What is the product of the complex numbers below? (4 - 21)(1 + 7) O A. 18 - 307 - OB B. -10 - 301 O C. -10 + 261 + O + D. 18 + 261
Answers
Given:
[tex](4-2i)(1+7i)[/tex]To find: The product of two complex numbers:
Explanation:
On expansion we get,
[tex](4-2i)(1+7i)=4+28i-2i-14(i^2)[/tex]As we know,
[tex]i^2=-1[/tex]So, we w
Related Questions
What is the equation of the line of best fit for the following data? Round the slope and y-intercept of the line to three decimal places.
Answers
The equation of the line of best fit for the following data is ŷ = 1.16393X + 0.88525
Option A
This is further explained below.
What is a regression equation?Generally, Y is represented by the equation Y = a + bX + e, which represents the regression equation. The value of the dependent variable, which is referred to as Y, is what is being explained or predicted.
a, also known as Alpha, is a constant; it is equal to the value of Y when the value of X is equal to 0. b, also known as Beta, is the coefficient of X; it is the slope of the regression line.
In conclusion,
Sum of X = 34
Sum of Y = 44
Mean X = 6.8
Mean Y = 8.8
Sum of squares (SSX) = 48.8
Sum of products (SP) = 56.8
Regression Equation = ŷ = bX + a
b = SP/SSX = 56.8/48.8 = 1.16393
a = MY - bMX = 8.8 - (1.16*6.8) = 0.88525
ŷ = 1.16393X + 0.88525
Read more about Regression Equation
https://brainly.com/question/14184702
#SPJ1
Write an equation that represents a reflection in the x -axis of the graph of g(x)=|x| .h(x)=
Answers
The equation that represents a reflection in the x -axis of the graph of g(x) is y = -|x|.
We are given a function g(x). The function g(x) is defined as the modulus of x. The equation is : g(x) = |x|.
We need to find the equation that represents the reflection of the graph of g(x). The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point but leave the x-value the same.
Let h(x) be the function that represents the reflection of the function g(x).
h(x) = -g(x)
h(x) = -|x|
The equation can be written as y = -|x|. The graph of the reflection is attached below.
To learn more about equations, visit :
brainly.com/question/10413253
#SPJ1
Number 14 please help I’m feolifn
Answers
Answer:
see explanation
Step-by-step explanation:
∠ R = 2x + 5 , ∠ S = x + 1 , ∠ T = 7x - 16
the sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
2x + 5 + x + 1 + 7x - 16 = 180
10x - 10 = 180 ( add 10 to both sides )
10x = 190 ( divide both sides by 10 )
x = 19
Then
∠ R = 2x + 5 = 2(19) + 5 = 38 + 5 = 43°
∠ S = x + 1 = 19 + 1 = 20°
∠ T = 7x - 16 = 7(19) - 16 = 133 - 16 = 117°
Suppose that y varies directly with x and that y=77 when x=7. What is the value of x when y=55
11
50
5
24
Answers
Answer: The correct answer is 5.
Step-by-step explanation:
Find the relationship between x & y:
y/x=77/7=11, therefore x equals the value of y divided by 11
x=y/11
x=55/11
x=5
if i had 90 days and i done did two months how many days do i have ???
Answers
Answer: 30 more days
Step-by-step explanation: two months equal to 30 days at most
Answer:30 days it can fluctuate on which month you pick
Step-by-step explanation:
Graph the line with slope of 4/5 and goes through the point (1, 3).
Answers
A graph is a diagram that depicts the connections between two or more objects. A pie chart is a type of graph.
Explain about the Graph?Common graph types include line graphs, bar graphs, pie charts, scatter plots, and histograms. Graphs are a great tool for presenting statistics and visualizing data. For example, numerical data that is unconnected to one another is shown in a bar graph or chart.The link between lines and points is described by a graph, which is a mathematical description of a network. A graph is made up of some points and the connecting lines. It doesn't matter how long the lines are or where the points are located. A node is the name for each element in a graph.Bar graphs, circle graphs, and line graphs are the three most often used types of graphs. Different types of data can be displayed using different types of graphs.The link between lines and points is described by a graph, which is a mathematical description of a network. A graph is made up of some points and the connecting lines. It doesn't matter how long the lines are or where the points are located. A node is the name for each element in a graph.To learn more about Graph refer to:
https://brainly.com/question/19040584
#SPJ10
Simplify
√
5
(
√
5
+
√
20
)
Answers
Answer:
√5(√5 + √20)
= √5√5 + √5√20
= √25 + √100
= 5 + 10
= 15
The ratio of smartphone to table sold at a store is 6:5. If 35 table are sold on Wednesday, how many smartphone were sold?
