Answer:
i is equal to the square root of -1, and -1 to any power equals -1
Step-by-step explanation:
[tex]i^18[/tex] must be equal to 1 because [tex]i^4[/tex] is equal to 1, and 18 is a multiple of 4.
The imaginary unit i is defined as the square root of -1. Therefore, by definition, [tex]i^2[/tex] = -1.
Now let's consider higher powers of i:
[tex]- i^3 = i^2 i = -1 i = -i[/tex]
[tex]- i^4 = i^2 = -1 = 1[/tex]
Notice that when we raise i to the fourth power, we get 1. This is a key observation because it means that the powers of i repeat every four powers. This is known as the cyclical nature of the powers of i.
Given that [tex]i^4 = 1[/tex], we can express any power of i that is a multiple of 4 as 1. This is because raising i to any multiple of 4 will result in an even number of -1 factors, which will always multiply to 1.
Now, let's consider [tex]i^18[/tex]:
- Since 18 is divisible by 4 (18 = 4 * 4.5), we can express [tex]i^18 as (i^4)^4.5[/tex].
- We know that [tex]i^4 = 1[/tex], so [tex](i^4)^4.5 = 1^4.5 = 1[/tex].
Therefore, [tex]i^18[/tex] = 1, not -1 as initially stated. The power of i cycles through -1, -i, 1, and i, repeating every four powers. Since 18 is a multiple of 4, i^18 lands on 1 in this cycle.
Estimate the sum or difference of 23/40 11/30
The least common multiple (and i apologize for my English) of 40 and 30 is 120.
23×3 69 11×4 44
-------= ------ -------= -------
40×3 120 30×4 120
69/120 - 44/120 = 25/120 witch is equal to 5/24 if you simplify with 5.
What is the answer to number 10?
Answer:
E 8
Step-by-step explanation:
y = w x^2
If we double w and x, replae w with 2w and x with 2x and solve for y
y = (2w) * (2x)^2
Do the powers first
y = 2w * (4x^2)
y = 8wx^2
Y is now increased by a factor of 8
Answer:
Y will be multiplied by 8.
Right option is (E)
Step-by-step explanation:
We have, y = wx²
y is not 0.
If w and x are doubled
That means,
w' = 2w and x' = 2x
So , y' =w'x'²
or y' = (2w)×(2x)²
or y' = 2w×4x²
or y' = 8wx²
Since y = wx²
so y' = 8y.
That means if we double the w and x then y will be multiplied by 8.
20 Points on the line here!
Deena works at a customer service call center. She fields an average of 7 calls per hour. Employees are encouraged to field more than 280 calls per week. Deena has already fielded 126 calls this week.
How many more hours, x, does Deena need to work this week to reach the weekly goal of fielded calls if she continutes to field an average of 7 calls per hour? Select the inequality that includes the fewest number of hours Deena can work this week and still reach the weekly goal.
A.
x > 40
B.
x > 29
C.
x > 22
D.
x > 2
Answer:
C.
x > 22
Step-by-step explanation:
Deena has already taken 126 calls
She takes 7 calls per hour ( think slope)
y = mx+b
y = 7x+126
She needs to take at least 280 calls. So what she does must be greater than 280
280 <7x+126
We need to isolate x. The first step is to subtract 126 from each side
280-126 < 7x + 126 -126
154 < 7x
Next, we divide by 7 on each side
154/7 < 7x/7
22 < x
8 out of the 20 students at a school assembly were first-grade students. What percentage of the students at the assembly were first-graders? Write your answer using a percent sign (%)
Answer:
40%
Step-by-step explanation:
Take 8 and divide it by 20 to get the percent.
Answer:
40%
Step-by-step explanation:
To find this, the method I personally like to use is the is over of equals percent over 100.
Your ratio should look like this:
[tex]\frac{8}{20}[/tex] = [tex]\frac{x}{100}[/tex]
Then I cross multiplied; 8 x 100 divide that product by 20.
Hope this helps!
Jenni buys a piece of fabric that is 4 7/8 yards long.What is the decimal equivalent of 4 7/8?
Answer: 4.875
Step-by-step explanation:
Starting fraction: 4 7/8
Make it mixed: 39/8
Now divide top by bottom: 4.875
What is the remainder when (4x3 + 2x2 − 18x + 38) ÷ (x + 3)?
