what does i^739 equal? explain how you found your answer.
========================================================
Explanation:
i = sqrt(-1)
Lets list out the first few powers of i
i^0 = 1i^1 = ii^2 = -1i^3 = i*i^2 = i*(-1) = -ii^4 = (i^2)^2 = (-1)^2 = 1By the time we reach the fourth power, we repeat the cycle over again (since i^0 is also equal to 1). The cycle is of length 4, which means we'll divide the exponent over 4 to find the remainder. Ignore the quotient. That remainder will determine if we go for i^0, i^1, i^2 or i^3.
For example, i^5 = i^1 because 5/4 leads to a remainder 1.
Another example: i^6 = i^2 since 6/4 = 1 remainder 2
Again, we only care about the remainder to find out which bin we land on.
-------------
Turning to the question your teacher gave you, we have,
739/4 = 184 remainder 3
So i^739 = i^3 = -i
-i is the final answer--------------
Side notes:
if i^a = i^b, then a-b is a multiple of 4Recall that the divisibility by 4 trick involves looking at the last two digits of the number. So i^739 is identical to i^39.Vincent saves $8 each week. How much does he save in a year?
$56
$60
$416
$2960
Answer:
$416
Step-by-step explanation:
weeks in a year is 52 weeks
52×8=416$
200m - 125m + 48,750 = 50,000 - 175m
Answer:
m = 5
Step-by-step explanation:
200m - 125m + 48,750 = 50,000 - 175m
=> 75m + 48,750 = 50,000 - 175m
=> 75m + 175m = 50,000 - 48,750
=> 250m = 1250
=> m = 5
Hoped this helped.
Lynne walks dogs every day to earn money. The fees she charges per month are 1 dog,$40;2 dogs,$37.25 each;3 dogs,$34.50 each;4 dogs,$31.75 each. A pet store wants her to walk 8 dogs if the pattern continues, how much will Lynne charge to walk each of the 8 dogs.
Answer:
The answer is $20.75
A dog: 40$
2: $37.25
3: $34.50
4: $31.75
5: $29
6: $26.25
7: $23.50
8: $ 20.75
Step-by-step explanation:
Minus $2.75 is the pattern
Answer:
$ 59.25
Step-by-step explanation:
The given rates form an AP (Arithmetic Progression).
Let the cost of walking 1 dog be taken as the first term
and,
cost of walking 2 dogs as second term,
we notice that the price per dog is decreasing by 2.75 $ each time the number of dogs is increasing by 1.
So, it's safe to say that
In the AP:
First term is $ 40
Common difference is $ 2.75
Finding the charge to walk each of the eight dogs is like finding the 8th term of the given Series.
Formula for n-th term of a depreciating AP in terms of common difference(d) and first term(a):
[tex] \boxed{ \mathsf{a _{n} = a - (n - 1)d}}[/tex]
[tex] \implies \mathsf{a _{8} = 40 - (8 - 1) \times 2.75}[/tex]
[tex] \implies \mathsf{a _{8} = 40 - 7 \times 2.75}[/tex]
[tex] \implies \mathsf{a _{8} = 40 - 19.25}[/tex]
[tex] \implies \mathsf{a _{8} = \underline{20.75}}[/tex]
Answer:Hence, the charge to walk each of the eight dogs is $ 20.75
please help me with this. really need this
Answer:
(a) 1
Step-by-step explanation:
When you draw a horizontal line on the graph at y=1, you see it intersects the curve in two places. That is, there will be 2 real solutions to f(x) = 1, not 4 solutions.
If you want 4 solutions, the value of c in f(x)=c cannot be 1.
8. Beth doesn’t begin receiving commission until she reaches $50,000 in sales. After that, her commission rate is 12%. If she ends up selling cars totaling $115,000, how much money would she make in commission?
A.$13,800
B.$6,000
C.$7,800
D.$8,400
Step-by-step explanation:
she is the only sales agent selling cars after totaling them ... :-)
she makes 12% commission on the amount of sales beyond $50,000.
so, total sales was $115,000.
the base for her commission is then
115,000 - 50,000 = $65,000
she gets 12% of these $65,000.
