[tex]Hey~freckledspots!\\----------------------[/tex]
[tex]We~will~solve~for~i^{425}![/tex]
[tex]Rule~of~exponent: a^{b + c} = a^ba^c\\Apply:~i^{425}~=~i^{424}i\\ \\Rule~of~exponent: a^{bc} = (a^{b})^c\\Apply: i^{424} = i(i^2)^{212} \\\\Rule~of~imaginary~number: i^2 = -1\\Apply: i(i^2)^{212} = -1^{212}i\\\\Rule~of~exponent~if~n~is~even: -a^n = a^n\\Apply: -1^{212}i = 1^{212}i\\\\Simplify: 1^{212}i = 1i\\Multiply: 1i * 1 = i\\----------------------\\[/tex]
[tex]Now~let's~solve~1^{14}!\\\\Rule~of~exponent: a^{b + c} = a^ba^c\\Apply: i^{14} = (i^2)^7\\\\Rule~of~imaginary~number: i^2 = -1\\Apply: (i^2)^7 = -1^7\\\\Rule~of~exponent~if~n~is~odd: (-a)^n = -a^n\\Apply: -1^7 = -1^7\\\\Simplify: -1^7 = -1\\----------------------\\Now,~we~have: i-1+i^{-14}+i^{44}\\----------------------[/tex]
[tex]Now~lets~solve~i^{-14}\\\\Rule~of~exponent: a^{-b} = \frac{1}{a^b} \\Apply: i^{-14} = \frac{1}{i^{14}} \\\\Rule~of~exponent: a^{bc} = (a^b)^c\\Apply: \frac{1}{i^{14}} = \frac{1}{(i^2)^7}\\ \\Rule~of~imagianry~number: i^2 = -1\\Apply: \frac{1}{(i^2)^7} = \frac{1}{-1^7} \\\\Simplify: \frac{1}{-1^7} = \frac{1}{-1} \\\\Rule~of~fractions: \frac{a}{-b} = -\frac{a}{b} \\Apply: \frac{1}{-1} = -\frac{1}{1} = -1\\----------------------\\Now,~we~have: i-1-1+i^44\\----------------------[/tex]
[tex]Now~let's~solve~i^{44}!\\\\Rule~of~exponent: a^{bc} = (a^b)^c\\Apply: i^{44} = (i^2)^{22}\\\\Rule~of~imaginary~numbers: i^2 = -1\\Apply: (i^2)^{22} = -1^{22}\\\\Rule~of~exponent~if~n~is~even: (-a)^n = a^n\\Apply: -1^{22} = 1^{22}\\\\Simplify: 1^{22} = 1\\----------------------\\Now,~we~have~i-1-1+1\\----------------------[/tex]
[tex]Now~let's~simplify~the~expression!\\\\= i-1-1+1 \\= 1 + i -2\\= -1+i\\----------------------[/tex]
[tex]Answer:\\\large\boxed{-1+i}\\----------------------[/tex]
[tex]Hope~This~Helped!~Good~Luck![/tex]
Answer:
[tex]i - 1[/tex]
Step-by-step explanation:
Complex Number System Rules
[tex]\sqrt{-1} = i \\ -1 = {i}^{2} \\ -i = {i}^{3} \\ 1 = {i}^{4} [Every \: multiple \: of \: four][/tex]
The Divisibilty Rule of 4 states that the last two digits of a number must be a multiple of four, so you will have this:
[tex]{i}^{425} + {i}^{14} + {i}^{-14} + {i}^{44} \\ \\ i - 1 - 1 + 1 = i - 1[/tex]
I am joyous to assist you anytime.
A number q plus 8 is less than or equal to 15
Answer:
q≤7
Step-by-step explanation:
q+8≤15
1) Subtract 8 from both sides:
q≤7
Answer:
[tex]\displaystyle 7 ≥ q; q + 8 ≤ 15[/tex]
Step-by-step explanation:
q + 8 ≤ 15
- 8 - 8
_______
[tex]\displaystyle q ≤ 7[/tex]
** The above answer is written in reverse, which is the exact same result.
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8-5b=-7 solve please
Answer:
Step-by-step explanation:
subtract 8
-5b=-15
divide negative 5
b=3
Answer the answer to your question is b=3
Solve a = 2x + 6xz for x
To solve the equation a = 2x + 6xz for x, isolate x on one side of the equation by following the steps: subtract 6xz from both sides, factor out x, and divide both sides by (2 + 6z).
