Point A is shown on the complex plane.What is the standard form of the complex number that point A represents?
Answers
Hello there. To solve this question, we have to remember some properties about the representation of a complex number in the complex or Argand-Gauss plane.
Given the complex plane with the point A representing a complex number:
We have to remember that in the complex plane, a complex number z:
[tex]z=a+ib[/tex]has coordinates
[tex](a,\,b)[/tex]And it is more commonly represented by a vector starting at the origin and with the tip on this point.
In this case, we find that the coordinates of the point A are:
[tex]A=(-5,\,3)[/tex]Which means that the complex number is
[tex]-5+3i[/tex]And this is the answer contained in the last option.
Related Questions
Solve by factoring. Be sure to look for a GCF first in case there is one-2x²-4x+70=0
Answers
ANSWER
x = 5 and x = -7
EXPLANATION
We want to solve the equation by factoring.
The equation is:
[tex]-2x^2\text{ - 4x + 70 = 0}[/tex]First, there is a greatest common factor that we can use to simplify the equation. That is -2, so, first we divide through by -2.
It becomes:
[tex]x^2\text{ + 2x - 35 = 0}[/tex]Now, factorise:
[tex]\begin{gathered} x^2\text{ + 2x - 35 = 0} \\ x^2\text{ + 7x - 5x - 35 = 0} \\ x(x\text{ + 7) - 5(x + 7) = 0} \\ (x\text{ - 5)(x + 7) = 0} \\ x\text{ = 5 and x = -7} \end{gathered}[/tex]Find the volume of a pyramid with a square base, where the side length of the base is19.3 ft and the height of the pyramid is 16.2 ft. Round your answer to the nearesttenth of a cubic foot.
Answers
Find the volume of a pyramid with a square base, where the side length of the base is
19.3 ft and the height of the pyramid is 16.2 ft. Round your answer to the nearest
tenth of a cubic foo
Remember that
the volume of the pyramid is equal to
[tex]V=\frac{1}{3}\cdot B\cdot h[/tex]where
B is the area of the base
h is the height
step 1
Find out the area of the base
B=19.3^2
B=372.49 ft2
h=16.2 ft
substitute the given values in the formula
[tex]V=\frac{1}{3}\cdot372.49\cdot16.2[/tex]V=2,011.4 ft3Evaluate the expression when a=3 and b=6. b2-4a
Answers
b² - 4a
evaluated when a = 3 and b = 6 is:
6² - 4(3) =
= 36 - 12=
= 24
Given a function described by the table below, what is y when x is 5?XY264859612
Answers
Given a function described by the table
We will find the value of (y) when x = 5
As shown in the table
When x = 5, y = 9
so, the answer will be y = 9
Determine the frequency of each class and the table shown
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Given:
The dataset and table with class.
Required:
Determine the frequency of each class.
Explanation:
Answer:
Answered the question.
Which of the following statements are true regarding functions? Check all that apply. A. The horizontal line test may be used to determine whether a function is one-to-one. B. The vertical line test may be used to determine whether a relatio is a function. C. A sequence is a function whose domain is the set of rational numbers. PREVIOUS
Answers
Statement A is true.
In the next example, we can see a function that is not one-to-one with the help of the horizontal line test:
Statement B is true.
In the next example, we can see a relationship that is not a function because it doesn't pass the vertical line test
Statement C is false.