100% = $65,000
1% = 100%/100 = 65,000/100 = $650.
12% = 1%×12 = 650 × 12 = $7,800
so, C is the right answer.
You go to your locker to get some supplies. You grab 3 pens and 6 markers, then you find 2 more markers on the bottom of your locker. Choose the equivalent expressions to represent the number of pens and markers you now have.
BoldItalicUnderline
someone should help me with this question
Answer:
option c.)
Step-by-step explanation:
m∠1 + m∠3 = 180°
(8y²)(-3x²y²)(2/3xy⁴)
HELP PLEASEEEEEEEE
Step-by-step explanation:
1 Remove parentheses.
8{y}^{2}\times -3{x}^{2}{y}^{2}\times \frac{2}{3}x{y}^{4}
8y
2
×−3x
2
y
2
×
3
2
xy
4
2 Use this rule: \frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}
b
a
×
d
c
=
bd
ac
.
\frac{8{y}^{2}\times -3{x}^{2}{y}^{2}\times 2x{y}^{4}}{3}
3
8y
2
×−3x
2
y
2
×2xy
4
3 Take out the constants.
\frac{(8\times -3\times 2){y}^{2}{y}^{2}{y}^{4}{x}^{2}x}{3}
3
(8×−3×2)y
2
y
2
y
4
x
2
x
4 Simplify 8\times -38×−3 to -24−24.
\frac{(-24\times 2){y}^{2}{y}^{2}{y}^{4}{x}^{2}x}{3}
3
(−24×2)y
2
y
2
y
4
x
2
x
5 Simplify -24\times 2−24×2 to -48−48.
\frac{-48{y}^{2}{y}^{2}{y}^{4}{x}^{2}x}{3}
3
−48y
2
y
2
y
4
x
2
x
6 Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x
a
x
b
=x
a+b
.
\frac{-48{y}^{2+2+4}{x}^{2+1}}{3}
3
−48y
2+2+4
x
2+1
7 Simplify 2+22+2 to 44.
\frac{-48{y}^{4+4}{x}^{2+1}}{3}
3
−48y
4+4
x
2+1
8 Simplify 4+44+4 to 88.
\frac{-48{y}^{8}{x}^{2+1}}{3}
3
−48y
8
x
2+1
9 Simplify 2+12+1 to 33.
\frac{-48{y}^{8}{x}^{3}}{3}
3
−48y
8
x
3
10 Move the negative sign to the left.
-\frac{48{y}^{8}{x}^{3}}{3}
−
3
48y
8
x
3
11 Simplify \frac{48{y}^{8}{x}^{3}}{3}
3
48y
8
x
3
to 16{y}^{8}{x}^{3}16y
8
x
3
.
-16{y}^{8}{x}^{3}
−16y
8
x
3
Done
PLSSS HELP!!
Which equation could have been used to create this graph?
y = x + 4
y = 2x
y = 4x
y = x + 2
find g12 in the sequence -1,-3,-9,-27,....
a. -59,049
b. -177,147
c. 118,098
d. -19,683
Answer:
b. [tex]a_{12}=-177147[/tex]
Step-by-step explanation:
This is a geometric sequence:
[tex]a_n=a_1x^{n-1}[/tex]
where n is the index in the sequence and x is the common scale factor.