Answers
Answer:
Explanation:
The ratio of smartphones to table sold = 6 : 5.
The number of tables sold = 35
Let the number of smartphones = x
Then:
[tex]undefined[/tex]4. Create an equation for a 6th degree polynomial that only has the zeros of x=5, -4, -6, 1 with a y-intercept of 3600. Explain how you found your equation.
Answers
Since the y-intercept of the polynomial must be 3600, then:
[tex]p(0)=3600[/tex]Since the only zeroes of the polynomial must be x=5, -4, -6 and 1, then the factors of the polynomial, are:
[tex]\begin{gathered} (x-5) \\ (x+4) \\ (x+6) \\ (x-1) \end{gathered}[/tex]Let the multiplicity of the factor (x-1) be equal to 3 and let the multiplicity of the rest of the factors to be equal to 1. Then:
[tex]p(x)=a(x-5)(x+4)(x+6)(x-1)^3[/tex]Where a is a constant. Notice that the degree of that polynomial is 6. Evaluate it at x=0 to find the value of a that makes the y-intercept to be equal to 3600:
[tex]\begin{gathered} p(0)=a(0-5)(0+4)(0+6)(0-1) \\ =a(-5)(4)(6)(-1) \\ =120a \end{gathered}[/tex]Since p(0)=3600, then:
[tex]\begin{gathered} 3600=120a \\ \Rightarrow a=\frac{3600}{120} \\ \Rightarrow a=30 \end{gathered}[/tex]Therefore, the following polynomial is a 6th degree polynomial with zeroes at the values of 5, -4, -6 and -1 with a y-intercept equal to 3600:
[tex]p(x)=30(x-5)(x+4)(x+6)(x-1)^3[/tex]What is the slope of the line on the graph?
Enter
your answer in the box
Answers
y2-y1/x2-x1 fill in the equation which would be 5 - -1 over 1-0 so you get 6/1 which is six. I hope this helped
Answer:
6
Step-by-step explanation:
Slope is represented by rise/run. Let's use the points (0, -1) and (1, 5). The "rise" from -1 to 5 is 6. The "run" from 0 to 1 is 1. 6/1 is just 6.
Aaron invested $740 in an account paying an interest rate of 5%
compounded continuously. Justin invested $740 in an account paying an interest rate of 5% compounded daily. After 18 years, how much more
money would Justin have in his account than Aaron, to the nearest dollar?
Answers
The amount of money Justin would have in his account than Aaron, to the nearest dollar is $0
What is the future value formula for continuous compounding cash flow?
The future value, which is used to determine the worth of this investment of $740 made now in 18 years is as shown below:
FV=PV*e^(rt)
FV=the worth of the investment in 18 years=unknown
PV=the amount invested today=$740
e=mathematical exponential value=2.7182818
r=rate of interest which compounded continuously=5%
t=time of investment in years=18
FV=$740*2.7182818^(5%*18)
FV=$740*2.7182818^(0.90)
FV=$740*2.459603087981220
FV=$1,820.11
Justin:
FV=PV*(1+r/m)^(n*m)
PV=$740
r=5%
m=number of times in a year that interest is compounded=365
m=number of years=18
FV=$740*(1+5%/365)^(18*365)
FV=$1,819.99
difference=$1,820.11-$1,819.99
difference=$0.12($0 to the nearest dollar)
Find out more about continuous compounding on:https://brainly.com/question/23136156
#SPJ1
Which of the following is an accurate description of the scatterplot?A. The more seeds that are planted per square foot the smaller the expected yield of the crop.B. the more seeds that are planted per square foot the larger the expected yield of the crop.C. The expected yield of a crop is high whenever the number of seeds planted per square foot is small or large. A larger yield is expected when the number of seeds per square is around 60.D.The expected yield of a crop is low whenever the number of seeds planted per square foot is small or large. A larger yield is expected when the number of seeds per square is around 60.
Answers
It would be
D. The expected yield of a crop is low whenever the number of seeds planted per square foot is small or large. A larger yield is expected when the number of seeds per square foot is arounf 60.
when x^3-2x^2+kx+3 is divided to x-1 the remainder is 3. find the value k.