A sequence is a function whose domain is the set of natural numbers
The top-selling Red and Voss tire is rated 60000 miles, which means nothing. In fact, the distance the tires can run until wear-out is a normally distributed random variable with a mean of 72000 miles and a standard deviation of 7000 miles.A. What is the probability that the tire wears out before 60000 miles?Probability = What is the probability that a tire lasts more than 80000 miles? Probability=
Answers
a. 0.0436
b. 0.1271
We are given the following:
Distance (x) = 60,000
Mean (u) = 72,000
Standard Deviation(s) = 7,000
We are also told that it is a normal disribution relationship. The formula for ND is as follows:
z = (x - u) / s
Now we can continue with part a and b as follows:
a) P (x < 60,000)
= P (z < (60000 - 72000) / 7000)
= P (z < -1.714)
We can find the corresponding z score by looking at a z score table, and we find th probability to be 0.0436
b) P ( x > 80,000)
= P(z > (80000 - 72000) / 7000)
= P( z > 1.143)
We find the corresponding z score to be 0.8729, now we can substract this from 1 sinsce our probability is larger than the given distance (meaning we are trying to find the area to the right of the z score) to find our final answer:
1 - 0.8729 = 0.1271
How do I find x I know you separate the shapes but I got it wrong…
Answers
Let's find this length first
6√2 is the hypotenuse, then
[tex]\begin{gathered} (6\sqrt{2})^2=6^2+y^2 \\ \\ y^2=(6\sqrt{2})^2-6^2 \\ \\ y^2=36\cdot2-36 \\ \\ y^2=36 \\ \\ y=\sqrt{36}=6 \end{gathered}[/tex]Then we can find x because
[tex]\begin{gathered} x^2=y^2+12^2 \\ \\ x^2=6^2+12^2 \\ \\ x^2=36+144 \\ \\ x^2=180 \\ \\ x=\sqrt{180} \\ \\ x=6\sqrt{5} \end{gathered}[/tex]The length of x is
[tex]x=6\sqrt{5}[/tex]Not sure on how to do this. Would really like some help.
Answers
Given:
[tex]\cos60^{\circ}[/tex]To find:
The value
Explanation:
We know that,
[tex]\cos\theta=\sin(90-\theta)[/tex]So, we write,
[tex]\begin{gathered} \cos60^{\circ}=\sin(90-60) \\ =\sin30^{\circ} \\ =\frac{1}{2} \end{gathered}[/tex]Final answer:
[tex]\cos60^{\circ}=\frac{1}{2}[/tex]A. Marvin worked 4 hours a day plus an additional 5-hour day for a total of 29 hours.B. Marvin worked 9 hours a day for a total of 29 hoursC. Marvin worked 4 hours one day plus an additional 5 hours for a total of 29 hours.D. Marvin worked 4 days plus 5 hours for a total of 29 hours.
Answers
May I please get help with this I have tried multiple times to get the correct answer but still could not get them right. I am confused on how I should draw the dilation as I have tried many times as well.
Answers
After performing dilation centered at the origin we get
(a) shortest side of original figure=2 units
shortest side of the final figure=6units
(b) shortest side of the final figure=3×shortest side of the original figure
(c) True
(d) False
What is the dilation of the figure centered at origin?A transformation called a dilatation alters a figure's size without altering its shape. A figure might become larger or smaller due to dilation. For instance.
The image is smaller than the preimage when the scaling factor is between 0 and 1. Reductions are referred to as dilations with scale factors between 0 and 1.
The image is larger than the preimage if the scaling factor is greater than 1. Enlargements are defined as a dilation with a scale factor greater than 1.
To get the size of the edge we multiply the size of original lenght by scale factor.
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im taking geometry A and i have a hard time with the keeping the properties straight in mathematical reasoning. the question im struggling with at the moment is in the picture here:thank you for your time
Answers
The given proposition is
[tex]m\angle UJN=m\angle EJN\rightarrow m\angle UJN+m\angle YJN=m\angle EJN+m\angle YJN[/tex]As you can observe, it was added angle YJN to the equation on both sides. The property that allows us to do that it's call addition property of equalities.
Therefore, the right answer is "addition property".A rectangular field of corn is averaging 125 bu/acre. The field measures 1080 yd by 924 yd. How many bushels of corn will there be?
Answers
Based on the dimensions of the rectangular field, and the corn per acre, the number of bushels of corn can be found to be 25,772 bushels
How to find the number of bushels of corn?First, find the area of the rectangular field:
= 1,080 x 924
= 997,920 yard²
Then convert this to acres with a single acre being 4,840 yards²:
= 997,920 / 4,840 square yards per acre
= 206.18 acres
The number of bushels of corn that can be grown is:
= 206.18 x 125 bushel per acre
= 25,772 bushels
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Write an equation of the line passing through the point (8,-3) that is parallel to the line y= -x -1. An equation of the line is
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The equation of the line, in slope-intercept form, that is parallel to the line y = -x - 1 is: y = -x + 5.
