ANSWER
[tex]{i}^{20} + 1 =2[/tex]
EXPLANATION
The given expression is;
[tex] {i}^{20} + 1[/tex]
Recall that, in complex numbers
[tex] {i}^{2} = - 1[/tex]
We use this identity to simplify the given expression:
[tex]{i}^{20} + 1 =( {i}^{2})^{10} + 1[/tex]
This implies that:
[tex]{i}^{20} + 1 =( - 1)^{10} + 1[/tex]
[tex]{i}^{20} + 1 =1+ 1[/tex]
[tex]{i}^{20} + 1 =2[/tex]
dani buys. a movie. at walmart on sale. the original. cost is $18 bit is 30% off. and there eis 5% sales tax. what the total cost she will pay for the movie
The total cost Dani will pay for the movie including discount and sales tax is $13.23
To find the total cost Dani will pay for the movie:
Calculate the discount: $18 x 0.30 = $5.40
Subtract the discount from the original price: $18 - $5.40 = $12.60
Calculate the 5% sales tax: $12.60 x 0.05 = $0.63
Total cost: $12.60 + $0.63 = $13.23
The length of a rectangle is 2 cm more than four times the width. If the perimeter of the rectangle is 84 cm, what are its dimensions
Answer:
Length 34 cm
Width 8 cm
Step-by-step explanation:
Let
x-----> the length of the rectangle
y----> the width of the rectangle
we know that
The perimeter of rectangle is equal to
P=2(x+y)
P=84 cm
so
84=2(x+y)
42=x+y ----> equation A
x=4y+2 -----> equation B
substitute equation B in equation A and solve for y
42=(4y+2)+y
5y=42-2
y=40/5=8 cm
Find the value of x
x=4y+2 ----> x=4(8)+2=34 cm
The dimensions are
Length 34 cm
Width 8 cm
The width of the rectangle is 8 cm and the length is 34 cm.
To determine the dimensions of the rectangle, we need to set up equations based on the given information.
Let's denote the width of the rectangle by W (in cm). According to the problem, the length L is 2 cm more than four times the width. Therefore, we can express the length as:
L = 4W + 2
The perimeter of a rectangle is calculated using the formula:
Perimeter = 2L + 2W
Given that the perimeter is 84 cm, we can substitute the expressions for L and W into the perimeter formula:
84 = 2(4W + 2) + 2W
Simplify the equation:
84 = 8W + 4 + 2W84 = 10W + 4Subtract 4 from both sides: 80 = 10WDivide both sides by 10: W = 8Now that we have the width, we can find the length:
L = 4(8) + 2 = 32 + 2 = 34
Thus, the dimensions of the rectangle are:
Width: 8 cmLength: 34 cm.A 13 ounces can of tuna costs 2.34$. What is the unit of price of 1 ounce of tuna
Answer:
0.18 cents
Step-by-step explanation:
2.34 divided by 13= 0.18
To check my answer, 0.18 x 13 = 2.34
Answer:
$0.18/ounce
Step-by-step explanation:
Divide the price by the weight.
($2.34)/(13 ounces) = $0.18/ounce
Please Help Quickly!!
What is the first step to prove that 9^n - 4^n is divisible by 5?
the answer should be,
A. shows that 9^1 - 4^1=5
hope this helps! :)
Solve 11cW+ 2k= 15cwfor k.
Answer:
k = 2cw
Step-by-step explanation:
1. 11cw + 2k = 15cw
2. Subtract 11cw from both sides:
2k = 4cw
3. Divide by 2 on both sides:
k = 2cw
Evaluate the dot product of (2,4) and (1,2)
ANSWER
The dot product is 10.
EXPLANATION
The given vectors are (2,4) and (1,2).
If we have the vectors
u=(a,b) and v=(c,d)
Then the dot product of the two vectors is given by
[tex]u \bullet \: v = ac + bd[/tex]
This implies that,
[tex](2,4) \bullet(1,2) = 2 \times 1 + 4 \times 2[/tex]
This simplifies to;
[tex](2,4) \bullet(1,2) = 2 + 8 = 10[/tex]
Answer:
-6
Step-by-step explanation:
took test
Below are two different functions, f(x) and g(x). What can be determined about their y-intercepts?
graph going through negative 1, negative 1 and negative 4, negative 1
x g(x)
4 | 9
6 | 13
8 | 17
A) The function g(x) has a higher y-intercept.
B) The function f(x) has a higher y-intercept.
C) They both have the same y-intercept.