A2
B96
C12
D110
Answer: A
Step-by-step explanation: I use synthetic division for problems like these:
-3 | 4 2 -18 38
4 -10 12 2
Since -3 + 3 = 0, we use -3 in this process. Write out the coefficients in order separate from -3. Next, bring down the 4 and multiply -3 by 4 = -12. Add 2 and -12 = -10. Multiply -10 by -3 = 30. Add 30 to -18 to get 12. Multiply 12 and -3 = -36. Add -36 and 38 = 2
Answer:
A) 2
Step-by-step explanation:
correct answer on my test
n triangle ABC, m∠BAC = 50°. If m∠ACB = 30°, then the triangle is triangle. If m∠ABC = 40°, then the triangle is triangle. If triangle ABC is isosceles, and AB = 6 and BC = 4, then AC =
Answer:
AB
Step-by-step explanation:
the shape is in the wrong place
A bank account earns 2.5% interest per year. If the account starts with $500, approximately how many years will it take for the value of the account to be $750?
Answer:
Step-by-step explanation: What you need to do is add if it has 2.5% interest per year. And t starts with 500 you could do 2.5 + 500 tell you get to 750 . Hope this helps
To find out how long it will take for a bank account with an initial balance of $500 and an annual interest rate of 2.5% to reach a balance of $750, we use the time formula for simple interest. Substituting the relevant amounts into the formula, it will take approximately 20 years for the account to reach $750.
Explanation:This problem pertains to simple interest in finance. The formula for simple interest is I = PRT, where I is the interest, P is the principal amount (the initial amount), R is the annual interest rate in decimal form, and T is the time in years. However, in this case, we want to find the time (T), so we will use the formula T = I / (PR).
In your case, the initial amount or principal (P) is $500, the interest (I) is the difference between the final amount and the initial amount ($750 - $500 = $250), and the interest rate (R) is 2.5% or 0.025 in decimal form.
Substituting these values into the formula, we will have T = $250 / ($500 * 0.025). Calculating this, we get approximately 20 years for the value of the account to be $750.
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a company uses paper cups shaped like cones for its water cooler. each cup has a height of 9cm, and the base has a diameter of 6 cm. the cooler had 12,717 cm to the third power of water in it. how many cups can be filled from the cooler?
use 3.14, do not round answer
Answer:
We can fill 150 paper cup cones.
Step-by-step explanation:
Volume of a cone is
V = 1/3 pi * r^2 *h
The volume of one cone is
pi = 3.14
r = d/2 = 6/2 =3
h=9
Substitute what we know
V = 1/3 * (3.14) * (3^2) * (9)
= 27* 3.14
= 84.78 cm^3
The water cooler has 12717 cm^3 water
Divide the water by the volume of the paper cup cone and we will know how many paper cup cones we can fill, assuming we fill them completely.
12717/ 84.78 = 150
We can fill 150 paper cup cones.
The volume of one cone-shaped paper cup is 84.78 cm³. With 12,717 cm³ of water in the cooler, approximately 150 cups can be filled.
To find out how many paper cups can be filled from the water cooler, we first need to calculate the volume of one paper cup. Given that the cup is shaped like a cone with a height of 9 cm and a base diameter of 6 cm, we can find the volume using the formula for the volume of a cone, which is V = (1/3)\u03c0r^2h, where V is the volume, r is the radius of the base, and h is the height of the cone.
The radius of the base is half the diameter, so r = 3 cm. Plugging in the values into the formula, we get: V = (1/3)*3.14*(3²)*9.
Calculating this, we get V \<= 84.78 cm³ per cup. Now, to determine how many cups can be filled from the cooler containing 12,717 cm³ of water, we divide the total amount of water in the cooler by the volume of one cup:
Number of cups = 12,717 cm³ / 84.78 cm³.
This gives us approximately 150 cups that can be filled from the water cooler.
Four less than the quotient of a number x and 5.
X divided by 5 minus 4 =
The number . . . . . x
The quotient of the number and 5 . . . x/5
Four less than that . . . . . (x/5) - 4
The library is 5 miles from the post office. How many yards is 5 miles?
Answer:
8800 yards.
Step-by-step explanation:
To convert miles to yards, you must multiply the amount of miles by 1760.
Because there are 5 miles, multiply 5 by 1760.
[tex]5(1760)=8800[/tex]
Answer:
Step-by-step explanation:To figure this out you must first put the equation up.1760 yards are in a mile so you can do 1760*5=y Just multiply 1760 to 5 which should give you 8800.Hope this helps!!!!!!!Please mark brainliest!!!!!
