The product of given complex number that is 8i and 4i will be -32 by the properties of complex number that states i*i will be -1 and 8*4 will be 32.
What is complex number?Every complex number can be expressed in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted I also known as the imaginary unit, and satisfying the equation i²=-1.
What are the property of complex number?Commutative, Associative, Distributive Properties: All complex numbers are commutative and associative under addition and multiplication, and multiplication distributes over addition.
Here,
The product of 8i*4i=-32
as 8*4=32
and i²=-1
32*-1=-32
Due to the properties of complex numbers, which state that i*i will be -1 and 8*4 will be 32, the product of the given complex number, which is 8i and 4i, will be -32.
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The original price of a sweater is $48. The sale price is 80%. What is the sale price of the sweater?
The system of equations may be solved by hand calculation or by using the crossing-graphs method.Solve the following system using the crossing-graphs method.2x - y = 04x + 2y = 48(x, y) = (_____,_____)
The first thing you can do is graph each of the equations. To do this, you can write the equations following the form
[tex]y=mx+b[/tex]Where m is the slope of the line and b the intersection point with the y axis. Then
[tex]\begin{gathered} 2x-y=0 \\ 2x=y \\ y=2x \\ \text{ And the other equation} \\ 4x+2y=48\text{ } \\ \text{To simplify the equation, you can divide by 2 both sides of the equation} \\ 2x+y=24 \\ y=-2x+24 \end{gathered}[/tex]Graphing you have
The solution of the system of equations will be the point at which both lines intersect. Therefore, the solution is (6,2).
Determine the shape when the following points are graphed one a coordinate plane. A(-3, 1), B(2, 1), C(2, 4), D(-3, 4)
The given points are A(-3, 1), B(2, 1), C(2, 4), D(-3, 4).
The image below shows the figure formed by these points.
As you can observe, the shape formed by the given points is a rectangle with dimensions 5 times 3.
Therefore, the answer is "rectangle".Write the equation of a line the goes through point
(3,-4) and is perpendicular to the line x = 1.
keeping in mind that x = 1 is just a vertical line, Check the picture below.
The table below shows the average price of a Miami Marlins baseball ticket between 2006 and 2021.
By evaluating the equation in x = 2040, we can estimate the price to be $1507.7.
How to evaluate the equation?To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.
Given that,
We know that the equation:
y = 1.83*x - 2225.5
Models the relationship between the year, x, and the average ticket price of a Miami Marlins baseball ticket.
We know that this relationship works for the years 2006 to 2021, but can be used to estimate the price for years after and before that.
if we use x = 2040
we will get
y = 1.83*2040 - 2225.5 = 1507.7
Hence, The price will be 1507.7, in dollars, of a game in the year 2040.
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URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Answer:
√52
Step-by-step explanation:
[tex] \sqrt{ {(4 - ( - 2))}^{2} + {(1 - ( - 3))}^{2} } [/tex]
[tex] \sqrt{ {6}^{2} + {4}^{2} } = \sqrt{36 + 16} = \sqrt{52} [/tex]
Braden owns a painting that is valued at $27,400. If the value of the artwork increases by 5% every year, how much will it be worth in 3 years?If necessary, round your answer to the nearest cent.
We know that the painting increase its value by 5% each year.
So, if P(1) is the value the next year and P(0) is the actual value ($27,400) we can write:
[tex]P(1)_{}=P(0)+0.05P(0)=1.05\cdot P(0)[/tex]In the same way, the following year, it will increase another 5% over its value:
[tex]P(2)=1.05P(1)=1.05(1.05\cdot P(0))=1.05^2\cdot P(0)=1.05^2\cdot27,400[/tex]We can generalize this as:
[tex]P(n)=27,400\cdot1.05^n[/tex]For n=3 (3 years) we will have a value of:
[tex]P(3)=27,400\cdot1.05^3\approx27,400\cdot1.1576\approx31,718.93[/tex]Answer: the value of the painting in 3 years is expected to be $31,718.93.
f A and B are independent events with P(A)=0.3 and P(B)=0.7, find P(A AND B). Provide your answer below:
If A and B are independent events with P(A) = 0.3 and P(B) = 0.7, then the value of P(A AND B) = 0.21
A and B are independent events
Independent events are events that does not depends on any other events.
