Tamara says that raising the number i to any integer power results in either -1 or 1 as the result, since i^2 = -1. Do you agreed or disagree with Tamera? Explain
Tamara's claim that raising the complex number i to any integer power results in either -1 or 1 is incorrect. The powers of i follow a cyclic pattern which includes i, -1, -i, and 1.
Explanation:I must disagree with Tamara's statement that raising the complex number i to any integer power results in either -1 or 1. The powers of i actually follow a recurring pattern: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1, and then the pattern repeats.
For i to the power of 1, the result is just i itself.For i to the power of 2 (i^2), the result is indeed -1.For i to the power of 3 (i^3), the result is -i.For i to the power of 4 (i^4), the result is back to positive 1.So, while -1 and 1 are indeed in the sequence of results, they're not the only possibilities. Specifically, -i and i are also possible results of raising i to an integer power.
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Two cities are 124 miles apart from each other. The cities are 4cm on a map, what is the Scale factor?
Given the whole number 3,257,098, in what place value is the 2? Ten thousands Millions Thousands Hundred thousands
Final answer:
In the number 3,257,098, the digit 2 is in the hundred thousands place, which is the sixth position from the right or the second position from the left.
Explanation:
In the number 3,257,098, the digit 2 is in the hundred thousands place. When examining place values, we count the positions of the digits from right to left, starting with the ones position immediately to the left of the decimal point (imaginary for whole numbers). The digit to the immediate left is in the tens place, followed by hundreds, thousands, ten thousands, and so on. In this case:
9 is in the ones place,8 is in the tens place,0 is in the hundreds place,7 is in the thousands place,5 is in the ten thousands place,2 is in the hundred thousands place,3 is in the millions place.Pleasee hurryyyy
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Correct as will get brainliest
i need to know how to make the equations
In the circle graph what is the measure of the central angle for carrots and potatoes combined
Potatoes 8%
Carrots 11%
Green beans 12%
Corn 15%
Broccoli 20%
Other 34%
Brian deposited $4000 into an account with 5.4% interest, compounded monthly. Assuming that no withdrawals are made, how much will he have in the account after 6 years?
What is the sum of the first eight terms of the series?
(−600)+(−300)+(−150)+(−75)+(−37.5)+...
Round the answer to two decimal places.
−1200.50
−1195.31
−1190.63
−1181.25
Which of the following functions best represents the graph?
A. f(x) = x3 + x2 − 4x − 4
B. f(x) = x3 + x2 − x − 1
C. f(x) = x3 + 3x2 − 4x − 12
D. f(x) = x3 + 2x2 − 2x − 1
Answer:
B. f(x)=x³+x²-x-1
Step-by-step explanation:
The value of the graph f(x) shows that at x=1 and x=-1 must yield f(x)=0
which is true in case B.
A. f(1)=1+1-4-4= -6≠0
C. f(1)= 1+3-4-12=-12≠0
D. f(-1)= -1+2+2-1= 2≠0
Hence, option B is correct
i.e. f(x)= x³+x²-x-1
What is the sum of 2 numbers is 100 and their difference is 6?
Quick question!
Which investment vehicles historically provide the lowest annual rates of return?
A)Government bonds and U.S. Treasury bills
B)Large company stocks and government bonds
C)Small company stocks and large company stocks
D) U.S. Treasury bills and small company stocks
What is the value of x?
a(1)= -2
a(n)=a(n-1)-5
whats the 4th term in the sequence?
Answer:
The fourth term in the sequence is -17
Step-by-step explanation:
To find the 4th term of the sequence, we will simply follow the steps below;
a(1) = -2
a(n) = a(n-1)-5
We will find the value of the sequence when n = 1, n= 2 n =3 n=4
The first one has been done for us, so we have the first term to be a(1) = -2
The next thing to do, is to find the second term, ie. when n=2
a(n) =a(n-1)-5
a(2) =a(2-1)-5
=a(1) - 5
but a(1) = -2
a(2) =a(1) - 5
=-2-5
=-7
a(2) = -7
next is to find the third term, ie. when n=3
a(n) =a(n-1)-5
a(3) =a(3-1)-5
=a(2) - 5
but a(2) = -7
a(3) =a(2) - 5
=-7-5
=-12
a(3) = -12
next is to find the fourth term, ie. when n=4
a(n) =a(n-1)-5
a(4) =a(4-1)-5
=a(3) - 5
but a(3) = -12
a(4) =a(3) - 5
=-12-5
=-17
a(4) = -17
Therefore, the fourth term in the sequence is -17
The probability that a bakery has demand for 2 3 4 or 5 birthday cakes on any given day are 0.32, 0.24, 0.25 and 0.19 respectively. construct a probability distribution for this data
A group of art students are painting a mural on a wall. The rectangular dimensions of (6x+7) by (8x+5) and they are planning the mural to be (x+4) by (2x+5). What is the area of the remaining wall after the mural has been painted?
Answer:
The area of remaining wall after the mural has been painted is [tex]46x^2+73x+15[/tex] square units.
