Answer:
The answer for the first one is 1 and the second answer is 12i.
Step-by-step explanation:
The value of the given imaginary number i¹² will be 1 thus option (A) is correct.
What is a complex number?A complex number is the sum of a real number and an imaginary number.
The idea of a complex number has come by solving a quadratic equation that has root as negative under root.
If we solve x² + 1 = 0 ⇒ x = √(-1) which is called as iota(i).
The value of iota(i) is given as i = √(-1).
By the law of indices,
i¹² = (i²)⁶
⇒ (-1)⁶
Since the even exponents of a negative number give positive output thus (-1)⁶ = 1.
Thus, i¹² = 1
Hence "The value of the given imaginary number i¹² will be 1".
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Find the value of x in each case:
angle FEB = angle ABE ( Alternate Interior Angles )
angle FEB = 4x = angle ABE
Solution:x + 4x + 65° = 180° ( sum of the Angles On the same line is equal to 18° )
or, 5x = 180° - 65°
or, x = 115/5
or, x = 23
Answer:The value of x is 23°.
4x = 4(23) = 92°.
Tina is saving to buy a notebook computer. She has two options. The first option is to put $300 away
initially and save $10 every month. The second option is to put $100 away initially and save $30 every
month. After how many months would Tina save the same amount using either option? How much
would she save with either option?
After
months, Tina will save $
with either option.
Answer:
Step-by-step explanation:
The number of months is our unknown, which we will call x. y is the amount she saves. Representing the fact that she puts $10 away per month is 10x. If she puts $300 down initially and then adds 10 per month to that, the first equation is
y = 10x + 300
The same goes for the second option. Putting $30 away every month is represented as 30x, and if she is starting with 100 and adding 30 a month to it, the second equation is
y = 30x + 100
We are being asked to find the number of months where the amount Tina saves is equal. Since y is the amount Tina has saved and we want to know when these amounts are equal, we will set the equations equal to each other and solve for x, the number of months.
10x + 300 = 30x + 100 and
200 = 20x so
x = 10. After 10 months, Tina will have saved the same amount of money regardless of which option she has chosen. This is only true for 10 months though. After that, one will show more of a savings than the other.
The length of a rectangle is twice the width. The perimeter is 48in. Find the dimensions of the rectangle.
Answer:
w = 6in
l = 12in
Step-by-step explanation:
To solve this problem we propose 2 equations
2w + 2l = 48in
l = 2w
We replace the value of l = (2w) into the first equation and solve
2w + 2(2w) = 48in
2w + 4w = 48in
6w = 48in
w = 48in/6
w = 8in
we replace the value of w and solve
l = 2(8in)
l = 16in
Today only, a table is being sold at a 62% discount. The sale price is $144.40.
What was the price yesterday?
$ 232.90
Step-by-step explanation:62% ........... $144.40
100% ..........$ x
x = 144.40×100/62
= 14440/62
= $ 232.90
The surface area Q of a certain shape is three times the product of u and the square of its width w.
Answer:
Q = 3uw
Step-by-step explanation:
There are 15 different pieces of cheese on the plate. Is it possible by dividing only one piece to divide all into two groups with equal weight and equal amount of pieces in each?
Answer:
It is possible.
Step-by-step explanation:
Each piece of cheese can be divided into two equal pieces.
Therefore, the 15 different pieces can produce 30 (15 * 2) equal pieces.
Then there will be 15 pieces in each group.
Provided during the division, it is ensured that equal weights were allocated to each piece, then each group will have the same weight as the other group.
Note that the division of the 15 pieces of cheese into two equal parts looks like the only way to have equal weight of two groups of the delicacy.
Find surface area of the regular pyramid plz help ASAP
Answer:
B. 3,157 in^2
Step-by-step explanation:
surface area of a pyramid shown = 3x lateral area + base area
given:
s1 = s2 = s3 = 42 in
L = 38 in
lateral area = ( 1/2 * 42 * 38 ) = 798 sq. in
base area = √3 * s^2
4
= √3 * 42^2
4
= 763.834 sq. in
therefore,
surface area of a pyramid shown = 3x 798 + 763.834 = 3,157 in^2
Answer:
= 3,157 in^2
Step-by-step explanation:
surface area = 3x lateral area + base area
given:
side lengths area s1 = s2 = s3 = 42 in
slant height = 38 in
lateral area = ( 1/2 * 42 * 38 )
= 798 sq. in
base area = (√3 * s^2 ) / 4
= (√3 * 42^2 ) / 4
= 763.83 sq. in
surface area = 3x 798 + 763.834
= 3,157 in^2
Which is equivalent to (3 + 4i )(3 - 4i )?
Use the FOIL method to solve.
(3 + 4i)(3 - 4i)
(3 * 3) + (3 * -4i) + (4i * 3) + (4i * -4i)
9 - 12i + 12i - 16i
9 - 16i
Best of Luck!
Jamila paid $6 for a movie ticket, $1.59 for a small box of popcorn, and $2.50 for a drink at a movie theater. Which operation(s) would help Jamila find the total amount she spent at the theater?
