The length of the ramp Tyree will need to make from window to the sidewalk is 5√17 feet .
In the question ,
it is given that ,
height of the window is = 5 feet ,
distance of sidewalk from the Tyree's house is = 20 feet ,
We know that the angle between the wall and the floor is 90° ,
So , the system is making a right triangle ,
let the length of the ramp be = "x" ,
So, According to Pythagoras Theorem ,
we get ,
x² = 5² + 20²
x² = 25 + 400
x² = 425
x = √425
x = 5√17 feet .
Therefore , the length of the ramp is 5√17 feet .
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Which statements are true? Select all that apply.
A) The equation |-x - 4| = 8 will have two solutions.
B) The equation 3.4|0.5x - 42.1| = -20.6 will have one solution.
C) The equation |1/2x - 3/4| = 0 will have no solutions.
D) The equation |2x - 10| = -20 will have two solutions.
E) The equation |0.5x - 0.75| + 4.6 = 0.25 will have no solutions.
F) The equation |1/8x - 1| = 5 will have infinitely many solutions.
Answer:
The following statements are true:
A) The equation |-x - 4| = 8 will have two solutions.
D) The equation |2x - 10| = -20 will have two solutions.
E) The equation |0.5x - 0.75| + 4.6 = 0.25 will have no solutions.
The other statements are not true. The equation 3.4|0.5x - 42.1| = -20.6 will not have one solution, as the absolute value of a number cannot be negative. The equation |1/2x - 3/4| = 0 will not have no solutions, as the absolute value of a number cannot be zero. The equation |1/8x - 1| = 5 will not have infinitely many solutions, as the absolute value of a number cannot be negative.
Step-by-step explanation:
What is 1 1/9 as an improper fraction?
Answer:
the right answer is
1,2/9
our test statistic z is found by taking the observed difference (81%-72%) minus the expected difference divided by the se for the difference. what is the expected difference in this problem? in other words, what would we expect the difference to be under the null hypothesis?
The expected difference under null hypothesis can be understood by the following :
The required null and alternate hypothesis will be
Null hypothesis : H0 : μ=μ0
Alternate Hypothesis: H1 : μ<μ0
To determine whether there is a difference in the means of two populations, the z test formula compares the z statistic to the z critical value.
The z critical value in hypothesis testing divides the distribution graph into acceptance and rejection regions. The null hypothesis can be rejected if the test statistic falls within the rejection region; otherwise, it cannot be rejected.
The z test formula to set up the required hypothesis tests for a one sample and a two-sample z test is
z = (( x−μ) /σ/√n )x
x = sample mean, μ = population mean, σ = standard deviation and n = sample size.To learn more about null hypothesis
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Solve: Show your work
0.321 x 50
Answer:
.321× 50
000
+ 1605X
therefore answer is 1.605
A homeowner uses a coordinate plane to map the locations of a birdbath, a birdfeeder, and a birdhouse. The birdbath is at (2,2), the bird feeder is at (8,2), and the birdhouse is at (5,7).If the birdhouse is the same distance from the birdbath and from the birdfeeder, what is the area of the triangle formed by these three objects?
The area of the triangle formed by the birdbath, bird feeder and the birdhouse is 15 squared units
How to find the area of the triangle formed by these three objects?Given: the birdbath is at (2,2), the bird feeder is at (8,2), and the birdhouse is at (5,7)
(Consider the image attached)
The distance between the points can be calculated using the formula:
d=√((x2 – x1)² + (y2 – y1)²)
birdbath (5,7) and birdhouse (2,2)
d=√((2 – 5)² + (2 – 7)²) = √34
bird feeder (8, 2) and birdhouse (2,2)
d=√((2 – 8)² + (2 – 2)²) = 6
birdbath (5,7) and bird feeder (8,2)
d=√((8 – 5)² + (2 – 7)²) = √34
The height of the triangle is:
h = √((√34)²-3²) = 5
Area of triangle = 1/2 × base × h
Area of triangle = 1/2 × 6 × 5 = 15 squared units
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according to census data, in 1950 the population of the u.s. amounted to 151.3 million persons, and 13.4% of them were living in the west. in 2000, the population was 281.4 million, and 22.5% of them were living in the west. is the difference in percentages practically significant? statistically significant? or do these questions makes sense? explain briefly.
The difference in percentages is practically significant but whether or not it is statistically significant cannot be determined.