Probability is the ratio of number of favorable outcomes to the total number of outcomes
The value of P(A) = 0.3
The value of P(B) = 0.7
If A and B are independent events, then P(A AND B) = P(A) × P(B)
Substitute the values in the equation
P(A AND B) = 0.3 × 0.7
= 0.21
Hence, if A and B are independent events with P(A) = 0.3 and P(B) = 0.7, then the value of P(A AND B) = 0.21
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To find the length of a side, a, of a square divide the perimeter, P by 4. Use the above verbal representation to express the function s, symbolically, graphically, and numerically.
Solution
- We are told to find the numerical, graphical, and symbolic expression for the side of a square, s, given its perimeter, P
Symbolic Representation:
- The symbolic representation simply means the formula we can use to represent the side of a square given its perimeter, P.
- The side of a square is simply the perimeter P divided by 4.
- Symbolically, we have:
[tex]\begin{gathered} s=\frac{P}{4} \\ \text{where,} \\ s=\text{side of the square} \\ P=\text{Perimeter of the square} \end{gathered}[/tex]Numerical Representation:
- We are given a set of numbers to create a table given some numbers for P.
- We are given a set of values for P: 4, 8, 10, 12.
- We can use the formula in the symbolic representation to find the corresponding values of s.
[tex]\begin{gathered} \text{When P = 4:} \\ s=\frac{4}{4}=1 \\ s=1 \\ \\ \text{When P=8:} \\ s=\frac{8}{4}=2 \\ s=2 \\ \\ \text{When P=10:} \\ s=\frac{10}{4}=2.5 \\ s=2.5 \\ \\ \text{When P=12:} \\ s=\frac{12}{4}=3 \\ s=3 \end{gathered}[/tex]- Now that we have the values of P and the corresponding values of s, we can proceed to create a table of values as the question asked of us.
How do I use the calculator to find log10 6, to 3 decimal places please?
Your calculator uses base 10 for its logs
There should be a button that says log
That is a base 10 log
log 6 = .77815125
To 3 decimal places
log 6 = .778
The base 10 is implied
1. Jessica finishes her book in 2 1
3
hours. Eric takes 11
2
times longer than
Jessica to finish his book.
This model represents the amount of time Jessica takes to finish her
book. It has a width of 1 and a length of 2 1
3
. The model is 2 1/3 out of 3
The time taken for Eric to finish the book is 3 1/2 hours.
What is a fraction?A fraction simply means a part of a whole. It van also refer to any number of equal parts.
The information illustrated that Jessica finishes her book in 2 1 / 3 hours and that Eric takes 1 1 / 2
times longer than Jessica to finish his book.
In this case, the time that was used by Eric will be the multiplication of the fractions given. This will be illustrated as:
= 2 1/3 × 1 1/2
Change to improper fraction
= 7/3 × 3/2
= 7 / 2
= 3 1 / 2
Eric used 3 1/2 hours.
This illustrates the concept of multiplication of fractions.
The complete question is written below.
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Jessica finishes her book in 2 1/3.hours. Eric takes 1 1/2 times longer than Jessica to finish his book. How long did Eric take yo finish the book?
6. A line goes through these two points, (-4, -1) anti (-9,-5).A. Find an equation for this line in point slope form.B. Find the equation for this line in slope intercept form. Be sure to show your work.C. If the y-coordinate of a point on this line is 7, what is the x-coordinate of this point?
A. In order to find the equation, first we need to find the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]m is the slope
(-4, -1)=(x1,y1)
(-9,-5)=(x2,y2)
we substitute the values
[tex]m=\frac{-5+1}{-9+4}=\frac{-4}{-5}=\frac{4}{5}[/tex]then we use the point-slope form
[tex]y-y_1=m(x-x_1)[/tex]we substitute the values
[tex]y+1=\frac{4}{5}(x+4)[/tex]B. in order to find the slope-intercept form we need to isolate the y
[tex]y=\frac{4}{5}x+\frac{11}{5}[/tex]C. if the y coordinate is 7
[tex]7=\frac{4}{5}(x)+\frac{11}{5}[/tex]then we isolate the x
[tex]\frac{4}{5}x=7-\frac{11}{5}[/tex][tex]\begin{gathered} \frac{4}{5}x=\frac{24}{5} \\ x=\frac{5\cdot24}{5\cdot4} \\ x=6 \end{gathered}[/tex]the value of the x-coordinate is 6 when the y-coordinate is 7
Graph the functions on the same coordinate plane.f(x) = −5g(x) = x^2 + 2x − 8What are the solutions to the equation f(x) = g(x)? Select each correct answer.−5−3−113
ANSWER
[tex]\begin{equation*} -3,1 \end{equation*}[/tex]EXPLANATION
The graphical solution to the given equation is obtained at the points where the two graphs of the two functions intersect each other on the coordinate plane.