Step-by-step explanation:
If the dimensions of a rectangle are l and w, then area of rectangle is
[tex]A=l\times w[/tex]
The dimensions of wall are (6x+7) and (8x+5). So, the area of wall is
[tex]A_1=(6x+7)\times (8x+5)[/tex]
[tex]A_1=6x(8x+5)+7(8x+5)[/tex]
[tex]A_1=48x^2+30x+56x+35[/tex]
[tex]A_1=48x^2+86x+35[/tex]
The dimensions of mural are (x+4) and (2x+5). So, the area of mural is
[tex]A_2=(x+4)\times (2x+5)[/tex]
[tex]A_2=x(2x+5)+4(2x+5)[/tex]
[tex]A_2=2x^2+5x+8x+20[/tex]
[tex]A_2=2x^2+13x+20[/tex]
The area of remaining wall after the mural has been painted is
[tex]A=A_1-A_2[/tex]
[tex]A=48x^2+86x+35-(2x^2+13x+20)[/tex]
[tex]A=48x^2+86x+35-2x^2-13x-20[/tex]
[tex]A=46x^2+73x+15[/tex]
Therefore area of remaining wall after the mural has been painted is [tex]46x^2+73x+15[/tex] square units.
Answer:
46x^2 + 73x + 15
Step-by-step explanation:
Which ordered pair (a, b) is a solution to the given system?
A 45 degree sector in a circle has an area of 13.75pi cm^2, what is the area of the circle? Enter your answer as a decimal.
Can someone check my answers?
1. Simplify the sum or difference.
sqrt 5 + 6 sqrt 5
A) 6 sqrt 5
B) 30
C) 6 sqrt 10
D) 7 sqrt 5
2. Simplify the sum or difference.
4 sqrt 2 - 7 sqrt 2
A) negative sqrt 6
B) -3 sqrt 2
C) -11 sqrt 2
D) 11 sqrt 2
3. Simplify the sum or difference.
3 sqrt 7 - sqrt 63
A) -2 sqrt 7
B) -6 sqrt 7
C) -4 sqrt 3
D) 0
4. Simplify the sum or difference.
-6 sqrt 10 + 5 sqrt 90
A) 9 sqrt 10
B) -9 sqrt 10
C) -39 sqrt 10
D) -10
5. Simplify the product.
sqrt 6 (sqrt 2 + sqrt 3)
A) sqrt 8 + 3
B) sqrt 30
C) 2 sqrt 3 + 3 sqrt 2
D) 4 sqrt 2 + 3
1 - D
2 - B
3 - D
4 - A
5 - C
6 - A
7 - D
8 - B
9 - B
10 - C
i just took the "Operations with Radical Expressions practice" for WA connexus, these answers are 100 percent correct
What types of numbers are undefined when they are under a radical sign? If you were dealing with the number √-1, would it be defined if you multiplied it by 2? Would it be defined if you subtracted some real number from it? Would it be defined if you squared it? Would it be defined if you cubed it?
Final answer:
In the complex number system, types of numbers that are undefined under a radical sign in the real number system, such as negative real numbers, become defined. For example, the square root of -1 is i, an imaginary unit. This allows operations like multiplication, subtraction, squaring, and cubing on complex numbers to be defined, illustrating the comprehensive nature of the complex number system.
Explanation:
The types of numbers that are undefined under a radical sign (specifically the square root) are negative real numbers in the context of the real number system. However, when we introduce the concept of complex numbers, every number, including negative ones, can have a defined square root. For example, the square root of -1 is defined as i, which is an imaginary unit.
When you handle the expression √-1 (which is i) in various operations:
If multiplied by 2, the result is still defined as 2i, which is a complex number.If a real number is subtracted from it, such as √-1 - 3, this is also defined and results in i - 3, another complex number.If squared (√-1)^2, it simplifies to -1, which is a defined real number.If cubed (√-1)^3, it results in -i, still defined within the complex number system.This illustrates that with the incorporation of complex numbers, operations on what would be undefined values in the real number system become fully defined. Additionally, the complex number system ensures that every polynomial equation has a root, fulfilling the Fundamental Theorem of Algebra. Complex numbers are a critical development in mathematics, allowing for the full spectrum of polynomials to be solvable and expanding our capability to model and solve a wide array of problems.
can someone help me find the y-intercept and explain how you got that answer?
Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, one chip has the number 3, and the other chip has the number 5. Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two chips he chooses have different numbers, he loses $1 (–$1). Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the table. (Hint: The total possible outcomes are six because there are four chips and you are choosing two of them.) Xi 2 –1 P(xi) What is Miguel’s expected value from playing the game? answer= $2 Based on the expected value in the previous step, how much money should Miguel expect to win or lose each time he plays? answer= $2 What value should be assigned to choosing two chips with the number 1 to make the game fair? Explain your answer using a complete sentence and/or an equation. A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two of the sectors are purple, two of the sectors are yellow, and one sector is blue. Landing on the blue sector will give 3 points, landing on a yellow sector will give 1 point, landing on a purple sector will give 0 points, and landing on a red sector will give –1 point. Let X = the points you have after one spin. Fill out the missing values in the table. Xi P(xi) If you take one spin, what is your expected value? What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values. The point guard of a basketball team has to make a decision about whether or not to shoot a three-point attempt or pass the ball to another player who will shoot a two-point shot. The point guard makes three-point shots 30 percent of the time, while his teammate makes the two-point shot 48 percent of the time. Xi 3 0 P(xi) 0.30 0.70 Xi 2 0 P(xi) 0.48 0.52 What is the expected value for each choice? Should he pass the ball or take the shot himself? Explain. Claire is considering investing in a new business. In the first year, there is a probability of 0.2 that the new business will lose $10,000, a probability of 0.4 that the new business will break even ($0 loss or gain), a probability of 0.3 that the new business will make $5,000 in profits, and a probability of 0.1 that the new business will make $8,000 in profits. Claire should invest in the company if she makes a profit. Should she invest? Explain using expected values. If Claire’s initial investment is $1,200 and the expected value for the new business stays constant, how many years will it take for her to earn back her initial investment?
Answer:
To check all the events (6), we label the chips. Suppose one chip with 1 is labeled R1 and the other B1 (as if they were red and blue). Now, lets take all combinations; for the first chip, we have 4 choices and for the 2nd chip we have 3 remaining choices. Thus there are 12 combinations. Since we dont care about the order, there are only 6 combinations since for example R1, 3 is the same as 3, R1 for us.
The combinations are: (R1, B1), (R1, 3), (R1, 5), (B1, 3), (B1, 5), (3,5)
We have that in 1 out of the 6 events, Miguel wins 2$ and in five out of the 6 events, he loses one. The expected value of this bet is: 1/6*2+5/6*(-1)=-3/6=-0.5$. In general, the expected value of the bet is the sum of taking the probabilities of the outcome multiplied by the outcome; here, there is a 1/6 probability of getting the same 2 chips and so on. On average, Miguel loses half a dollar every time he plays.
find all the zeros for each function.
p(x)=2x^3-3x^2+3x-2
*show work*
HELP!!!!! 8 POINTS!!!!!! Rachel decided to have bouncy balls as a party favor. She determines that her ratio of bouncy balls to guests is 9:3. Explain how to find the number of balls needed for 30 guests.
The firing of a Revolutionary War cannon is used to open the local Fourth of July festivities. The muzzle of the cannon barrel is 6 feet above ground level. The height of the cannon ball being fired from the Revolutionary War cannon as a function of elapsed time is modeled by the function h(t) = –16t2 + 75t + 6, where h(t) is the height of the cannon ball in feet, and t is the elapsed time since firing in seconds. Determine at approximately what elapsed time(s) the cannon ball will be at a height of 55 feet.
What is the measure of angle x? Enter your answer in the box. x = º Three intersecting lines. Three of the six angles formed by the intersecting lines are labeled. Every other angle is labeled. Going clockwise, they are labeled 56 degrees, x, and 41 degrees.
83 i am quite certain hope this helps (why did echo delete my answer the first time could of gave me a reason why because that was rude!)
im pretty sure it is 83
hope this help you guys
What is the area of the manhole if it is 2 ft wide use 3.14 as pi and round to the nearest hundredth
Find the missing measure for a right circular cone given the following information. Find L.A. if r = 6 and h = 8 48 60 96
Final answer:
The Lateral Area (L.A.) of a right circular cone with a base radius of 6 and a height of 8 is 60π square units, calculated by finding the slant height using the Pythagorean theorem and then applying the formula for L.A.
Explanation:
The student is asked to find the Lateral Area (L.A.) of a right circular cone given the base radius (r) is 6 and the height (h) is 8. First, we need to find the slant height of the cone, which can be done using the Pythagorean theorem in a right triangle where one leg is the height of the cone, the other leg is the radius of the base, and the hypotenuse is the slant height (l). The formula is l = [tex]\sqrt{(r^2 + h^2)[/tex]. After calculating l, we use the formula for the Lateral Area: L.A. = π r l.
Calculating the slant height: l = [tex]\sqrt{(6^2 + 8^2)}[/tex] = [tex]\sqrt{(36 + 64)[/tex]= [tex]\sqrt{100[/tex]= 10.
Now, we calculate the Lateral Area: L.A. = π * 6 * 10 = 60π. Hence, the Lateral Area of the cone is 60π square units.
What is the length of JK, to the nearest tenth of a millimeter?
The length of JK to the nearest tenth is; 4.5 mm
What is the Length of a side of the triangle?From the given triangle, we see the following parameters;
JL = 3 mm
KL = 5 mm
angle JLK = 62 °
Use the Law of Cosines, we can find the length of JK as;
|JK| = √(3² + 5² − 2(3 * 5) cos62°)
|JK| = √(34 - 14.084)
|JK| = 19.916
|JK| = √19.916
|JK| = 4.463
Approximating to the nearest tenth; JK = 4.5 mm
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7 cakes cost £5.60 , what would be the cost of:
10 cakes
5 cakes
12 cakes
Factor the polynomial. 6x2 - 7x - 3 A) (6x - 1)(x + 3) B) (6x + 3)(x - 1) C) (2x - 3)(3x + 1) D) (3x - 3)(2x + 1)