Answers
The value of the 'k' for the given polynomial is found as 1.
What is termed as the division of polynomial?The algorithm for dividing polynomials is used to accomplish a rational number which symbolizes a polynomial divided by the a monomial or the other polynomial. The divisor and dividend are placed in the same manner as in regular division. Dividing polynomials is a math operation in which we divide one polynomial by another, usually with a lower degree than the dividend.For the given question;
Dividend = x³ - 2x² + kx + 3Divisor = x - 1Remainder = 3By the remainder theorem,
Put x - 1 = 0. x = 1, in the polynomial will be equal to its remainder.
Put x = 1 in the polynomial.
x³ - 2x² + kx + 3 = 3
1³ - 2(1)² + k(1) + 3 = 3
1 - 2 + k = 0
k = 1
Thus, the value of the 'k' for the given polynomial is found as 1.
To know more about the division of polynomial, here
https://brainly.com/question/12520197
#SPJ10
What is the coefficient of the first term in this expression?
x+9y^3 +4
Answers
The coefficient of the first term of the polynomial is 1.
How to find the coefficient of the first term in an expression?
Polynomials are algebraic expressions of the following form:
f = Σ (cₙ · xₙⁿ)
Where:
cₙ - n-th Coefficient of the polynomial.xₙ - n-th Variable associated with the n-th term of the polynomial.The order of the terms of a polynomial is usually from the left to the right. Then, the first term of the polynomial x + 9 · y³ + 4 is x = 1 · x, whose coefficient is equal to 1.
To learn more on polynomials: https://brainly.com/question/20121808
#SPJ1
Steven recorded the times for the race as well but the clock he used recorded the times rounded time to the nearest tenth, Steven would have recorded when Steven tried to award medals for first place second and third place what problems might he face?
Answers
The major problem that Steven will face is he can't decide the winner among the racers who have very little difference in time.
What is time?
Time is the continuous movement of existence and the events that take place from the past, present, and onward into the future in what appears to be an unbreakable order. It is a quantity that is a component of numerous measurements that are used to rank events, compare how long they endure, compare the length of occurrences or the gaps between them, and measure how quickly things change in the real world or in our conscious experience. Time is frequently referred to as a fourth dimension in addition to the three spatial dimensions.
The major problem that Steven will face is he can't decide the winner among the racers who have very little difference in time. Since, the clock he uses recorded the times rounded time to the nearest tenth so the racers who completed race in almost equal time with a little difference will be showed as to same tenth value and then, he can't decide the winner among them.
To know more about time, go to link
https://brainly.com/question/13893070
#SPJ13
when jess is mailing a jewelry box to a customer, she packs it inside a larger shipping box. The sides of a shipping box are 2 inches longer than the sides of a jewelry box
Answers
The volume of the jewelry box is 8 cubic inches. Volume exists as a measurement of three-dimensional space that is occupied.
What is meant by volume?Every three-dimensional object requires some amount of space. The volume of this space is measured. Volume is defined as the space occupied by an object within the boundaries of three-dimensional space. It is also known as the object's capacity. The basic formula for volume is length × width × height, whereas the basic formula for area of a rectangular shape is length width height. The calculation is unaffected by how you refer to the various dimensions: you can, for example, use 'depth' instead of 'height.' A 3D object's volume is the amount of physical space it occupies. It is the 3D equivalent of a 2D shape's area.
Therefore,
The computation of the volume of the jewelry box is shown below:
The Volume of the jewelry box = Length × height × weight
∴ 2 × 2 × 2 = 8
To learn more about volume, refer to:
https://brainly.com/question/24284033
#SPJ9
What is the answer to the equation:
1 + 6p = 7(6p -4) -7p
PLEASE HELP ME I NEED ANSWER IN % MINUTES BECAUSE IMA HAVE TO LEAVE SOON< NEED ANSWER ASAP!!!!
Answers
Answer:
p = 1
Step-by-step explanation:
1+6p = 7(6p-4)-7p
multiply 7
1 + 6p = 42p - 28 - 7p
simplify
1 + 6p = 35p - 28
p's on one side
-29p = -29
p = 1
A. What is the difference in total area of Alaska and Connecticut? Express your answer in scientific notation. Show your work or explain your answer.
3. What is the difference in total population of California and Alaska? Express your answer in scientific notation. Show
your work or explain your answer.