D) The relationship between y-intercepts cannot be determined.
The answer is:
The correct option is:
A) The function g(x) has a higher y-intercept.
Why?To solve the problem, we need to find the y-intercept of the g(x) function, and then, compare to the y-intercept of the f(x) function which is equal to -1 (we can see it on the picture).
Also, we need to remember the slope-interception form of the line:
[tex]y=mx+b[/tex]
So,
Finding the y-intercept of the g(x) function, we have:
Calculating the slope of the function, using the first two points (4,9) and (6,13), we have:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{13-9}{6-4}=\frac{4}{2}=2[/tex]
Now,
Calculating the value of "b", we have:
Using the first point (4,9), the slope of the function, and the slope-intercept form of the function, we have:
[tex]y=mx+b[/tex]
[tex]y=2x+b[/tex]
[tex]9=2*(4)+b[/tex]
[tex]9=8+b[/tex]
[tex]9-8=b[/tex]
[tex]b=1[/tex]
So, the equation of the line will be:
[tex]y=2x+1[/tex]
We know that "b" represents the y-intercept, so, the function g(x) has its y-intercept at y equal to 1.
Comparing, we have that the function f(x) has a y-intercept located at y equal to "-1" and the g(x) function has a y-intercept located at y equal to "1".
Hence, the correct option is:
A) The function g(x) has a higher y-intercept.
Have a nice day!
A bag contains 5 blue marbles, 2 black marbles, and 3 red marbles. A marble is randomly drawn from the bag. The probability of not drawing a black marble is . The probability of drawing a red marble is .
Answer:
The probability of not drawing a black marble is : 8/10, 4/5, 80%
The probability of drawing a red marble is: 3/10, or 30%
Step-by-step explanation:
Blue marbles: 5
Black marbles: 2
Red marbles: 3
Total marbles: 10
The probability of not drawing a black marble is :
NOT drawing a black marble means you'll draw either a blue or a red one. Combined, red and blue marbles account for 8 marbles out of 10.
So the probability of NOT drawing a black marble is 8/10, 4/5 or 80%
The probability of drawing a red marble is:
There are 3 red marbles, out of 10 marbles.... so the probability of drawing a red marble is 3/10, or 30%
Factor the polynomial.
2y2 – 14y + 20
A.(y + 2)(y + 5)
B.2ly - 2)(y + 5)
C.(y-2)(x - 5)
D.2(y-2)(y-5)
2y^2- 14y+ 20
By splitting the middle term:
2y^2 -10y -4y +20
By taking the common outside:
2y(y-5) -4(y-5)
=(2y-4)(y-5)
=2(y-2)(y-5)
Therefore D is the right answer
Answer:
D
Step-by-step explanation:
Given
2y² - 14y + 20 ← factor out 2 from each term
= 2(y² - 7y + 10)
To factor the quadratic
Consider the factors of the constant term (+ 10) which sum to give the coefficient of the y- term (- 7)
The factors are - 2 and - 5, since
- 2 × - 5 = 10 and - 2 - 5 = - 7, so
y² - 7y + 10 = (y - 2)(y - 5) and
2y² - 14y + 20 = 2(y - 2)(y - 5) → D
(x 4 - 3x 3 + 3x 2 - 3x + 6) (x - 2)
Answer:
x^5 - 5 x^4 + 9 x^3 - 9 x^2 + 12 x - 12
Step-by-step explanation:
(x ^4 - 3x^3 + 3x^2 - 3x + 6) (x - 2)
Distribute the x to all the terms in the first parentheses
(x^ 4 *x - 3x^ 3 *x + 3x^ 2 *x - 3x *x + 6*x)
Then simplify
(x^5 - 3x^4 + 3x^ 3 - 3x2 + 6x)
Distribute the -2 to all the terms in the first parentheses
(x^ 4 *(-2) - 3x^ 3 *(-2) + 3x^ 2 *(-2) - 3x *(-2) + 6*(-2))
Then simplify
(-2x^4 +6x^3 -6x^ 2 +6x -12)
Add the terms together
(x^5 - 3x^4 + 3x^ 3 - 3x2 + 6x) +(-2x^4 +6x^3 -6x^ 2 +6x -12)
x^5 - 5 x^4 + 9 x^3 - 9 x^2 + 12 x - 12
Answer:
x^3 -x^2 + x -1 + 4/x-2
Step-by-step explanation:
;)
7cm
10cm
4cm
The area of the compound shape is 106cm.
work out the size of x.