To graph f(x), we simply draw a straight horizontal line at the point y = -5.
To graph g(x), we have to find coordinate points by substituting values of x into the function and obtaining values for g(x).
Let us find the value of g(x) when x = -3, -1, 1:
[tex]\begin{gathered} x=-3: \\ g(-3)=(-3)^2+2(-3)-8=9-6-8 \\ g(-3)=-5 \\ x=-1: \\ g(-1)=(-1)^2+2(-1)-8=1-2-8 \\ g(-1)=-9 \\ x=1: \\ g(1)=(1)^2+2(1)-8=1+2-8 \\ g(1)=-5 \end{gathered}[/tex]Now, we have three points to plot the graph with: (-3, -5), (-1, -9), (1, -5)
Let us now plot the graphs of the functions:
Therefore, the solutions to the equation f(x) = g(x) are:
[tex]\begin{gathered} x=-3,x=1 \\ \Rightarrow-3,1 \end{gathered}[/tex]Subtract 9 1/4 - 4 3/4 . Simplify the answer and write as a mixed number.
Upon subtracting 9 1/4 from 4 3/4 we get 18/4.
Given
9 1/4 - 4 3/4
solution:
[tex]9\frac{1}{4}[/tex] can be written as 37/4 ( 9 * 4 + 1 thus 37/4) and
[tex]4\frac{3}{4}[/tex] can be written as 19/4 ( 4 * 4 + 3 thus 19/4)
37/4 - 19/4 as 4 is the common denominator for both the fractions so take 4 as the denominator
[tex]= \frac{37-19}{4}[/tex] = 18/4 if we further simplify 18/4 = 4.5
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The chart below shows how many newspapers each person stacked. Which operation would be used to find the total number of newspapers Diane stacked?
Answer:
Where's the chart?
Step-by-step explanation:
Hello everybody! I would really appreciate it if Somebody could give me the answer for this question and give a brief explanation on how they got it. Look at the photo for instructions!
Recall that the constant of variation of a straight line is the slope of the line.
To compute the slope we will use the following formula for the slope of a line:
[tex]s=\frac{y_2-y_1}{x_2-x_1}\text{.}[/tex]Now, notice that points (-1,3) and (1,-3) are on the line, then substituting these points in the above formula we get:
[tex]s=\frac{3-(-3)}{-1-1}=\frac{6}{-2}=-3.[/tex]Answer: -3.
a can of juice is 5.5 inches high and its base has a diameter or 6 inches what is the volume of the can? round to the nearest hundredth
According to the problem, the can of juice has the form of a cylinder, so we have to use the following formula
[tex]V=\pi(r)^2h[/tex]Where the radius is half the diameter, r = 3 in, h = 5.5 in, and pi = 3.14. Replacing these values, we have
[tex]V=3.14\cdot(3in)^2\cdot5.5in=155.43in^3[/tex]Hence, the volume of the can is 155.43 cubic inches.F(x)=1/x g (x)=x-4 can you evaluate (golf)(0)? Explain why or why not.
If f(x) = 1/x and g(x) = x-4 , then (gof)(0) cannot be evaluated as the function becomes not defined .
In the question
it is given that the functions
f(x) = 1/x
and g(x) = x-4
to find g=(gof)(x) ,
(gof)(x) = g(f(x))
= g(1/x) ... because f(x) = 1/x
= 1/x - 4 ....because g(x) = x-4
On simplifying further , we get
= (1-4x)/4x
On substituting x=0 , we get
gof(0) = (1-0)/4(0)
= 1/0
which is not defined , hence cannot be evaluated.