In the given sequence here, the common factor is 3:
[tex]-3\div-1=3\\-9\div-3=3\\-27\div-9=3[/tex]
That's the factor, and we know the first term is -1, so you can write the equation for this sequence:
[tex]a_n=(-1)(3)^{n-1}[/tex]
Finally, plug in 12 for n and solve:
[tex]a_{12}=(-1)(3)^{12-1}\\a_{12}=(-1)(3)^{11}\\a_{12}=(-1)177147\\a_{12}=-177147[/tex]
Multiply the monomials:
(3/4)pq, (1/2)qr^2, -5q^2r^3 and -6r^5
Given monomials are (3/4)pq , (1/2)qr² , -5p²r³ and -6r⁵
On multiplying them then
⇛ [(3/4)pq]×[(1/2)qr²]×[-5p²r³]×[-6r⁵]
⇛ [(3/4)×(1/2)×(-5)×(-6)]×(pq×qr²×p²r³×r⁵)
⇛[(3×1×-5×-6)/(4×2)](p×p²)×(q×q)×(r²×r³×r⁵)
⇛ (90/8)×p³×q²×r¹⁰
Since a^m × a^n = a^(m+n)
⇛ (45/2)×p³×q²×r¹⁰
⇛( 45/2 ) p³q²r¹⁰
Answer:- [(3/4)pq]×[(1/2)qr²]×[-5p²r³]×[-6r⁵] = (45/2)p³q²r¹⁰
I promise y’all this is the last question I need to be answered
Answer:
sorry there's no results
Step-by-step explanation:
just skip it
Which ratio is equivalent to the rate
8 meters
1 second
?
The ratio as a unit rate is 0.8 meters per second.
What is a Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
The given statement is "8 meters in 10 seconds".
It can be written as:
= 8/10 meters per second
= 0.8 meters per second
Thus, the ratio as a unit rate is 0.8 meters per second.
learn more about ratio here:
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The Question attached here seems to be incomplete, the complete Question is
Write the ratio as a unit rate. 8 meters in 10 seconds.
A. 0.8 meters per second
B. 1.125 meters per second
C. 2 meters per second
D. 80 meters per second
What is the equation of the line that passes through the point(-6,-5) and has a slope of -1/2
Answer:
y=-1/2x-8
Step-by-step explanation:
y-y1=m(x-x1)
y-(-5)=-1/2(x-(-6))
y+5=-1/2(x+6)
y=-1/2x-6/2-5
y=-1/2x-3-5
y=-1/2x-8
Help me with this I can’t ;c
Hello there, this is how we would solve this problem, we can see that angle KAE equals 90° and we have an angle that equals 62° now since angle GCJ or also known as x is a vertical angle with IAD we can make the following equation
[tex]x+62+90=180[/tex] subtract 62 and 90 from both sides and we get that [tex]x=28[/tex]°
What is the value of the expression
3-4 ?
Answer:
[tex]3 - 4 = 1[/tex]
✨✨
3-4
you just need to subtract 3 from -4
so , your answer is -1
simplify 3^-6x(3^4 divided by 3^0)^2
Answer:
Step-by-step explanation:
Changes made to your input should not affect the solution:
(1): "^-6" was replaced by "^(-6)".
Equation at the end of step
1
:
34
{——}2
1
STEP
2
:
34
Simplify ——
1
Equation at the end of step
2
:
((3-6) • x) • (34^2)
Equation at the end of step
3
:
((3)(-6) • x) • 38
Dividing exponents:
4.1 38 divided by 36 = 3(8 - 6) = 32
Final result :
9x
The simplification of the given expression gives the value 9.
What is simplification?Simplification is defined as a process in mathematics to operate and interpret an expression to make the expression simpler.
This can be done using various results or the basic operations of numbers.
Given expression is 3⁻⁶ × (3⁴ / 3⁰)².
We have to use product rule and quotient rule of exponents to simplify this.
We know that,
xᵃ × xᵇ = xᵃ⁺ᵇ
xᵃ / xᵇ = xᵃ⁻ᵇ
Also, (xᵃ)ᵇ = xᵃᵇ
3⁴ / 3⁰ = 3⁴⁻⁰ = 3⁴
Substituting,
3⁻⁶ × (3⁴ / 3⁰)² = 3⁻⁶ × (3⁴)²
= 3⁻⁶ × 3⁸
= 3⁻⁶⁺⁸
= 3²
= 9
Hence the simplified form of the given expression is 9.