How to Write the Equation of Parallel Lines?Parallel lines have equal slope value, "m". In slope-intercept form, the equation y = mx + b represents a line, where the slope is "m" and the y-intercept is "b".
The slope of y= -x -1 is -1. This means the line that is parallel to y= -x -1 will also have a slope that is equal to -1.
Substitute m = -1 and (x, y) = (8, -3) into y = mx + b to find the value of b:
-3 = -1(8) + b
-3 = -8 + b
-3 + 8 = b
5 = b
b = 5
Substitute b = 5 and m = -1 into y = mx + b to wrote the equation of the line that is parallel y = -x -1:
y = -x + 5
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A cashier has 24 bills, all of which are $10 or $20 bills. The total value of the money is $410. How many of each type of bill does the cashier have?
Answers
The cashier has 7 bills of $10 and 17 bills of $20 (found using linear equation).
According to the question,
We have the following information:
A cashier has 24 bills, all of which are $10 or $20 bills. The total value of the money is $410.
Now, let's take the number of $10 bills to be x and the number of $20 bills to be y.
So, we have the following expression:
x+y = 24
x = 24-y .... (1)
10x+20y = 410
Taking 10 as a common factor from the terms on the left hand side:
10(x+2y) = 410
x+2y = 410/10
x+2y = 41
Now, putting the value of x from equation 1:
24-y+2y = 41
24+y = 41
y = 41-24
y = 17
Now, putting this value of y in equation 1:
x = 24-y
x = 24-17
x = 7
Hence, the cashier has 7 bills of $10 and 17 bills of $20 when the total value of the money is $410.
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create an original function that has at least one asymptote and possibly a removable discontinuity list these features of your function: asymptote(s) (vertical horizontal slant) removable discontinuity(ies) x intercept(s) y intercept and end behavior provide any other details that would enable another student to graph and determine the equation for your function do not state your function
Answers
We have to create a function that has at least one asymptote and one removable discontinuity (a "hole").
We then have to list the type of feature.
We can start with a function like y = 1/x. This function will have a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.
We can translate it one unit up and one unit to the right and write the equation as:
[tex]y=\frac{1}{x-1}+1=\frac{1}{x-1}+\frac{x-1}{x-1}=\frac{x}{x-1}[/tex]Then, the asymptotes will be x = 1 and y = 1. We have at least one asymptote for this function.
We can now add a removable discontinuity. This type of discontinuity is one that is present in the original equation but, when factorizing numerator and denominator, it can be cancelled. This happens when both the numerator and denominator have a common root: the rational function can be simplified, but the root is still present in the original expression.
We than can add a removable discontinuity to the expression by multiplying both the numerator and denominator by a common factor, like (x-2). This will add a removable discontinuity at x = 2.
We can do it as:
[tex]y=\frac{x(x-2)}{(x-1)(x-2)}=\frac{x^2-2x}{x^2-3x+2}[/tex]This will have the same shape as y =x/(x-1) but with a hole at x = 2, as the function can not take a value that makes the denominator become 0, so it is not defined for x = 2.
Finally, we can find the x and y intercepts.
The y-intercepts happens when x = 0, so we can calculate it as:
[tex]\begin{gathered} f(x)=\frac{x^2-2x}{x^2-3x+2} \\ f(0)=\frac{0^2-2\cdot0}{0^2-3\cdot0+2}=\frac{0}{2}=0 \end{gathered}[/tex]The y-intercept is y = 0, with the function passing through the point (0,0).
As the x-intercept is the value of x when y = 0, we already know that the x-intercept is x = 0, as the function pass through (0,0).
Then, we can list the features as:
Asymptotes: Vertical asymptote at x = 1 and horizontal asymptote at y = 1.
Removable discontinuity: x = 2.
y-intercept: y = 0.
End behaviour: the function tends to y = 1 when x approaches infinity or minus infinity.
With that information, the function can be graphed.
A ball is thrown from an initial height of 4 feet with an initial upward velocity of 23 ft/s. The ball's height h (in feet) after 1 seconds is given by the following.h=4+231-167Find all values of 1 for which the ball's height is 12 feet.Round your answer(s) to the nearest hundredth.(If there is more than one answer, use the "or" button.)Please just provide the answer my last tutor lost connection abruptly.