Here, we are given that 13.4% of the population in the US lived in the West in 1950 and 22.5% in 2000.
Thus, the difference in percentage = 22.5 - 13.4 = 9.1%
We observe that the difference is large, this means that the difference in percentages is practically significant.
Now, to determine whether the difference is statistically significant it is appropriate to conduct a two-sample z-test and it is only appropriate to conduct the test of significance when the samples are simple random samples.
In this case, the samples are not simple random samples, because the data given contains information on all individuals in the population. Moreover, it is not appropriate to determine whether the difference in percentages is statistically significant as the samples are not probability samples.
Thus, the difference in percentages is practically significant but whether or not it is statistically significant cannot be determined.
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a store offered a price discount of 20% on all items over one weekend. by what fraction of the discounted price of an item did the price increase after the weekend?
The discounted price of an item did the price increased after the weekend by a fraction of 1/5.
A fraction can be referred to or considered as a divisional representation of a whole number or a percentage, usually represented as a bigger numerical. A fraction denotes the representation of a number in such a way that the meaning or the accuracy of the number is not disturbed, but is shown differently. One-fifth is 20 percent of the total five parts of a number, and thus, the price increased by 1/5th after the weekend.
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The following tree heights were recorded on a school campus:
61, 72, 84, 88, 77, 67, 76, 79, 63, 79, 69, 70, 86, 78, 82, 82, 80, 73, 87, 90, 73, 76, 79, 71, 75, 79, 76, 83, 84, 87, 72, 81, 89, 74, 77, 78, 81, 84
A science teacher wants to choose a data display that will highlight every height. Which display will present the information in this way?
Box plot
Circle graph
Histogram
Line plot
A line plot would be the best data display to highlight every height.
A line plot, also known as a dot plot, is a type of graph that displays data as a series of dots on a number line. Each dot represents a single data point, and the dots are placed above the corresponding value on the number line.
Line plots are useful for displaying small data sets because they provide a simple visual representation of the data. They can quickly show the range of values in the data set, as well as any outliers or clusters of data points. Line plots are commonly used in elementary and middle school classrooms to teach basic data analysis and graphing skills. They are also used in scientific research and statistical analysis to visualize small data sets and identify patterns in the data.
A line plot, also known as a dot plot, displays the data as points on a number line. Each data point is represented by a dot, making it easy to see every height in the data set. Here is an example of a line plot for the given data:
A display that will highlight every height would be a line plot, which would show each individual height as a dot along a number line.
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Find the partial fraction decomposition of the rational expression with repeated factors.
The partial fraction decomposition of the expression with repeated factors is given as follows:
[tex]\frac{1}{x} - \frac{2}{x + 4} - \frac{1}{(x + 4)^2}[/tex]
How to obtain the partial fraction decomposition of the function?The function in this problem is defined as follows:
(-x² - x - 16)/(x³ + 8x² + 16x).
The decomposition is made considering the factors of the denominator, which are obtained as follows:
x³ + 8x² + 16x = 0.
x(x² + 8x + 16) = 9
x(x + 4)² = 0.
Hence the denominators are as follows:
x.x + 4.(x + 4)².Then the decomposition is of:
A/x + B/(x + 4) + C/(x + 4)²
Then the expression will be given as follows:
[tex]\frac{A(x + 4)^2 + Bx(x + 4) + Cx}{x^3 + 8x^2 + 16x} = \frac{-x^2-x+16}{x^3 + 8x^2 + 16x}[/tex]
Then the system of equations, equaling the numerators, is given as follows:
A + B = -1. -> terms with x².8A + 4B + C = -1 -> terms with x.16A = 16 -> independent term.Hence:
16A = 16
A = 1.
B = -1 - A
B = -2.
C = -1 - 8A - 4B
C = -1.
Meaning that the third option is correct.
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some other policies for fairness in congestion control are additive increase additive decrease (aiad), multiplicative increase additive decrease (miad), and multiplicative increase multiplicative decrease (mimd). discuss these three policies in terms of convergence and stability.
Congestion management allows for more efficient use of a shared network infrastructure by managing the flow of data packets into the network.
Additive increase and additive decrease (AIAD) This is the policy which follows the below rule
a(i)>0, b(i) =1, a(d)<0 b(d)=1
This policy doesn't converge to fairness which means that it is not stable.