To solve the equation a = 2x + 6xz for x, we need to isolate x on one side of the equation. Here are the steps:
Start with the equation: a = 2x + 6xz
Subtract 6xz from both sides: a - 6xz = 2x
Factor out x on the right side: a - 6xz = x(2 + 6z)
Divide both sides by (2 + 6z): (a - 6xz) / (2 + 6z) = x
Therefore, the solution for x is x = (a - 6xz) / (2 + 6z).
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20/30 as a decimal rounded to the nearest tenth
Answer:
1.5
Step-by-step explanation:
Answer:
0.7
Step-by-step explanation:
30 cannot be multiplied to give a power of 10, so to find the decimal you have to divide: 2/3 = 2/3 + 2 ÷ 3
2 divided by 3 is 0.6666666... It is a recurring decimal.
However it is not practical to use recurring decimals in calculations, so the decimal is usually rounded off to 2 or 3 decimal places depending on the accuracy required for the answer.
Sergei estimated 149% of 67 by performing the following steps. Which statement is true?
(70)(150%)
- (70)(100% + 50%)
- (70)(100%) + (70)(50%)
- (70)(1)+ (70) )
- 70+35
- 105
The estimate is less than the actual answer because the percent and the number were both rounded down.
The estimate is less than the actual answer because the percent and the number were both rounded up.
The estimate is greater than the actual answer because the percent and the number were both rounded down.
The estimate is greater than the actual answer because the percent and the number were both rounded up.
Answer: Last option.
Step-by-step explanation:
In order to estimate the percent "n" of a number"x", you need easy numbers to work with, therefore you can round "n" and "x" up or down; but it is important to remember that this estimation does not give you an exact value.
You can observe that Sergei's first step was to round 149% and 67 up, getting this result:
[tex]=105[/tex]
To verify if this estimate is less or greater than the actual answer, we can find the actual answer. This is:
[tex]\frac{67*149}{100}=99.83[/tex]
Therefore, we can conclude that the estimate is greater than the actual answer because the percent and the number were both rounded up.
Answer:
D
Step-by-step explanation:
I did it on Edgen 2020
a cheetah can run 27 m per second that means that a travels 27 m in 1 second at this rate how far can it travel in 8 Seconds
Answer:
5.4 m/s2
Step-by-step explanation:
Answer: 216 meters per 8th second
Step-by-step explanation:
do 27 times 8 it will give you 216
Verbal expression for r+4
Answer:
a number increased by 4
Step-by-step explanation:
r = a number
increased by four = +4
four more than the number R
Step-by-step explanation: with the word than you would flip it to r+4
A regular prism has two congruent rectangles as its bases. How can one base be transformed to carry onto the other?
One base must be translated to carry onto the other base
One base must be rotated to carry onto the other base
It is impossible to carry one base onto the other base
One base must be reflected to carry onto the other base
Answer:
One base must be translated to carry onto the other base
Step-by-step explanation:
A regular prism has two congruent rectangles as its bases. Since the bases of the prism are congruent and oriented the same way, neither reflection nor rotation will work to carry one base onto the other. It doesn't matter how many sides a geometric shape has.
Therefore the correct option is:
One base must be translated to carry onto the other base.
What is the lcm of 24,36,and, 60?
Answer: 360
Step-by-step explanation:
LCM is least common multiple. In other words, what number is divisible by 24, 36, and 60?
Factor each term. See what they have in common and then multiply the common term by all of the leftovers.
24 36 60
∧ ∧ ∧
12 2 12 3 12 5
They all have a 12 in common. The leftovers are 2, 3, & 5.