(-6,3)(8,-1) what is the slope
The formula of a slope m:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-6, 3) and (8, -1). Substitute:
[tex]m=\dfrac{-1-3}{8-(-6)}=\dfrac{-4}{8+6}=\dfrac{-4}{14}=-\dfrac{2}{7}[/tex]
Hi there!
Step-by-step explanation:
[tex]Slope=\frac{Y_2-Y_1}{X_2-X_1}=\frac{Rise}{Run}[/tex]
[tex]\frac{(-1)-3}{8-(-6)}=\frac{-1-3}{8+6}=\frac{-4}{14}=\frac{-4/2}{14/2}=\frac{-2}{7}=-\frac{2}{7}[/tex]
Slope is -2/7.
Final answer is -2/7.
Hope this helps!
Have a nice day! :)
:D
-Charlie
Thank you so much! :)
:D
The Science Club went on a two-day field trip. The first day the members paid $60 for transportation plus $12 per ticket to the planetarium. The second day they paid $95 for transportation plus $9 per ticket to the geology museum. Write an expression to represent the total cost in dollars for two days for the n members of the club.
Write the pair of fractions as a pair of fractions with a common denominator 3/10 and 2/5
Answer:
2/10 = 3/10, 2/5 = 4/10
For the given fractions, the pair of fractions are 6/20 and 4/10 ; 9/30 and 6/15 and this can be determined by using the arithmetic operations.
Given :
Fractions - 3/10 and 2/5
The following steps can be used to determine the pair of fractions:
Step 1 - Multiply 2 in the numerator and denominator in the given fractions.
[tex]\dfrac{3\times 2}{10\times 2}=\dfrac{6}{20}[/tex] and [tex]\dfrac{2\times 2}{5\times 2}=\dfrac{4}{10}[/tex]
Step 2 - Multiply 3 in the numerator and denominator in the given fractions.
[tex]\dfrac{3\times 3}{10\times 3}=\dfrac{9}{30}[/tex] and [tex]\dfrac{2\times 3}{5\times 3}=\dfrac{6}{15}[/tex]
In this way pair of fractions can be determined.
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In its first year of business, Arlo’s Dry Cleaners had a closing balance of –$1,500. The second year it lost an additional $1,200. What is the closing balance at the end of year two?
Answer:
-2700 dollars
Step-by-step explanation:
The first year we have a loss of 1500 dollars. On the balance sheet we write -1500, with the negative indicating loss. Some accounting practices will use parenthesis to mean loss, so you might see it as (1500). But in this problem, we'll use negative signs for loss.
The second year is loss of 1200. Add up the two losses (the positive versions of each) to get 1500+1200 = 2700. Then make the result negative. Taking one loss and adding more loss to it means your loss has gotten bigger. So that's why the closing balance at the end of year 2 is -2700 dollars, which is a loss of 2700 dollars.
Answer:
1.
a. -3
b. 9
c. 5
d. -12
2.
a. 9 + (–6) = 3
b. (–5) + 8 = 3
c. (–12) + (–6) = -18
d. 10 – (–8) = 18
e. (–4) – (+2) = -6
f. –9 – (–5) = 4
3.
a. 8 * 3 = 24
b. -7 * 5 = -35
c. -6 * -9 = 54
d. 8 / -2 = -4
e. -24 / -3 = 8
f. -36 / 6 = -6
4.
$65.00 - $82.00 = -$17
5.
$84
6.
-$1,500 + -$1,200 = -$2,700
Step-by-step explanation:
What is the measure of AC?
Answer: B. [tex]150^{\circ}[/tex]
Step-by-step explanation:
From the given picture, we can see a circle with two perpendicularly intersecting chords .
The measure internal angle made by intersecting of chords : [tex]90^{\circ}[/tex]
The measure of minor arc : [tex]30^{\circ}[/tex]
The formula to find the internal angle is given by :-
[tex]\theta=\dfrac{\text{Minor arc + major arc}}{2}[/tex]
Let x be the Major arc AC, the we have the following equation:-
[tex]90^{\circ}=\dfrac{30^{\circ}\text{ + x}}{2}\\\\\Rightarrow\ 30^{\circ}+x=180^{\circ}\\\\\Rightarrow\ x=180^{\circ}-30^{\circ}\\\\\Rightarrow\ x=150^{\circ}[/tex]
Hence, the measure of [tex]\overarc{AC}=150^{\circ}[/tex]
The measure of the major arc AC is 150°.