Answers
Answer:
A. Total area of Alaska is considerable larger than total area of Connecticut.
B. Population of California is considerably larger that population of Alaska.
Step-by-step explanation:
A. What is the difference in total area of Alaska and Connecticut?
According to the US government, total areas of Alaska and Connecticut are 663,268 square miles and 5,567 square miles, respectively.
The difference between both quantities is:
[tex]x=6.633 \times 10^{5} mi^{2} -5.567 \times 10^{3} mi^2\\x=6.577 \times 10^{5} mi^2[/tex]
Which means that total area of Alaska is considerable larger than total area of Connecticut.
B. What is the difference in total population of California and Alaska?
According to the US government, total populations of California and Alaska are 39,512,223 people and 710,249 people, respectively.
The difference between both quantities is:
[tex]x=3.951 \times 10^7 people - 7.103 \times 10^5 people\\x=3.880 \times 10^7 people[/tex]
Which means that population of California is considerably larger that population of Alaska.
calculate y-7 when y=20
Answers
The value of the expression is 13 that is formed by subtraction .
A mathematical expression that uses integer variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division, and exponentiation by a rational exponent).
However, transcendental numbers like such and e are not algebraic because they are not created by employing integer constants and algebraic processes.Although the definition of e necessitates an infinite number of algebraic operations, the generation of is frequently expressed as a geometric expression.Using the properties of arithmetic operations, an expression can be reduced to a rational fraction ( associative properties and commutative properties of addition and multiplication, distributive property and rules for the various operations on the given fractions).now we use subtraction:
y-7
= 20-7
= 13
To learn more about expression visit:
brainly.com/question/14083225
#SPJ1
Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. r=7 inches,s=35 inches.
Answers
The central angle has a measure of 5 rad in radians
How to determine the measure of the angle in radians?The given parameters are:
Length of the arc, s = 35 inches
Radius of the circle, r = 7 inches
The length of an arc can be calculated using the following formula
s = r∅
Where
s represents the length of the arcr represents the radius of the circle∅ represents the central angleSubstitute the known values in the above equation
So, we have
35 = 7 * ∅
Divide both sides by 7
∅ = 5
Hence, the measure of the angle in radians is 5 rad
Read more about arc lengths at
https://brainly.com/question/2005046
#SPJ1
A large university accepts %50 of the students who apply. Of the students the university accepts, %45 actually enroll. If 30,000 students apply, how many actually enroll?
Answers
Explanation:
30,000 students applied and the university only accepts 50%
50% of 30,000 is 15,000
So 15,000 students were accepted
But 45% actually enroll.
45% of 15000 that was accepted = 6,750 students actually enrolled.
the time t required to repair a machine is an exponentially distributed random variable with mean 2.5 (hours). what is the probability that a repair takes at least 1212 hours given that its duration exceeds 12 hours?
Answers
The probability that a repair takes at least 1212 hours is 0.67.
With a mean of 2.5 hours, the repair time is treated as an increasingly random variable.
Because the inverse of the mean is the parameter of the exponential distribution, λ = 0.4 [tex]h^{-1}[/tex].
The probability that a repair duration will transcend k hours may well be described as follows:
P(t > K) = [tex]e^{-\lambda t}[/tex] = [tex]e^{-0.4t}[/tex]
Given that a repair takes over 11 hours, the conditional likelihood that it will take at least 12 hours,
The exponential distribution has a discrete-time feature, which means that the probability of future events is not affected by previous events.
In this example, the conditional chance that a repair will take at least 10 hours is equal to the possibility that a repair will take at least (12 - 11) = 1 hour.
P(t > 12| t > 11) = P(t > 1)
P(k > 1) = [tex]e^{-0.4 * 1}[/tex] = 0.67
Read more about the exponential distribution at
https://brainly.com/question/15711014?referrer=searchResults
#SPJ4
An aquarium can hold 3,744 cubic inches of water. ben fills the aquarium 9/10 full of water. water weighs about 0.036 pound per cubic inch. which estimate of the weight of the water in the aquarium is closest to the exact value?
Answers
Answer:i think its 120.
Step-by-step explanation:
When the add-or-subtract method for a system of linear equations finds a solution of (3, –4), what does that tell you about the equations?Group of answer choicesWhether you add or subtract the equations, you get the same resulting equation in one variable.The graphs of the lines are parallel.The graphs of the lines are the same line.The graphs of the lines intersect at point (3, –4).