So, the LCM is 12 × 2 × 3 × 5 = 360
2(4+2x) > 5x+5
Solve the inequality
Answer:
x < 3
Step-by-step explanation:
Apply distributive property on the left of the inequality to get rid of the parenthesis:
8+4x > 5x+5
subtract 4x from both sides to group all terms with x on the right:
8 > 5x-4x+5
8 > x +5
Now subtract 5 from both sides to collect all numerical terms on the left:
8 - 5 > x
3 > x
Therefore the solution to the inequality are of those real numbers strictly smaller than 3.
The inequality can be written as x < 3 or also as we had it initially: 3 > x
Notice that the opening of the angle symbol is always facing the number 3 , meaning that 3 is the larger of the two numerical objects that are compared.
2 cubed minus 2 squared
Hello!
your answer is: 4
2 cubed is also written as: 2³
2 squared is also written as: 2²
so the re-written equation is: 2³ - 2²
To solve, simplify by doing the exponents.
2³ = 8
2² = 4
8 - 4 = 4
I hope this helps, and have a nice day!
Cask’n’Cork wine shop has a markup rate of 15%. What price will the shop charge for a bottle of zinfandel wine that costs $12.48 wholesale?
Answer:$14.35
Step-by-step explanation:
The shop will charge $14.352 as markup price.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have Cask’n’Cork wine shop that has a markup rate of 15%. A bottle of zinfandel wine costs $12.48 wholesale.
Assume that the shop charges $x. Then, we can write -
x = 12.48 + 15% of 12.48
x = 12.48 + (15/100) x 12.48
x = 12.48 + (3/20) x 12.48
x = 12.48 + 1.872
x = 14.352
Therefore, the shop will charge $14.352 as markup price.
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Which scale would produce the largest scale drawing of an object when compared to the actual object?
A. 1 inch : 5 feet
B. 1 inch : 30 inches
C. 1 foot : 12 yards
D. 1 centimeter : 1 meter
Covert the ratios so they are all the same measurement type.
A. 5 feet = 5 x 12 = 60 inches.
The scale becomes 1:60
B. 1:30
C. 12 yards = 12 x 3 = 36 feet x 12 = 432 inches.
The scale is 12:432 = 1:36
D. 1 meter = 39.37 inches.
1 inch = 2.54 cm
39.37 x 2.54 = 99.99 inches
The scale converted to inches becomes 1 :100 inches.
The first number would be the size of the drawing, the second number is the size of the actual object
If you use all 4 scale factors for a real object that is 100 inches:
A would need 100/60 = 1.67 inches.
B would need 100/30 = 3.3 inches.
C would need 100/36 = 2.78 inches.
D would need 100/100 = 1 inch.
The larger scaled drawing would be B.
Answer:
Option B.
Step-by-step explanation:
We need to find which scale would produce the largest scale drawing of an object when compared to the actual object.
First of all cover all units in inches.
In option 1,
1 inch : 5 feet
We know that
1 feet = 12 inch → 5 feet = 60 inch
So the ratio in inches is 1:60. It means the scale factor is 60.
In option 2,
1 inch : 30 inches
So the ratio in inches is 1:30. It means the scale factor is 30.
In option 3,
1 foot : 12 yards
12 inches : 12 yards (1 feet = 12 inch)
1 inch : 1 yards
1 inch : 36 inch (1 yard = 36 inch)
So the ratio in inches is 1:36. It means the scale factor is 36.
In option 4,
1 centimeter : 1 meter
1 centimeter : 100 centimeter (1 m = 100 cm)
1 inch : 100 inch
So the ratio in inches is 1:100. It means the scale factor is 100.
Option B has smallest scale factor, so it will produce the largest scale drawing of an object when compared to the actual object.
Therefore, the correct option is B.
find the slope of the line
Answer:
Undefined or No solution
Step-by-step explanation:
Because this line is a straight, vertical line, it means that the slope is undefined, or no solution. Any time you see a straight line going up and down, this will be true. However, if you see a horizonal line, this will not be true.
12 less than m is no less than 132
The number will be "m = -120".