In the given picture, a circle with two perpendicularly intersecting chords is shown. The angle formed by the intersection of the chords is labeled as 90°. Additionally, the minor arc formed by these chords has a measure of 30°.
To find the measure of the major arc, we use the formula: θ = (minor arc + major arc) / 2.
Let x represent the measure of the major arc AC.
The formula can be set up as follows: 90° = (30° + x) / 2.
Solving for x, we first multiply both sides by 2 to eliminate the fraction: 180° = 30° + x.
Next, we isolate x by subtracting 30° from both sides:
x = 180° - 30°.
Simplifying further, we get x = 150°.
Therefore, the measure of the major arc AC is 150°. This calculation ensures that the angle formed by the intersecting chords is indeed 90°, and the given information about the minor arc aligns with the solution.
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Laverne earns $560 a week and she works 5 days a week. What is her daily wage
Answer: 112
112 dollars because 560 divided by 5 equals 112
Answer:
$112
Step-by-step explanation:
You are going to take your total and divide that by how many it is to get the single one your looking for if that makes sense..
560(total)/5(how many)=$112
Hope that helps feel free to ask more questions
Brainliest??
A phone company offers two monthly plans. Plan A costs $24 plus an additional $0.09 for each minute of calls. Plan B costs $20 plus an additional $0.14 for each minute of calls. For what amount of calling do the plans equal the same cost? What is the cost when the two plans cost the same?
x = number of minutes used, y = total cost in dollars
Plan A: y = 0.09x + 24
Plan B: y = 0.14x + 20
Equate the two right hand side (RHS) expressions and solve for x
0.14x + 20 = 0.09x + 24
0.14x - 0.09x = 24 - 20
0.05x = 4
x = 4/0.05
x = 80
The two plans will cost the same amount of money if you use up 80 minutes
Plug in x = 80 into either equation to find y
y = 0.09*x + 24
y = 0.09*80 + 24
y = 31.20
or
y = 0.14*x + 20
y = 0.14*80 + 20
y = 31.20
So both plans will cost $31.20 if you use up 80 minutes
krystal wanted to make note cards by cutting pieces of paper in half. Before starting she got seven more pieces to use. When she was done she had 28 half pieces of paper. With how many did she start?
Simplify using the distributive property, Show all work (-2x - 9)(-4).
Kim's furniture store is offering a 30% discount on all its armchairs. Using a proportion, find the discount of the price of an armchair that originally cost $266.00.
Answer:
The discount is $79.80
Step-by-step explanation:
We need to solve this using proportions. We take the percent out of 100 on one side of the ratio and the discount over the total price on the other.
30 discount
----- = ----------
100 266
30* 266 = 100 * discount
7980=100 discount
Divide each side by 100
7980/100 = discount
79.80 = discount
Answer for some points
Answer: 17.3 ft
Step-by-step explanation:
Perimeter = 2 ( l + w ). So I did 45 divided by 2 which would be 22.5 then subtract that by 5.2 ft which is 17.3. 17.3 + 5.2 = 22.5 x 2 = 45 ft.
The maximum speed an animal can walk in feet per second is a 5.7VI, where l is the animal's leg length in feet. What is the maximum walking speed for a camel with a leg length of 5.7 feet?
Answer:
Maximum walking speed of camel is 31.749V feet per second
Step-by-step explanation:
Walking speed of an animal is given by :
Speed = 5.7VI (in feet per second) where l is the animal's leg length.
For a camel, leg length is 5.7feet.
So maximum walking speed of camel will be:
Speed of camel = 5.7V * 5.7 = 5.7² V feet per second
Speed of camel = 31.749V feet per second
hence, maximum walking speed of camel is 31.749V feet per second
The maximum walking speed for a camel with a leg length of 5.7 feet is calculated using the formula 5.7 x / (leg length) and is approximately 13.5945 feet per second.
The question asks us to calculate the maximum walking speed of a camel with a leg length of 5.7 feet using the formula provided, which is maximum speed = 5.7 x /(leg length). To find the camel's speed, we simply plug the leg length into the formula:
Maximum speed = 5.7 x / 5.7 = 5.7 x 2.385 = 13.5945 feet per second.
Thus, the maximum walking speed for a camel with a leg length of 5.7 feet is approximately 13.5945 feet per second.