Therefore , if f(x) = 1/x and g(x) = x-4 , then (gof)(0) cannot be evaluated as the function becomes not defined .
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I need help ASAP
Jeannette is participating in a hot-dog-eating contest. She has already eaten 18 hot dogs but needs to eat more than 35 hot dogs to win. Jeannette is eating 2.6 hot dogs per minute. Which of the following inequalities could be used to solve for x, the number of minutes Jeannette needs to continue eating hot dogs to win the contest
A.
2.6x > 35
B.
2.6x - 18 > 35
C.
2.6x > 18
D.
2.6x + 18 > 35
Answer:
I may be wrong but I think it's D.
Step-by-step explanation:
I made an educated guess.
Question 5 Multiple Choice Worth 1 points)(05.02 MC)A nurse collected data about the average birth weight of babies in the hospital that month. Her data is shown using the dot plot. Create a box plot to represent the data.Monthly Birth Weight:8.28.3 8.4 8.5 8.6Birth Weight (in pounds)82 83 8.4 85 86 87 8.882 8384 8.5 86 87 60 6.982 83 84 8.5 8.6 8.7 8.0 8.9 98283 84 85 86 87 88 8.998.1816.181$F
Given:
Here we have data about the average birth weight of babies in the hospital that month.
Required:
We need to create a box plot to represent the data.
Explanation:
Here we have monthly birth weight in pounds as
8.2 , 8.2 , 8.3 , 8.3 , 8.4 , 8.4 , 8.5 , 8.5 , 8.5 , 8.7 , 8.9
now by data we get Q2 is 8.4
now for this data
8.2 , 8.2 , 8.3 , 8.3 , 8.4
we get Q1 is 8.3
by this data
8.5 , 8.5 , 8.5 , 8.7 , 8.9
we get Q3 is 8.5
and we have maximum 8.9 and minimum 8.2
now make a box plot
Final answer:
Andre and Lin are discussing whether it is possible to define latitude and temperature in a way that makes sense to talk about temperature as a function of latitude. They are considering different options. Here are the options: a. Finding the temperature right now in cities with different latitudes b. Finding the daily high temperature at cities that have different latitudes c. Finding the average high temperature in a specific month, e.g., September, at cities that have different latitudes d. Finding the average yearly temperature at cities that have different latitudes None of these options are perfect. All have flaws. Choose one option and give the advantages and disadvantages of the option for talking about temperature as a function of latitude. Answer in the space below
All answers are kind of similar and none of these options are perfect.
We are going to chose the opcion b, the advantage is that the daily high temperature at cities give us a statistical sample about how latitude impact the temperature and how is the clime in those days.
Disadvantages is that we dont know the lower temperature and how the latitude impact in this case.
A line passes through the point -8, -5 and has a slope of -3/2 Write an equation in slope-intercept form for this line.
Answer:
[tex]y = - \frac{3}{2} x - 17[/tex]
Step-by-step explanation:
[tex] - 5 = - \frac{3}{2} ( - 8) + b[/tex]
[tex] - 5 = 12 + b[/tex]
[tex]b = - 17[/tex]
[tex]y = - \frac{3}{2} x - 17[/tex]
The endpoints of diameter in a circle form an angle with point C. What is the measure of angle BCD?
Answer:
90 degrees
Explanation:
Please note that whenever a triangle is inscribed in a circle and one side of the triangle is a diameter of the circle as in the given figure, then the angle that is opposite the diameter of the circle is a right angle;
[tex]\therefore\angle BCD=90^{\circ}[/tex]Explain why m<1>m<3.which statement below can be made, according to the corollary to the Triangle Exterior Angle Theorem?
In the given image you have that m∠1 is lower than angle m∠3 becasue it is clear that angle ∠1 is an angle greater than 90° and angle ∠3 is lower than 90°. Then m∠1 > m∠3.
Now, in order to determine which of the given statements is true for the given figure, you take into account that the exterioir angle theorem stablishes that the measure of an exterior angle of the triangle is greater that any of the measure of the remote interioir angles of the triangle.
Thus, you can notice that the measure of the external angle ∠1 is greater than the measure either angle ∠4 or angle ∠2.