Let,
The number be "m".According to the question,
The expression will be:
→ [tex]m-12=-132[/tex]
By adding "12" both sides of the expression, we get
→ [tex]m-12+12=-132+12[/tex]
→ [tex]m = -120[/tex]
Thus the response above is right.
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To solve the given statement '12 less than m is no less than 132', we set up the inequality m - 12 ≥ 132. Adding 12 to both sides, we find that m ≥ 144.
Explanation:Given the statement '12 less than m is no less than 132', we can set up an inequality to represent this relationship: m - 12 ≥ 132. To solve for m, we can add 12 to both sides of the inequality: m ≥ 132 + 12. Simplifying, we find that m ≥ 144. So, any value of m that is greater than or equal to 144 will satisfy the given statement.
Represent the following sentence as an algebraic expression, where "a number" is the letter x. number is decreased by 2.
Answer:
x-2
x decreased by 2 equals x-2.
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KA
write an expression for the amount of money (in dollars) in n nickels
Answer:
m1.00 +n0.20
Step-by-step explanation:
20 times 5 equal one dollar
The amount of money in n nickels can be expressed as 5n.
Explanation:The expression for the amount of money in n nickels can be written as 5n. Since each nickel is worth 5 cents, multiplying the number of nickels by 5 will give the amount in dollars. For example, if you have 3 nickels, the expression would be 5 x 3 = 15 dollars.
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Markus receives dollar bills from his grandfather for on week. On the first day he received $1; on the second day he received $2, on third day he received $4, and on the fourth day he received $8. If this continues, how much money will Markus have by the end of the week?
Answer: $127
Step-by-step explanation:
5th day: 8 * 2 = 16
6th day: 16 * 2 = 32
7th day: 32 * 2 = 64
Then add all the money he got throughout the week,
1 + 2 + 4 + 8 + 16 + 32 + 64
= 127
If K={(x, y) I x-y=5), is Set K a function?
Yes
No
Answer:
NO!
NO NUMBER VARIABLES CAN BE CALLED A FUNCTION
For which equation would x = 12 be a solution?
12 ÷ x > 12
12 - x ≥ 4
12x < 200
Answer:
12x < 200
Step-by-step explanation:
Substitute x = 12 into the left side of the inequality and compare with right side, that is
12 ÷ 12 = 1 < 12 ← not a solution
12 - 12 = 0 < 4 ← not a solution
12 × 12 = 144 < 200 ← this is a solution
I need urgent!!
The first people answer this question I give brainliest.
Directions:use the chart below to help answer the questions that follow
C.jeremy sister,Susie ,borrowed the money from their mom to pay for her order. The mother has agreed to deduct an equal amount of money from suzie allowance each week for the next five weeks to repay the loan . What is the weekly change in suzie allowance?
Numerical answer:
Explanation:
D. Jeremy grandparents want to change their order. They want to order three daisies and one geranium, instead of your daisies. How does this change affect the amount of their order? Explain how you arrived at your answer.
E. Jeremy approaches three people who do not want to buy any plants; however,they wish to donate some money for the fundraiser when Jeremy delivers the plants one week later. If the people promise to donate a total of $14.40, what will be the average cash donation?
F. Jeremy spends one week collecting orders.If 22 people purchase plants totaling $270,what is the average amount of Jeremy sale?
Numerical answer:
Explanation:
A) The total for the plants she buys is 8.50, so the change in her checking account would be -8.50, because they will take 8.50 out of her account when the check is cashed, the amount in her account is lowered.
B) Mr. Clark's total is 11.25. If he pays with a 20, subtract the plant total from 20:
20 - 11.25 = 8.75 is the amount of change Jeremy owes him.
The amount of money Jeremy collects would be that amount higher than what he needs.
C) Suzie owed 2.50, divide the amount she borrowed by the number of weeks her mom is keeping money:
2.50 / 5 = 0.50
Her allowance will be 0.50 less than what she normally would get.