Determine the direction that this parabola opens y= 4x^2 -8x+8
Answer:
see explanation
Step-by-step explanation:
given a parabola in standard form : y = ax² + bx + c : a ≠ 0
• If a > 0 then parabola opens up
• If a < 0 then parabola opens down
given y = 4x² - 8x + 8 ← in standard form
with a = 4, b = - 8 and c = 8
here a > 0 then parabola opens up
What are the actual dimensions of a television that has a 15:9 aspect ratio and a screen that is 42 inches?
Answer:
Let x be the number.
It is given that a 15 : 9 aspect ratio and a screen that is 42 inches.
Aspect ratio states that the ratio of the display image’s width to its height.
Then;
Width of the television of(w) = 15x
and height of the television(h) = 9x.
Since, television is in the form of Rectangle.
And it is also, given that the screen is 42 inches .
⇒Diagonal of the television(D) = 42 inches
Using formula of diagonal of the rectangle :
[tex]D^2 =w^2+h^2[/tex]
Substitute the given values to solve for x;
[tex]42^2 = (15x)^2+(9x)^2[/tex]
[tex]1764 = 225x^2 + 81x^2 = 306x^2[/tex]
or
[tex]x^2 = \frac{1764}{306} = 5.76[/tex]
[tex]x = \sqrt{5.76} = 2.4[/tex]
Then:
width of the television (15x) = 15(2.4) = 36 inches and
Height of the television (9x) = 9(2.4) = 21.6 inches.
Therefore, the actual dimensions of the television are;
width = 36 inches and height = 21.6 inches.
Can someone help me with this question
Answer: Both 110 degrees
Step-by-step explanation:
2= 110 thanks to corresponding angles theorm
1=2 because of vertical angles theorom
A moving van rents for $29.95 a day plus $.12/mi.Mmi.Ms Smiths bill for a two day rental was $70.46. how many miles did she drive
Answer:
She drove 88 miles
Step-by-step explanation:
Total cost = fee per day + cost per mile * miles driven
We know the total cost was 70.46
The fee per day was 29.95 *2 =59.90. She kept the van 2 days.
The cost per mile was .12
Substitute in what we know
70.46 = 59.90 +.12 m
Subtract 59.90 from each side
70.46-59.90 = 59.90-59.90 +.12 m where m is the miles driven
10.56 = .12m
Divide each side by .12
10.56/.12 = .12m/.12
88=m
There will be 6 people at ellies pie party she wants to bake enough pie so each person can eat at least 1/5 of pie what is the minimum number of pies ellie should bake?
Answer:
2
Step-by-step explanation:
She needs to have 6 portions of 1/5 pie size.
6 portions of 1/5 pie size is 6/5 of a pie.
6/5 of a pie is the same as 1 1/5 (one and one-fifth) pies.
Since she only bakes full pies, she must round up to the next higher whole number, so she must bake 2 pies.
PLEASE HELP!!!
Sam (4, 2) Theater (-3, 5)
Describe Sam's location relative to the theater.
Answer:
The theater is approximately 3.16 units from Sam's location.
Step-by-step explanation:
The distance between points [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] is given by:
[tex]d=\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1} )^{2} }[/tex]
So, the distance of the theater from Sam's location is:
[tex]d=\sqrt{(-3-(-4) )^{2}+(5-2 )^{2} }[/tex]
[tex]=\sqrt{1^{2}+3^{2} }[/tex]
[tex]=\sqrt{10}[/tex]
= 3.16 approximately
Hence, the theater is approximately 3.16 units from Sam's location.
The bill at a restaurant came to $136.40. The patrons decided to leave a 15% tip. What was the total bill including tip?
Help me please !
Answer:
156.86
Step-by-step explanation:
136.40 + 15% is 20.46 added to 136.40 is 156.86
Answer:
$156.86.
Step-by-step explanation:
We have been given that the bill at a restaurant came to $136.40. The patrons decided to leave a 15% tip.
The total bill including tip would $136.40 plus 15% of $136.40.
[tex]\text{Total bill}=\$136.40+\frac{15}{100}\times \$136.40[/tex]
[tex]\text{Total bill}=\$136.40+0.15\times \$136.40[/tex]
[tex]\text{Total bill}=\$136.40+\$20.46[/tex]
[tex]\text{Total bill}=\$156.86[/tex]
Therefore, the total cost of bill including tip would be $156.86.