Learn more about Simplification of Expressions here :
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Find the area of the shape. Either enter an exact answer in terms of π or use 3.14, point, for π and enter your answer as a decimal.
Answer:
25π
Step-by-step explanation:
1) for whole circuit: A=π*r², where r - radius of the given circle;
2) for a quater of the circuit: A=πr²/4;
3) finally, A=π*100/4=25π.
What common side does ΔABC share with ΔADC?
BC
AD
BD
AC
Answer:
it's a and c
luk closely
What is the value of x?
Answer:
I am not sure the answer is , if its minus ,divade ,multiply or plus but down the answer is correct
Step-by-step explanation:
17x - 75
× = 75÷17
x= 4.4117647059
what is the slope of the line
Answer:
The slope is 1.Step-by-step explanation:
Let's take two points on a line. (2,0) and (0,2).
Now, determine the rise and run.
Rise: 2 Run: 2Slope = Rise/Run
=> 2/2
Conclusion:
Therefore, the slope is 1.
Hoped this helped.
Graph the function f(x)=3/2x-4. Use the line tool and select two points to graph.
Answer:
Slope = 3/2
y-intercept = -4
x | y
0 -4
2 -1
Step-by-step explanation:
Please answer really quick
Answer:
A, 94
Step-by-step explanation:
4. A since that is the tallest of the bars
5. 51 + 9 + 34 = 94 people
find the degree desirous the number of turning point in the y-intercept of the given graph of each polynomial function below
pasagot po ako
Answer:
2
Step-by-step explanation:
There are two turning points, therefore this is a cubic function. The degree is 3
Divide. Give the exact answer, written as a decimal.
Answer: 554
Step-by-step explanation: cause yeah
How is the graph of y = log (x) transformed to produce the graph of y = log (2 x) + 3?
It is stretched horizontally by a factor of 2 and translated up 3 units.
It is compressed horizontally by a factor of 2 and translated up 3 units.
It is stretched vertically by a factor of 2 and translated up 3 units.
It is compressed vertically by a factor of 2 and translated up 3 units.
Transformation involves changing the form of a function
The true statement is (a) it is stretched horizontally by a factor of 2 and translated up, 3 units.
The function is given as:
[tex]y = \log(x)[/tex]
Start by stretching the graph of [tex]y = \log(x)[/tex], horizontally by a factor of 2.
So, we have:
[tex]y = \log(2 \times x)[/tex]
[tex]y = \log(2x)[/tex]
Next, shift the function up by 3 units.
So, we have:
[tex]y = \log(2x) + 3[/tex]
Hence, the true statement is (a)
Read more about transformations at:
https://brainly.com/question/12619643
Answer:
its b on edge
Step-by-step explanation:
There are 3 times as many books in the town library as there are in the school library. The town library has 2,676 books.
How many books are in the school library?
Answer: First we know the Town Library has 3 times as many books as there are in the School Library. The Town Library has 2,676 books.
Divide 2,676 by 3. 2676÷3= 892
So your answer is: 892 books.
Hope I helped. :)
The number of books in the library will be 892.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that there are 3 times as many books in the town library as there are in the school library. The town library has 2,676 books.
The number of books will be calculated as,
Number = 2676 / 3
Number = 892
Hence, the number of books will be 892.
To know more about an expression follow
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What is the common ratio for the geometric sequence?
18,12,8, ...
16/3
Enter your answer in the box.
Answer:
Answer below
Step-by-step explanation:
basically, what should we multiply each term by to get next term
18 times what=12
what=12/18=2/3
12 times what=8
what=8/12=2/3
common ratio is 2/3
_____________________________________________________
(hope this helps can I pls have brainlist (crown)☺️)
Solve for x.
2x + 20=2x - 4
+
x = [?]
Enter
Answer:
x=24
Step-by-step explanation:
2x+20=2x-4+x
Subtract 2x from both sides
2x+20-2x=2x-4+x-2x
Simplify
20=-4+x
Add 4 to both sides
24=x
Switch sides
x=24