Moreover, this doesn't converges to efficiency and if it is need to be stable then it must satisfy the condition a(d) = a(i)
Multiplicative increase and additive decrease (MIAD) This is the policy which follows the rule of a(i) =0, b(i) >1, a(d)<0, b(d)=1
This policy doesn't converge to fairness which means that it is not stable.
Moreover, this doesn't converges to efficiency and if it is need to be stable then it must satisfy the condition b(i)a(d)/ 1- b(i)
Multiplicative increase multiplicative decrease (MIMD) This is the policy which follows the below rule a(i) =0 , b(i) >1 , a(d)=0, 0<b(d)<1
This policy doesn't converge to fairness which means that it is not stable.
Moreover, this doesn't converges to efficiency and if it is need to be stable then it must satisfy the condition b(i)≥ 1 and 0≤ b(d)<1.
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Simplify
8(x + 3)^2 divided by 2(x + 3)
Answer:4(x+3)
Step-by-step explanation:
8(x + 3)^2 /2(x + 3)
4(x+3)
Answer:
4x³+36x²+108x+108
Step-by-step explanation:
Simplify
8(x + 3)^2 divided by 2(x + 3)
8·(x + 3)² : 2·(x + 3) =
8⋅(x²+6x+9):2⋅(x+3) =
(8x²+48x+72):2⋅(x+3) =
(4x²+24x+36)⋅(x+3) =
4x³+36x²+108x+108
The regular admission price for an amusement park is $72. For a group of 15 or more, the admission price is reduced by $25 per person. How many people need to be in a group to save $500?
20 people need to be in a group in order for them to save $500.
If there are 15 people or more, people will save $25 on each ticket.
In order to save a total of $500, the number of people who are needed is:
= Amount to be saved / Amount to be saved per ticket
= 500 / 25
= 20 people
In conclusion, if a group of 20 people came, they would save $500.
(a) calculate a 95% confidence interval for the average difference between the reading and writing scores of all students. (b) interpret this interval in context. (c) does the confidence interval provide convincing evidence that there is a real difference in the average scores? explain.
a.)The 95% Confidence interval for the average difference between the reading and writing scores of all students is 0.545 ± 1.232.
b.) Since independent random samples are chosen from a population that is roughly typical
The number of degrees of freedom with an unknown standard deviation is n-2.
c.)The null hypothesis could not be rejected because the aforementioned interval contains zero.
Using a confidence interval does not show conclusive proof that there is a genuine difference in the average results .
Therefore there is no real difference in the average scores.
Z = X +- 1.96 ( SD/ √n )
= 0.545 ± 1.96 × 8.887
√2000.545 plus or minus 1.96 times 8.887 over the square root of 200
= 0.545 ± 1.232
Out of 100 samples, the population mean would range between -0.687 and 1.777 on average in 95 of them.
explanation for part b,
n = 7, CL = 90%
df= 7-2=5t*=1.476(one tail),
2.015(both tails)
n = 26, CL = 98%
df= 26-2=23t*=2.177(right tail),
2.5(both tail)
n = 28, CL = 95%
df=28-2=26t*=1.706(one tail),
2.056(both tail)
n = 11, CL = 99%
df= 11-2=9t*=2.821 (one tail),
3.250(both tail)
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The girls' soccer team wants to raise at least $2000 to buy new goals. If
they make $1.00 from each hot dog and $1.25 from each soda, how many of each item
do they need to sell?
a. Write an inequality to represent the situation.
b. Graph an inequality to represent the situation.
c. Plot at least 5 possible solutions on your graph.
The inequality to represent the problem is x + 1.25y ≥ 2000 and it's graph is attached below
Linear InequalityLinear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in mathematics. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠).
Let;
x = number of hot dogy = number of sodaa) The inequality to represent the situation can be expressed as
1x + 1.25y ≥ 2000
This is further expressed as;
x + 1.25y ≥ 2000
b) The graph of the inequality x + 1.25y ≥ 2000 is attached below.
c) The possible solutions are at (2000, 0) and (0, 1600)
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Here’s a box plot that summarizes how many eggs Corey’s chickens laid last week. 0 2 4 6 8 10 12 find the interquartile range (iqr) of the data
The value of interquartile range (IQR) of the data set which is plotted in the dot plot 0 2 4 6 8 10 12 is 6
What is the interquartile range (IQR) of the data?