D) Grandparents original amount = $15.00
3 daises = 3 x 3.75 = 11.25
1 geranium = 2.25
Total for new order = 11.25 + 2.25 = 13.50
Difference = 15 - 13.50 = 1.50
The new order would be $1.50 less.
E) Divide the total amount of the donation by the number of people:
14.40 / 3 = $4.80
F) Divide total amount by total people:
270 / 22 = $12.27 average
How many user must mike recruit in order for him to steam movies for free? The service costs $43.75 a month, but mikes rate is reduced by $1.25 for each new subscriber that he gets to sign up.
Answer:
35 subscribers
Step-by-step explanation:
Divide $43.75 by $1.25.
$43.75/$1.25 = 35
For each subscriber he gets, his service goes down by $1.25.
Since 35 * $1.25 = $43.75, for 35 new subscribers, his service will go down by $43.75.
He pays $43.75, so if the service goes down by $43.75, he will pay nothing since $43.75 - $43.75 = 0.
Answer: 35 subscribers
Follow below steps:
To determine how many users Mike must recruit for him to stream movies for free, we need to set up a simple algebraic equation. Mike's service costs $43.75 per month, and for each new subscriber he recruits, his rate is reduced by $1.25. Let's say the number of users Mike needs to recruit is represented by x.
The cost reduction for recruiting x users would be $1.25x. To get a free service, the total cost reduction must equal the monthly service cost of $43.75. Thus, the equation is $1.25x = $43.75.
To solve for x, we divide both sides by $1.25:
x = $43.75 / $1.25
x = 35
Therefore, Mike must recruit 35 new subscribers to stream movies for free.
Kyle gave 2/7 of his money to his wife and spent 3/5 of the remainder. If he had $300 left, how much money did he have at first?
Answer:
Kyle gave 2/7th of his money to his wife and spent 3/5 of the remainder. If he had $300 left, the money had by Kyle at first is $1050
Solution:
Step 1:
Consider “x” as the money which Kyle had initially.
From question, Kyle gave 2/7th of his money to his wife. So the remaining money left with Kyle is given as,
[tex]= 1 - \frac{2}{7}[/tex]
[tex]= \frac{7 - 2}{7} = \frac{5}{7}[/tex] ----- eqn 1
Now the remaining money left with Kyle is 5/7th.Given that Kyle spent 3/5 of the remaining money.
Now the remaining money left with Kyle is given as
[tex] = 1 - \frac{3}{5} = \frac{5 - 3}{5} = \frac{2}{5}[/tex]
Now kyle is left with $300, which is 2/5th of the initial money x .
We get equation as
[tex]\frac{2}{5} x=300[/tex]
2x = 1500
x = 750
Now Kyle is left with 750$ which is 5/7th of the initial amount x.( by using eqn 1)
We get equation as
[tex]\frac{5}{7} x = 750[/tex]
5x = 5250
x = 1050
So the amount had by Kyle at first is $1050
Final answer:
Working backward from the $300 Kyle had after spending and giving some away, we find that the original amount of money was $1050, which is determined by reversing the operations he performed on his money.
Explanation:
To solve how much money Kyle had at first, we need to work backwards from the amount he had left ($300) after he spent some and gave some to his wife. First, we determine how much was left before he spent the 3/5 of the remainder.
Let's denote Kyle's initial amount of money as x. The equation representing what Kyle did with his money is
x - (2/7)x = Remaining Amount After Giving to Wife
Kyle then spends 3/5 of this remaining amount, and is left with $300, so we can represent this as:
(1 - 3/5)(Remaining Amount After Giving to Wife) = $300
Substituting the first equation into the second we get:
(1 - 3/5)(x - (2/7)x) = $300
Simplifying, we find that (2/5)(5/7)x = $300.
This simplifies down to:
(2/5)(5/7)x = (10/35)x = $300
Finally, solving for x, we multiply both sides by the reciprocal of (10/35),
x = $300 × (35/10)
x = $300 × 3.5
x = $1050
So, Kyle originally had $1050.
How many times dose 24 go into 1,392
Answer:
58
Step-by-step explanation:
1392/24=58
Answer: 24 goes into the number 1,392, 58 times
How do you solve this?