Answer: 9cm
Step-by-step explanation:
[tex]7x10=70cmx^{2}[/tex]
4(x)=4x
1.) 70+4x=106 (subtract 70 on both sides)
2.)4x=36 (divide 4 on both sides)
3.)x=9
answer=9
7x10=70cmxsquare
4(x)=4x
70+4x=106
4x=36
x=36/4
x=9
Much of Ann’s investments are in Cilla Shipping. Ten years ago, Ann bought seven bonds issued by Cilla Shipping, each with a par value of $500. The bonds had a market rate of 95.626. Ann also bought 125 shares of Cilla Shipping stock, which at the time sold for $28.00 per share. Today, Cilla Shipping bonds have a market rate of 106.384, and Cilla Shipping stock sells for $30.65 per share. Which of Ann’s investments has increased in value more, and by how much? a. The value of Ann’s bonds has increased by $45.28 more than the value of her stocks. b. The value of Ann’s bonds has increased by $22.64 more than the value of her stocks. c. The value of Ann’s stocks has increased by $107.81 more than the value of her bonds. d. The value of Ann’s stocks has increased by $8.51 more than the value of her bonds.
Answer:
A.
The value of Ann’s bonds has increased by $45.28 more than the value of her stocks.
Step-by-step explanation:
The value of Ann’s bonds has increased by $45.28 more than the value of her stocks. Option A is correct.
We have given that,
Much of Ann’s investments are in Cilla Shipping.
What is the stock increase?
By this, we mean that share prices change because of supply and demand. If more people want to buy a stock (demand) than sell it (supply), then the price moves up.
Ten years ago, Ann bought seven bonds issued by Cilla Shipping, each with a par value of $500. The bonds had a market rate of 95.626.
Ann also bought 125 shares of Cilla Shipping stock, which at the time sold for $28.00 per share.
Today, Cilla Shipping bonds have a market rate of 106.384, and Cilla Shipping stock sells for $30.65 per share.
The value of Ann’s bonds has increased by $45.28 more than the value of her stocks. Option A is correct.
To learn more about the stock increase visit:
https://brainly.com/question/25818989
#SPJ2
The wavelength of a radio wave varies inversely as its frequency. A wave with a frequency of 720 kilohertz has a length of 500 meters. What is the length of a wave with a frequency of 450 kilohertz?
.......... meters
Answer:
800 meters
Step-by-step explanation:
y is inversely proportional to x is the same as y is inversely proportional to [tex]\frac{1}{x},[/tex] that means
[tex]y=\dfrac{k}{x}.[/tex]
If a wave with a frequency of x=720 kilohertz has a length of y=500 meters, then
[tex]500=\dfrac{k}{720}\\ \\k=500\cdot 720=360000.[/tex]
Hence, the length of a wave y with a frequency of x=450 kilohertz is
[tex]y=\dfrac{360000}{450}=800[/tex]
The relationship between the frequency and wavelength of a wave is given by the formula:
\[ c = f \times \lambda \]
where:
- \( c \) is the speed of light (or the speed of the wave in another medium, but for radio waves in the air or vacuum, it's approximately the speed of light),
- \( f \) is the frequency of the wave,
- \( \lambda \) is the wavelength of the wave.
Given that the relationship is inverse, when the frequency goes up, the wavelength goes down, and vice versa.
We are given that a wave with frequency 720 kilohertz has a length of 500 meters. We can represent this with the equation:
\[ c = 720 \times 500 \]
We are asked to find the wavelength when the frequency is 450 kilohertz. Since the speed of light doesn't change, we set up the proportion using the formula, keeping \( c \) constant:
\[ 720 \times 500 = 450 \times \lambda_{\text{new}} \]
Now we solve for \( \lambda_{\text{new}} \):
\[ \lambda_{\text{new}} = \frac{720 \times 500}{450} \]
To simplify this, we can divide both the numerator and the denominator by a common factor. In this case, let's divide by 90:
\[ 720 \div 90 = 8 \]
\[ 450 \div 90 = 5 \]
\[ 500 \text{ remains unchanged} \]
Now we can substitute these simplified numbers back into our equation:
\[ \lambda_{\text{new}} = \frac{8 \times 500}{5} \]
\[ \lambda_{\text{new}} = \frac{4000}{5} \]
\[ \lambda_{\text{new}} = 800 \]
So the length of a wave with a frequency of 450 kilohertz is 800 meters.