Answer:
addition
Step-by-step explanation:
Answer:
It would be addition since you can see thats litterly the problem
Step-by-step explanation:
A student moves into a bigger apartment that rents for $550 per month. That rent is $300 less than twice what she had been paying. Find her former rent in dollars.
$
Answer:
Step-by-step explanation:
Her former rent is $ x
Twice the former rent: 2*x = 2x
$300 less than 2x: 2x - 300
2x - 300 = 550
Add 300 to both sides
2x - 300 + 300 = 550 + 300
2x = 850
Divide both sides by 2
2x/2 = 850/2
x = 425
Her former rent = $425
In this question, the older and newer rents of a student in two apartments in given. And some conditions and information is also provided,
GiveN:
New rent = $ 550This is $ 300 less than twice the previousWe have find her rent in the previous apartment.
Let her previous rent be $ x
Then according to question,
➝ $ 550 = 2x - $ 300
Adding $ 300 both sides,
➝ $ 550 + $ 300 = 2x
Flipping it,
➝ 2x = $ 850
➝ x = $ 425
So, The previous rent of the student:
[tex] \huge{ \boxed{ \bf{ \$ \: 425}}}[/tex]
And we are done !!
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The selling price for a classic speedboat is $12,000. what was the speedboats original price if it is currently selling for $2,000 less than two times its original price?
Answer:
$7,000
Step-by-step explanation:
Let [tex]x[/tex] equal the original price.
[tex]12,000+2000=2x[/tex]
Combine like terms.
[tex]14,000=2x[/tex]
Divide by the coefficient of [tex]x[/tex], which in this case is [tex]2.[/tex]
[tex]7,000=x[/tex]
If you like the variable on the left, rewrite:
[tex]x=7,000[/tex]
yall imma fail if you don't help me. what is the scientific notation for 0.12? I need answers asap
Answer:
1.2 x 10^-1
Step-by-step explanation:
So you are going to move the decimal to the right once, since it is where the first number is. Since you only moved the decimal once it is 10^-1. It is negative because you moved the the right. If you had moved the decimal to the left it would be positive.
What is the length of EF?
6 units
10
8 units
7 units
10%
-2 0
-2-
2 units
H Н
-4
G
-6
-B
10
Answer:
7
Step-by-step explanation:
The statistic used in the sign test measures ____.
Answer:
the comparisms between pairs of scores
Step-by-step explanation:
The sign test can also called statistical test , this test is essential in the determination of group size. It also give comparisms between the given value and median of datas
It should be noted that The statistic used in the sign test measures the comparisms between pairs of scores
zales bought a tea set for $1400. zales wants to mark up the set 55% of the selling price. the selling price of the tea set should be?
Answer:
The selling price of the tea set should be: The selling price of the tea set is $2170
$1400 x . 55 = $770.
The double number line shows that
4
44 pounds of almonds cost
$
34
$34dollar sign, 34.
Answer:
round them up
Step-by-step explanation:
what is 8653 × 8975??????????????????????????????
Answer:
8653 × 8975= 77660675.
So the answer is 77660675
Hope I helped you
Answer:
the answer is 77660675
Step-by-step explanation:
What is 17% of 425=?
How do you write 8.095 in word form?
Answer:
How to Write Out Number 8.095 in Words:
eight and ninety-five thousandths in (US) American English, Number Converted (Spelled Out) to Words.
Answer:
eight and ninety five thousandths
Step-by-step explanation:
I got this question wrong. So the 50% is not right. Please help.
Answer:
25%
Step-by-step explanation:
sorry if its wrong but im pretty sure its 25%
the answer is 3/8
give me a brainliest
anyone do the Algebra 2 unit 1 test on edg?
Step-by-step explanation:
no not me .. I'm doing math unit test
The solution to the equation 3x + 7 = 16 - 2x is x = 9/5.
Option A is the correct answer.
We have,
To solve the equation 3x + 7 = 16 - 2x for x, we need to isolate the variable x on one side of the equation.
Let's solve it step by step:
Start with the original equation:
3x + 7 = 16 - 2x
- Add 2x to both sides of the equation to get rid of the -2x on the right side: 3x + 2x + 7 = 16 - 2x + 2x
- Simplifying, we have: 5x + 7 = 16
- Next, subtract 7 from both sides of the equation to isolate the term with x: 5x + 7 - 7 = 16 - 7
- Simplifying, we have: 5x = 9
- Finally, divide both sides of the equation by 5 to solve for x: (5x)/5 = 9/5
- Simplifying, we have: x = 9/5
Therefore,
The solution to the equation 3x + 7 = 16 - 2x is x = 9/5.
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The complete question:
Solve the following equation for x: 3x + 7 = 16 - 2x
a) x = 9/5
b) x = 5
c) x = 4
d) x = 6
The monthly snowfall totals from December 2010 through April 2011 were 22, 38.3, 18.5, 1.3, 0.9.
What was the average monthly snowfall during those months?