The interquartile range (IQR) of the data is the middle half of the data, which contains 2nd and 3rd quartiles.
Interquartile range is the difference of third quartile and first quartile.
IQR = Q₃ - Q₁
According to the given question:
In the dot plot below, the data is given as,
0 2 4 6 8 10 12
The first quartile is the medium of the lower half, while the third quartile is the medium of the upper half. For the above data,
Q1 = 3
Q3 = 9
Thus, Interquartile range is,
IQR = Q₃ - Q₁
IQR = 9 - 3
IQR = 6
Hence, the value of interquartile range (IQR) of the data set which is plotted in the dot plot 0 2 4 6 8 10 12 is 6
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Hi can someone please help me with this!!!
Answer:
q = 50
r = 75
s = 115
t = 30
Step-by-step explanation:
Which of the following is the basis of diminishing marginal utility Mcq?
O MCN = TFCN - TFCN-1
O MCN = ACN - ACN-1
O MCN = AVCN - AVCN-1
O MCN = TCN - TCN-1
MCN= ACN-ACN-1 is the basis of diminishing marginal utility.
What is marginal utility?
The additional pleasure a consumer has from owning one extra unit of an item or service is known as marginal utility. Economists utilize the idea of marginal utility to estimate the quantity of a good that consumers will buy.
When positive marginal utility occurs?When the overall utility is increased by the consumption of an additional item, positive marginal utility occurs. On the other side, negative marginal utility arises when the overall utility is reduced by the consumption of one extra unit.
According to the law of diminishing marginal utility, as consumption rises, the marginal utility gained from each additional unit decreases, all other things being equal. The incremental improvement in utility brought on by consuming one more unit is known as marginal utility. An economic term for happiness or contentment is "utility."
So
MCN= ACN-ACN-1
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18/100 = 90/p
PLEASE HELP!!!!
Answer:
p=500
Step-by-step explanation:
18/100=90/p
First, set up equation
90x100=18xp
9000=18p
9000/18=18p/18
500=p
Answer:
[tex]p = 500[/tex]
Step-by-step explanation:
Use the cross-multiplication method. Multiply 18 with p, and 90 with 100, respectively:
[tex]\frac{18}{100} = \frac{90}{p} ; \\ 18p = 90 * 100\\ 18p = 9000[/tex]
Isolate the variable, p. Note the equal sign, what you do to one side, you do to the other. Divide 18 from both sides of the equation:
[tex]\frac{(18p)}{18} = \frac{(9000)}{18} \\p = \frac{9000}{18} \\p = 500[/tex]
[tex]p = 500[/tex] is your answer.
~
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Triangle ABC is reflected over the x-axis. What are the coordinates of the image of the vertex A?
The image of vertex A will be at point (2,-5).
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The perimeter will be P = sum of all three side.
Point A is located at (2, 5), thus you look at the y-coordinate since you are reflecting it across the x-axis.
Given that it is five above the x-axis, you must travel five below it, or you can simply enter the opposite of five, which is -5.
So, A' is at (2, -5).
Hence, The image of vertex A will be at point (2,-5).
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please help me
100 points
Answer:
100 is the answer
Step-by-step explanation:
Edpuzzle Fractions Equivalent
A) The decimal 2.256 in expanded form and word form are respectively; 2 + 0.2 + 0.05 + 0.006; Two and three hundred fifty six one - thousandths
B) The decimal 24.09 in expanded form and word form are respectively; 20 + 4 + 0 + 0.09; Twenty four and 9 one - hundredths.
How to write decimals in expanded form?The expanded form used when writing decimals is the mathematical expression that shows the sum of the values of each digit in the given number.
A) We are given the decimal 2.256
Thus, in expanded form, the given decimal can be expressed as;
2 + (2/10) + (5/100) + (6/1000)
= 2 + 0.2 + 0.05 + 0.006
In word form, we can write the decimal as;
Two and three hundred fifty six one - thousandths
B) We are given the decimal 24.09
Thus, in expanded form, the given decimal can be expressed as;
20 + 4 + (0/10) + (9/100)
= 20 + 4 + 0 + 0.09
In word form, we can write the decimal as;
Twenty four and 9 one - hundredths.
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describe the solution set for the system of equations that consists of the equation of the line shown and .y=1/2x-3
The correct statement according to the given equation is statement (D)"They have a single solution since they have various y-intercepts but the same slopes."