Tell me how to do it and why please
Answer:
It would take them 6.667 minutes to paint 50 square feet together.
Step-by-step explanation:
This is a classic work problem. If Sam can do the job in 10 minutes, she can get done 1/10 of the job in one minute. If you can do the job in 5 minutes, you can 1/5 of the job done in one minute. To find out how many minutes it will take them together to paint 25 square feet, set the addition of their times equal to 1/x:
[tex]\frac{1}{10}+\frac{1}{5}=\frac{1}{x}[/tex]
x is how long it takes them to get the job done together. Find the common denominator and multiply it through be everything to get rid of the denominators altogether. That denominator is 10x:
[tex](10x)\frac{1}{10}+(10x)\frac{1}{5}=(10x)\frac{1}{x}[/tex]
Simplify to get the simple equation x + 2x = 10 and 3x = 10. That means that x=3 1/3. That's how long it takes to do 25 square feet. Double that time for 50 square feet.
help needed! 20 points and brainliest if answered right
Answer:
1. Simple random sampling
2. Systematic random sampling
A moving person travels 24 feet in 7 seconds.The moving sidewalk has a length of 180 feet.how long will it talk to move from one end of the sidewalk to the other
Answer:
=53 seconds.
Step-by-step explanation:
24ft=7sec
180
180 x 7
_______=52.5=53
24
what is the average of these numbers 23 33 31?
Answer:
29
Step-by-step explanation:
Answer: 29
Step-by-step explanation:
It is important to know the definition.
The average of a set of number is defined as the sum of all these numbers divided by the total numbers that are in this set.
So, knowing this, we know that if we have a set of three numbers:"a", "b" and "c" , we can calculate the average of them with this procedure:
[tex]average=\frac{a+b+c}{3}[/tex]
Therefore, we can calculate the average of the numbers 23, 33 and 31. This is:
[tex]average=\frac{23+33+31}{3}=\frac{87}{3}=29[/tex]
PLEASE HELP & FAST!
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind. Drag the item to the trash can. Click the trash can to clear all your answers. Click the place the appropriate equivalent forms of the numbers shown.
Please help and fast!
Answer:
64% as a fraction and decimal: 16/25 and .64
1/8 as a percent and decimal: 12.5% and .125
1.4 as a percent and fraction: 140% and 1 2/5
2 3/4 as a percent and decimal: 275% and 2.75
8 percent as a decimal and fraction: .08 and 2/25
Step-by-step explanation:
a rectangular prism is 4 units by 2 1/2 units by 1 1/2 units how many cubes with a side length of 1/2 units will compleat fill the prism
Answer:
Step-by-step explanation:
X+Y=0 someone please explain
Answer: Because there are no values
Step-by-step explanation: Since there are no numbers in the problem, there is no sum. making it 0. You can't add two letters to make another letter, So it becomes a 0. anything with a variable subtracted, divided, added, ect by another variable, is 0
Which is a property of an angle
Answer:
has two rays that share a common end point.
Answer:
Angle has two rays that share a common endpoint.
Step-by-step explanation:
Given : Angle.
To find : Which is a property of an angle.
Solution : We have given properties of an angle .
Angle : the space between two intersecting lines or surfaces at or close to the point where they meet.
Vertex is also called the angle.
Therefore, Angle has two rays that share a common endpoint.
Determine the next term in the sequence. 4, -2, 1, -0.5, ...
-1.5
1.5
-0.25
0.25
.25 is the answer because the next number should be half of the previous number and the opposite sign of the previous number.
0.25 is the best answer for the sequence :D
what is the slope of a line that is perpendicular to the line shown?
*please help
Answer:
[tex]m=\frac{3}{4}[/tex]
Step-by-step explanation:
We can use the slope formula in order to find the slope of the line
[tex]m=\frac{-2-2}{0-(-3)} \\m=\frac{-4}{3}[/tex]
For a line to be perpendicular, it must have a slope that is the negative reciprocal, so that means that we swap the numerator and denominator and then multiply it by -1, this means that
[tex]m=\frac{-4}{3}\\\\m=\frac{3}{-4} \\\\m=\frac{-3}{-4} \\\\m=\frac{3}{4}[/tex]
if f(x) and f^-1(x) are inverse functions of each other adn f(x) - 2x+5, what is f^-1(8)?