Which of the following r-values indicates the strongest correlation? r-value = 0.73 r-value = 0.73 r-value = 0.99 r-value = 0.99 r-value = - 0.85 r-value = - 0.85 r-value = - 0.17
Answer:
[tex]r-value = 0.99[/tex]
Step-by-step explanation:
Given
The list of options
Required
Which represents the strongest correlation.
When [tex]r-value > 0.7[/tex], it is considered to be strong.
Compare this condition with the given options, we're left with:
[tex]r-value = 0.73[/tex]
[tex]r-value = 0.99[/tex]
The above r-values show strong correlation.
However
[tex]r-value = 0.99[/tex] is stronger
because [tex]0.99 > 0.73[/tex]
Hence;
[tex]r-value = 0.99[/tex] answers the question
how to combine two integers
The simplest approach to do this is:
Convert both numbers to string
Concatenate both strings into one, as this is comparatively easy
Convert this concatenated string back to integer
Step-by-step explanation:
Given two integers n1 and n2, the task is to concatenate these two integers into one integer.
Example:
Input: n1 = 12, n2 = 34
Output: 1234
Input: n1 = 1, n2 = 93
Output: 193
Kinda confused!! need help!!
Answer:
I think last option is correct
Answer:
Option 2. EG, DH, CG, FH
Step-by-step explanation:
Skew lines are lines that do not lie on the same plane, and they also never intersectLet's verify options
Option 1
AC is an exception, it intersects ABOption 2
All good, all lines are skew with ABOption 3
GH is an exception, Can be on the same plane with ABOption 4
CD is an exception, can be on the same plane with ABJasmine is in charge purchasing tubes of silicone sealant, used for finishing
restroom facilities. She finds that she is able to purchase silicone sealant in cone
tubes. She knows that a jumbo cone of sealant has a top diameter of 8 inches and
a height of 12 inches, and a regular cone of sealant has a top diameter of 4 inches
and a height of 6 inches. Jasmine believes that with her order of sealant, that she
can get the same amount of silicone sealant from two regular cones as from one
jumbo cone,
a) Is Jasmina correct about the silicone sealant cones?
If you think Jasmina is correct explain why.
If you think she is incorrect replace the statement with one that is correct.
Explain why your statement is correct.
b) If the price for a regular cone of sealant is $3.40, what is a 'fair price' for a
jumbo cone?
Answer:
a) Jasmine or Jasmina is correct about the silicone sealant cones.
If Jasmine orders two regular cones of regular sealant, it will be equal to the Jumbo cone of sealant, because the top diameter when put together in a Jumbo cone will give the same result as a Jumbo cone, since 4 * 2 = 8 inches (top diameter) and 6 * 2 = 12 inches (height).
b) If the price for a regular cone of sealant is $3.40, the 'fair price' for a jumbo cone should be $6.80 ($3.40 * 2).
Step-by-step explanation:
Jumbo cone of sealant has top diameter of 8 inches and a height of 12 inches
Regular cone of sealant has top diameter of 4 inches and a height of 6 inches
If Jasmine orders two regular cones of regular sealant, it will be equal to the Jumbo cone of sealant, because the top diameter when put together in a Jumbo cone will give the same result as a Jumbo cone, since 4 * 2 = 8 inches (top diameter) and 6 * 2 = 12 inches (height).
If the price for a regular cone of sealant is $3.40, the 'fair price' for a jumbo cone should be $6.80 ($3.40 * 2), since two of the regular cone will give the value of a Jumbo cone.
Giselle bought a dress for $35 and three t-shirts. She used a coupon for $2.50 off each t-shirt. The total cost can be modeled by the expression 35 + 3(n - 2.5) . What does n - 2.5 represent?
Duncan is excited to begin diving lessons. He starts on the diving board, 5 feet above the surface of the pool. Then, Duncan dives off the board and ends up 7 feet below the surface of the pool. What is the total distance from Duncan's start on the diving board to his lowest point beneath the surface of the pool?
Answer: -13
Step-by-step explanation:
The total distance from Duncan's start on the diving board to his lowest point beneath the surface of the pool will be 12 feet.
What is an expression?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 Duncan is excited to begin diving lessons. He starts on the diving board, 5 feet above the surface of the pool. Then, Duncan dives off the board and ends up 7 feet below the surface of the pool.
Distance = 7 + 5
Distance = 12 feet
Therefore, the total distance from Duncan's start on the diving board to his lowest point beneath the surface of the pool will be 12 feet.
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In science class, Sarah calculates the mass of a planet to be 918,000,000,000,000,000,000 kg. What is the mass of the planet in scientific notation? 91.8×1019 kg 9.18×10−20 kg 918×1018 kg 9.18×1020 kg
Answer:
Step-by-step explanation:
↘↘↘↙↙↖↗↙↖
Which of the following relations is a function? A. (5, 11), (-9, 2), (-1, 8), (-6, 11) B. (11, 5), (2, -9), (8, -1), (11, -6) C. (-1, 11), (-9, 2), (-1, 8), (-9, -6) D. (5, 11), (-9, 2), (-1, 8), (-1, -6)
Answer:
A
Step-by-step explanation:
It is a function if none of the x-values are the same