What is the equation?
The relationship between two terms on either side of an equal sign is easily demonstrated using a simple equation.
Additionally, one or more of the four arithmetic operations that simple equations do include addition, fundamental arithmetic, multiplication, and division.
The three possible forms of the equation system are point-slope form, standard form, and slope-intercept form.
So, given equations:
y = 1/2 * x - 3
y = - 1/2 * x - 3
As we are aware, a line's slope-intercept form is:
y = m x + c
Therefore, it is clear from equations 1 and 2 that:
m1 = 1/2 and c1 = -3
m2 = -1/2 and c2 = -3
Therefore, the correct statement according to the given equation is statement (D)"They have a single solution since they have various y-intercepts but the same slopes."
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Complete question:
A system of equations is given below. y=1/2x-3 and -1/2x-3. Which of the following statements best describes the two lines?
a. They have the same slope but different y-intercepts, so they have no solution.
b/. They have the same slope but different y-intercepts, so they have one solution.
c. They have different slopes but the same y-intercept, so they have no solution.
d. They have different slopes but the same y-intercept, so they have one solution.
A photograph has a length that is 3 inches longer than its width, x. So its area is given by the expression x(x+3) square inches. If the area of the photograph is 70 square inches, what is the width of the photograph?
The width of the photograph is 10 inches if the length of the photograph is 3 inches.
What is meant by length?Any arbitrary reference standard for measuring length that has gained acceptance is referred to as a unit of length. The metric system, which is adopted by every nation on earth, is the most prevalent system in use today. The US customary units are also used in the US. The United Kingdom and a few other nations continue to utilize British Imperial units for specific purposes. SI units and non-SI units are subsets of the metric system.
Given,
The expression is:
x(x + 3) = 70
x² + 3x = 70
Now, we have to subtract 70 on both the sides, we get:
x² + 3x - 70 = 0
(x-7)(x + 10) = 0
x-7=0
x=7
x+10=0
x= -10
Since distance cannot be negative, the correct answer is x = 7. We are now plugging in the length (x + 3).
=x + 3
=7 + 3
=10
Therefore, the width of the photograph is 10 inches.
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Kyle uses a calculator to figure out
the total cost of a $1.60 cookie jar.
Including sales tax, the total is
$1.62. What is the sales tax
percentage?
The Rate of Sales Tax in Percentage is 1.25%
What is Percentage?
Percentages: The percentage is one of the most used methods to portray statistics. Percentage simply means "per hundred," and the sign for percentage is %. One percent (or 1%) is one hundredth of a total or whole number and is computed by dividing the whole or entire number by 100.
Solution:
Cost Price of the Cookie Jar is given as $1.60
And, Selling Price is $1.62 including Sales Tax
We need to calculate the Rate of Sales Tax
So, the amount of Sales Tax is 0.02$
Percentage is 0.02/1.6 * 100 = 1.25%
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A car takes 5 hours to cover a distance if it is moving with a speed of 40 mph. Find the time taken by the car if it is moving with a speed of 50 mph.
The time required = 4 hours
The time required by the car to move at a speed of 50 mph to reach a distance of 200 miles is 4 hours
What is Speed?
Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude
Speed = Distance / Time
Given data ,
Let the distance traveled by the car be = D
Now , the speed S of the car = 40 miles per hour
The time required by the car to travel D distance is T = 5 hours
So , the Distance D is calculated from the formula
Distance D = Speed S x Time T
So , substituting the values in the equation , we get
Distance D = 40 x 5
Distance D = 200 miles
Now , the distance traveled by the car remains the constant
The speed of the car is S = 50 miles per hour
And let the time taken by the car to cover 200 miles at 50 mph be = T
Now to calculate Time T ,
Time T = Distance D / Speed S
Substituting the values in the equation , we get
Time T = 200 / 50
Time T = 4 hours
Therefore , the value of T is 4 hours
Hence , The time required by the car to move at a speed of 50 mph to reach a distance of 200 miles is 4 hours
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you're interested in predicting college grades (y) from sat scores (x). you know that the mean of the sat scores is 485 with a standard deviation of 85. the average college gpa is 3.1 within a standard deviation of 0.4. the correlation between sat scores and college grades is 0.71. what is the equation of the regression of grades (y) on scores (x)?