Which ordered pair is a solution of the equation? -3x-y=6
The correct answer is (B) Only (-3, 3).
To determine which ordered pair is a solution of the equation, you need to substitute the values of \( x \) and \( y \) into the equation and see if it holds true. Let's check:
For option A: (-4, 4)
Substituting into the equation: \( -3(-4) - 4 - 6 = 12 - 4 - 6 = 2 \) which is not equal to 0, so it's not a solution.
For option B: (-3, 3)
Substituting into the equation: \( -3(-3) - 3 - 6 = 9 - 3 - 6 = 0 \) which is equal to 0, so it is a solution.
Thus, the correct answer is (B) Only (-3, 3).
Complete question :
Which ordered pair is a solution of the equation?
-3x-y-6
Choose 1 answer:
A Only (-4, 4)
B Only (-3, 3)
C Both (-4, 4) and (-3,3)
D Neither.
64.8 divided by 7 showing using long division
Answer:
9.257
Step-by-step explanation:
7 goes into 64 nine times with the remainder of 1. Bring the decimal point up and the 8 down. 7 goes into 18 two times with the remainder of 4. 7 goes into 40 5 times with the remainder of 5. 7 goes into 50 7 times. That equals 9.257.
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To divide 64.8 by 7 using long division, calculate how many times 7 can be subtracted from each part of the number 64.8 in sequence. This results in the final answer of 9.25.
Explanation:To find 64.8 divided by 7 using long division, first write down 64.8 with a division bar over it and 7 on the left side of the bar. You would write:
7 | 64.8
Next, ask: How many times does 7 go into 64? This is 9 times since 7 times 9 is 63. Record the 9 above the line and record the product (63) below 64. Subtract 63 from 64 to get 1.
Bring down the 8 (from 64.8) to the right of the 1. Now you have 18. Ask how many times does 7 go into 18? This is 2 times. So you add the digit 2 next to 9 on top of the bar. 7 times 2 is 14.
Subtract 14 from 18 to get 4. As the decimal point should be straight up from where it is in the 64.8, record a decimal point.
Now, since there's no more numbers to bring down, you can add a 0 to 40. 7 goes into 40, 5 times. Therefore, we add 5 next to the 2 after the decimal point. So, 64.8 divided by 7 is 9.25.
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the lines below are parallel if the slope of the green line is -2 what is the slope of the red line
Answer:
-2
Step-by-step explanation:
Since they are parallel, they have the same slope. This will be true for any set of lines.
the output of a function is 7 more than 3 times the input find the input when the output is -8
Answer:
The input is -5 when the output is -8
Step-by-step explanation:
Let
y-----> the output
x ----> the input
we know that
The linear equation that represent this problem is
[tex]y=3x+7[/tex]
so
For y=-8
substitute in the equation and solve for x
[tex]-8=3x+7[/tex]
Subtract 7 both sides
[tex]-8-7=3x\\-15=3x[/tex]
Divide by 3 both sides
[tex]x=-5[/tex]
therefore
The input is -5 when the output is -8
A gas engine is 6% efficient. What portion of a 12 gallon tank of gas is wasted?
Answer:
282/25
Step-by-step explanation:
[tex]efficient \: = 12 \times \frac{6}{100} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{72}{100} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{18}{25 } \\ so \: \\ west \: = 12- \frac{18}{25} \\ \: \: \: \: \: \: \: \: \: \: \: \: = \frac{282}{25} \: \: gallon[/tex]
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mark it as a brilliant answer
The wasted portion of gallon tank will be "[tex]\frac{282}{25}[/tex]". A further solution is provided below.
Given:
Efficient percent = 6%Number of gallon = 12Now,
The efficient portion will be:
= [tex]12\times \frac{6}{100}[/tex]
= [tex]\frac{72}{100}[/tex]
= [tex]\frac{18}{25}[/tex]
hence,
The wasted portion of gallon tank will be:
= [tex]12-\frac{18}{25}[/tex]
= [tex]\frac{282}{25} \ gallon[/tex]
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