Answers
The answer is:
Whether you add or subtract the equations, you get the same resulting equation in one variable.
Which of the following is completely factored?O 5x2 (2xy + 12x2)O 3.r(522 - 6x + 3)O r(14.ry + 5.0 - 10x2)
Answers
ANSWER
[tex]3x(5x^2-6x+3)[/tex]EXPLANATION
We want to identify the option that is completely factored.
For an expression to be completely factored, it means that there are no more common terms between the terms in the expression.
That means it can not be factored any further.
Therefore, the only correct option is:
[tex]3x(5x^2-6x+3)[/tex]for a singles match, a tennis court is 78 feet long and 27 feet wide. Which calculation would give the perimeter of a tennis court for a singles match?
Answers
Answer: 3 miles
Step-by-step explanation:
15840 feet
= 15840 ÷ 5280 miles
= 3 miles
what is the perimeter of a semicircle when the radius is 5cm
Answers
Answer:
25.707 units
Step-by-step explanation:
A rectangular window is 3/8 yard wide and 4/5 yard long. What is the area of the window in square yards?
Answers
Answer:
3/10 yds ^2
Step-by-step explanation:
To find the area, multiply the length times the width
A = l*w
= 3/8 * 4/5
Rearranging
= 3/5 * 4/8
Simplify
= 3/5 * 1/2
= 3/10 yds ^2
A number cube with faces labeled from 1 to 6 was rolled 20 times. Each time the number cube was rolled, the
number showing on the top face was recorded. The table shows the results.
Results
Number Showing on Top Face Frequency
Answers
For the cube to land with a 5 or 6 on the top face, a 2/5 probability is needed.
The table displays the outcomes of 20 rolls of a number cube with faces labeled from 1 to 6.
To ascertain the experimental likelihood that 5 or 6 will appear on the top face of the number cube the following time it is rolled.
The ratio of likely outcomes to all possible outcomes is known as the probability.
Total frequency = 3 plus 3 plus 6 plus 3 plus 5 equals 20.
Total frequency of positive results = 3 + 5 = 8
Therefore according to the probability it is no. of possible outcomes divided by total outcomes.
Here favorable cases are 8 which are positive results
Total out come ( frequency) is 20
Probability is 8/20, or 2/5.
Therefore, there is a 2/5 chance that the cube will land with a 5 or 6 on the top face.
Learn more about probability at
https://brainly.com/question/21455222
#SPJ1
A graphic designer charges an hourly rate. In July, the only expense is for advertising. The function graphed models the designer's net income, y, for July for x hours of work.
Select True or False to describe each statement.
True False
The x-intercept represents the amount the designer charges for 1 h of work.
True – The , x, -intercept represents the amount the designer charges for 1 h of work.
False – The , x, -intercept represents the amount the designer charges for 1 h of work.
The difference between 0 and the y-intercept represents the amount the designer spent on advertising.
True – The difference between 0 and the , y, -intercept represents the amount the designer spent on advertising.
False – The difference between 0 and the , y, -intercept represents the amount the designer spent on advertising.
The slope represents the designer's hourly rate.
True – The slope represents the designer's hourly rate.
False – The slope represents the designer's hourly rate.
Graph of a line on a coordinate plane. The graph titled Net Income for July. The horizontal axis is labeled Time Worked (h) and vertical axis is labeled Net Income (S). The horizontal x axis ranges from 0 to 18 in increments of 2. The vertical y axis ranges from negative 400 to 400 in increments of 100. A line passes through the coordinate points begin ordered pair 0 comma negative 300 end ordered pair and begin ordered pair 6 comma 0 end ordered pair
Answers
False: The x-intercept represents the amount the designer charges for 1 h of work.
True: The difference between 0 and the y-intercept represents the amount the designer spent on advertising.
True: The slope represents the designer's hourly rate.
What is y-intercept?In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
By critically observing the graph (see attachment), the coordinates of the y-intercept of this line is given by y-intercept = (0, 6), which represents the graphic designer's expenses on advertising for the month of July.
What is x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of any function crosses the x-coordinate and the value of "y" is equal to zero (0).
From the graph (see attachment), we can logically deduce that the x-intercept represents the number of hours which the graphic designer would have to work, in order to cover his expenses (on advertising) for the month of July.
In conclusion, the hourly rate of this graphic designer for the month of July is represented by the slope of the graph.
Read more on y-intercept here: https://brainly.com/question/6240745
#SPJ1