The equation of the regression of grades on scores is y = 0.003x + 1.645
The mean of the sat scores = 485
The standard deviation = 85
The average college gpa = 3.1
The standard deviation = 0.4
The correlation between sat scores and college grades = 0.71
The regression equation is
y = mx + b
The value of m = (0.71) × (0.4/85)
= 0.003
Substitute the values in the regression equation and find the value of b
3.1 = 0.003×485 + b
3.1 = 1.455 + b
b = 3.1 - 1.455
b = 1.645
The equation is
y = 0.003x + 1.645
Therefore, the regression equation is y = 0.003x + 1.645
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Light travels at the speed of 3,00,000 km per second. Light from the sun reaches us in 8 minutes. If a supersonic jet were to travel from the sun at the speed of 1000 km per hour, approximately how long would it take to travel the same distance?
please tell anyone of you very fast
options are
A)3 months B)5 years
C)17 YEARS D)221 YEARS
The time taken by the jet to reach the earth form sun is 3 months
The correct option is option A)
What is speed?
Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance.
We are given that
Light travels at the speed of 3,00,000 km per second. Light from the sun reaches us in 8 minutes
We first find the distance between sun and earth
to do that we multiply speed of light and time taken by light to reach earth
D = 300000*8
D= 2400000km
Now we are given the speed of the jet which is 1000km/hr
We have to find the time taken by the jet to reach the earth
To do that we divide the distance by speed we get
t = 2400000/1000
t =2400 hr.
3 months
The time taken by the jet to reach the earth form sun is 3 months
The correct option is option A)
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Which of the following is the vertex form of Y = X² - 2x + 5 *?
(x -1)2 = y - 4 is the vertex form of the equation Y = X² - 2x + 5.
What is the vertex form?A quadratic function has the vertex form f(x) = a(x - h)2 + k, where a, h, and k are constants.
Obtain the equation y = ax2 + bx + c.
Determine -b / 2A.
The vertex's x-coordinate is given here.
Simply enter the value of -b / 2a into the equation for x and solve for y to obtain the vertex's y-coordinate.
The vertex's y-coordinate is given here.
So, we have the equation:
Y = X² - 2x + 5
Now, calculate as follows:
⇒ y = (x2 - 2x + 1) + 5 -1
⇒ y - 4 = (x -1)2
⇒ (x -1)2 = y - 4
Therefore, (x -1)2 = y - 4 is the vertex form of the equation Y = X² - 2x + 5.
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How do you use De Moivre's theorem to express (1 + i)^8?
The value of (1 + i)^8 is 16. De Moivre's describes how the power of a complex number can be calculated using the properties of its modulus and argument.
De Moivre's theorem states that for any complex number z = r * (cos(θ) + i * sin(θ)) and any integer n, we have:
zⁿ = rⁿ * (cos(n * θ) + i * sin(n * θ))
To use this theorem, we need to first express the complex number (1 + i) in terms of its magnitude and angle. We can do this by using the Pythagorean theorem to find the magnitude of the complex number, which is the square root of the sum of the squares of the real and imaginary parts.
In this case, the magnitude is the square root of 1^2 + 1^2, or √2.
The angle of the complex number can be found using the inverse tangent function. In this case, the angle is 45 degrees, since the tangent of 45 degrees is 1. Now that we have the magnitude and angle of the complex number, we can use De Moivre's theorem to find the value of (1 + i)^8. Substituting the values we found into the formula above, we get:
(1 + i)^8 = √2^8 * (cos(8 * 45) + i * sin(8 * 45))
= 2^4 * (cos(360) + i * sin(360))
= 16 * (1 + i * 0)
= 16
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(3,3) and (1,-3) in linear equation
Answer:
3 x - y = 6
Step-by-step explanation:
the equation of a line is
ax + by = c
express the slope initially in the form of y=mx+b
b is the y- intercept (the point where it crosses the y axis)
m is basically the slope, to find m, you have to use a specific formula...
m = (y2 – y1) / (x2 – x1)
(x1, y1) (x2, y2) are 2 coordinate points...
(3,3) and (1, -3)
m = -3 -3 divided by 1 - 3 = -6/-2 = 3
so your formula for now is .. y = 3x + b (you dont know what b is yet)
Now, substitute the points into the equation.
3 = 9 + b. b = -6
final formula is,
Y=3x -6
u can also rearrange the formula in a standard form:
3x - y = 6
I REALLY HOPE THIS HELPS U!!