Hence, following statement is true:
m∠1 > m∠4 and m∠1 > m∠2
Help math help math
What is the answer
The ratio 25 : 15 as a fraction in the simplest form can be written as 5/3.
What is ratio?The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. Ratio are represented in the following way - a : b, c : d etc
Given is 25 to 15.
We can express this ratio as a fraction in the simplest form as -
25 : 15 = 25/15
Now, we have to ensure that only whole numbers are their in the numerator and denominator. So in simplest form, we can write -
25 : 15 = 25/15 = (5 x 5)/(5 x 3) = 5/3
Simplest form in fraction will be 5/3
Therefore, the ratio 25 : 15 as a fraction in the simplest form can be written as 5/3.
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you can help me ??? only 24, 26 and 27
Answer:
∠VYZ = 65
∠VXY = 75
∠WZY = 50
∠XWZ = 80
∠WXY = 150
Explanation:
The angle ∠VYZ and the angle ∠VZY are complementary , meaning they add up to 90 degrees. Since ∠VZY = 25 we have
[tex]undefined[/tex]1. Which fraction equals a repeatingdecimal?530АC503013B.1325D1013
5/30 = 1/6 = 0.16666667
13/25 = 0.52
30/50 = 3/5 = 0.6
13/10 = 1.3
As you can see the fraction which is equal to a repeating decimal is:
5/30 = 1/6 = 0.16666667
Can you do the bottom please which it says lesson 11.9 - 11.10
1.19)
In general, the area of a rectangle is given by the formula
[tex]\begin{gathered} A=lw \\ l\to\text{ length} \\ w\to\text{width} \end{gathered}[/tex]In our case,
[tex]\begin{gathered} A_A=4\cdot4=16 \\ A_B=3\cdot4=12 \\ A_C=6\cdot2=12 \end{gathered}[/tex]The area of figure A is 16 square units, the area of B is 12 square units and the area of shape C is 12 square units.
As for the area of a rectangle, in general,
[tex]P=2l+2w=2(l+w)[/tex]Then, in the case of each rectangle,
[tex]\begin{gathered} P_A=2(4+4)=2\cdot8=16 \\ P_B=2(3+4)=2\cdot7=14 \\ P_C=2(2+6)=2\cdot8=16 \end{gathered}[/tex]11.10)
Therefore, figures A and C have the same perimeter, whereas rectangles B and C have the same area.
Which values are solutions to the inequality below?Check all that apply.√x ≤ 5A. 1B. 18C. -5D. 25E. 24F. 625
Given the inequality:
[tex]\sqrt[]{x}<5[/tex]We need to solve the inequality to get a range of values for x.
This we can do by finding the square of both sides:
[tex]\begin{gathered} (\sqrt[]{x})^2<5^2 \\ x<25 \end{gathered}[/tex]On checking the options given, we will pick the numbers that are strictly less than 25.
Therefore, the correct options are:
OPTION A
OPTION B
OPTION C
OPTION F
Two systems of equations are given below For each system, choose the best description of its solution If applicable, give the solution 7 System The system has no solution The system has a unique solution 5x-*= -1 5x+y=1 The system has infinitely many solutions Systeme The system has no solution The system has a unique solution: *+ 2y 13 -* + 2y = 7 The system has infinitely many solutions.
If we sum both equations, we have the next result:
[tex]0\text{ = 0}[/tex]Since we have this, we can say that the system has infinite solutions. We sum both equations, and we finally get that 0 = 0. In this case, the system has infinite solutions.
All these solutions are expressed by (solving for y):
[tex]y=\text{ 1 + 5x}[/tex]For example, for a value of x = 1, y is a function of x; then, y = 1 + 5 = 6, or (1, 6), and so on.
For the next system of equations:
[tex]\begin{gathered} x\text{ + 2y = 13} \\ -x\text{ + 2y = 7} \end{gathered}[/tex]Adding both equations, we finally have:
[tex]4y\text{ = 20}\Rightarrow\text{ y = 5}[/tex]Then, solving for x, we have (using the first equation):
[tex]x\text{ + 2(5) = 13 }\Rightarrow x\text{ = 13 - 10 }\Rightarrow x\text{ = 3}[/tex]Then, this last system has a unique solution, which is (3, 5) or x = 3 and y = 5.
