

1/3 n = n - 12 Cross multiply

n = 3(n - 12)

n = 3n -36

2n = 36

n = 36/2

n = 18

let the number = n
(1/3)n=n-12
(3)(1/3)n=(3)n-12
n=3n-36
-2n=-36
n=18

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UQuestion 23 ptsSelect the three equations that are also equivalent to 0.5 +10b+4= 19.5A. 106 +4= 19.5B. 10b +4=19C. 2(0.5 +10b+ 4) = 39D. 10b= 19.5E. 10b= 15