Answer:
[tex]f^{-1}(8)=1.5[/tex]
Step-by-step explanation:
If y=f(x)=2x+5, to find the inverse function express x n terms of y:
[tex]y=2x+5\\ \\2x=y-5\\ \\x=\dfrac{y-5}{2}[/tex]
Now, change y into x and x into y:
[tex]y=\dfrac{x-5}{2}\\ \\f^{-1}(x)=\dfrac{x-5}{2}[/tex]
Substitute x=8 into [tex]f^{-1}(x)[/tex] expression:
[tex]f^{-1}(8)=\dfrac{8-5}{2}\\ \\f^{-1}(8)=\dfrac{3}{2}=1.5[/tex]
Answer:
3/2
Step-by-step explanation:
f(x) = 2x+5
f⁻¹(2x+5) = x
2x+5 = 8 => 2x+5 = 8 => 2x = 3 =>
=> x = 3/2
=> f⁻¹(8) = 3/2
I need help on my math homework
Answer: the first one is True and the second one is false
Step-by-step explanation:
3 + 5x = 23
so replace x with 4 you get 3 + 5 * 4 = 3 + 20 = 23
this is equal to 23 so it is true
2x - 6 = 9
do the same you get
2 * 8 - 6 = 9
16 - 6 = 10
the answer is 10 not nine therefore it is false
Identify the real zeros for f(x) = 3x2 + 2x + 4.
A) 1 and −1
B) 0 and −1
C) no solution
D) infinite solutions
sqrt (b^2 -4ac ) =sqrt (4-4•3•4) = sqrt (-44) so the parabola does not have real solutions. Answer C)
Answer:
c
Step-by-step explanation:
What is the value of -5(3+4)
-35
First, add the contents of the parentheses. 3 + 4 = 7. This gives you -5 * 7.
Now, just multiply. -5 * 7 = -35, so -35 is the answer.
please help . tjjhhhhhhhh
Answer:
19 - 8√3
Step-by-step explanation:
(-4 + √2)^2
= (-4)^2 + 2(-4)(√3) + √3)^2
= 16 - 8√3 + 3
= 19 - 8√3
Answer:
D
Step-by-step explanation:
note that ([tex]\sqrt{3}[/tex] )² = 3
Given
(- 4 + [tex]\sqrt{3}[/tex] )² = (- 4 + [tex]\sqrt{3}[/tex])(- 4 + [tex]\sqrt{3}[/tex])
Expand using (a + b)² = a² + 2ab + b²
= (- 4 )² + 2(- 4[tex]\sqrt{3}[/tex] ) + ( [tex]\sqrt{3}[/tex] )²
= 16 - 8[tex]\sqrt{3}[/tex] + 3
= 19 - 8[tex]\sqrt{3}[/tex]
A kite has diagonals 7.8 ft and 6 ft. What is the area of the kite? (1 point)
A. 23.4 ft?
B. 46.8 ft
C. 41.4 ft?
D. 10.8 ft?
The area of a kite is half the product of the diagonals.
Area = ½(d1 x d2)
Plug in the values of the diagonals.
Area = ½(7.8 * 6)
Multiply, and you should get -
Area = 23.4 ft²
Answer: Option 'A' is correct.
Step-by-step explanation:
Since we have given that
Diagonals of kite are as follows:
7.8 ft and 6 ft
As we know the formula for "Area of kite":
Area of kite is given by
[tex]\dfrac{1}{2}\times d_1\times d_2\\\\=\dfrac{1}{2}\times 7.8\times 6\\\\=3\times 7.8\\\\=23.\ ft^2[/tex]
Hence, Option 'A' is correct.
Select all the correct answers
Which equations have a lower unit rate than the rate represented in this table?
To determine which equations have a lower unit rate than the rate in the table, calculate the unit rate or slope from the table and compare it to the slopes of the other equations. Equations with a smaller slope have a lower unit rate.
Explanation:To answer this question, we need to calculate the unit rate of the original equation. The unit rate is the ratio of the increase in the dependent variable (usually represented by y) to the increase in the independent variable (usually represented by x).
For example, if the table shows x increasing by 2 and y increasing by 4, then the unit rate is 4/2 = 2 which is the slope.
The equations with a lower unit rate than this would have a smaller ratio of the increase in y to the increase in x. For instance, if the slope of another equation is 1, that means for each unit increase in x, y increases by only 1, which is less than the original rate of 2.
Therefore, to decide which equations have a lower unit rate, compare the slopes of the equations to the unit rate calculated from the original table. Any equation with a smaller slope has a lower unit rate.
Learn more about Unit Rate here:https://brainly.com/question/38777061
#SPJ2