Answers
Answer
t = 0.59 seconds or t = 0.85 seconds
Step-by-step explanation:
[tex]\begin{gathered} Given\text{ the following equation} \\ h=4+23t-16t^2\text{ } \\ h\text{ = 12 f}eet \\ 12=4+23t-16t^2 \\ \text{Collect the like terms} \\ 12-4=23t-16t^2 \\ 8=23t-16t^2 \\ 23t-16t^2\text{ = 8} \\ -16t^2\text{ + 23t - 8 = 0} \\ \text{ Using the general formula} \\ t\text{ }=\text{ }\frac{-b\pm\sqrt[]{b^2\text{ - 4ac}}}{2a} \\ \text{let a = -16, b = 23, c = -8} \\ t\text{ = }\frac{-23\pm\sqrt[]{(23)^2\text{ - 4}\cdot\text{ }}(-16)\text{ x (-8)}}{2(-16)} \\ t\text{ = }\frac{-23\pm\sqrt[]{529\text{ - 512}}}{-32} \\ t\text{ = }\frac{-23\pm\sqrt[]{17}}{-32} \\ \text{t = -23+}\frac{\sqrt[]{17}}{-32}\text{ or -23-}\frac{\sqrt[]{17}}{-32} \\ t\text{ = -23 }+\text{ 4.12/-32 or t = }\frac{-23\text{ - 4.12}}{-32} \\ t\text{ = }0.59\text{ seconds or t =0.85 seconds} \end{gathered}[/tex]Therefore, t = 0.59 seconds or t = 0.85 seconds
•is this function linear? •what’s the pattern in the table•what would be a equation that represents the function
Answers
Given data:
The given table.
The given function can be express as,
[tex]\begin{gathered} y-0=\frac{2-0}{1-0}(x-0) \\ y=2x \end{gathered}[/tex]As the equation of the above function is in the form of y=2x, it is linear function because for single value of x we got single value of y.
Thus, the function can be express as y=2x form which is linear function.
Drag the correct algebraic representation of the reflection to the white box
Answers
Question 1
When any point (x,y) is reflected over the x-axis, the reflection coordinate is (x,-y).
So, the x coordinate remains the same, and the y coordinate goes negative.
A = ( -6, 6 ) → A' = (-6,-6 )
B = (-2,6 ) → B' = (-2,-6)
C= (-6,1 ) → C' = (-6,- 1)
Algebraic representation: ( x, -y )
The slope of the line containing the points (-2, 3) and (-3, 1) is
Answers
Hey :)
[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]
Apply the little slope equation. By doing that successfully, we should get our correct slope.
[tex]\large\boldsymbol{\frac{y2-y1}{x2-x1}}[/tex]
[tex]\large\boldsymbol{\frac{1-3}{-3-(-2)}}[/tex]
[tex]\large\boldsymbol{\frac{-2}{-3+2}}[/tex]
[tex]\large\boldsymbol{\frac{-2}{-1}}[/tex]
[tex]\large\boldsymbol{-2}}[/tex]
So, the calculations showed that the slope is -2. I hope i could provide a good explanation and a correct answer to you. Thank you for taking the time to read my answer.
here for further service,
silennia[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]
Use the drawing tools to the graph the solution to this system of inequalities on the coordinate plane.
y> 2x + 4
x+y≤6
Answers
The solution to the system of inequalities y> 2x + 4 , x+y≤6 on the coordinate plane is shown below .
in the question ,
the system of inequality is given
y> 2x + 4
x+y≤6
to plot these inequalities on the coordinate plane ,we need to find the intercepts of both.
y>2x+4
put x = 0 we get y as 4 , (0,4)
put y = 0 we get x as -2 ,(-2,0)
x+y≤6
put x = 0 , we get y as 6 , (0,6)
put y = 0 , we get x as 6 , (6,0)
the solution of both the inequality is shown below .
Therefore , the solution to the system of inequalities y> 2x + 4 , x+y≤6 on the coordinate plane is shown below .
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Professor Ahmad Shaoki please help me! The length of each side of a square is extended 5 in. The area of the resulting square is 64 in,2 Find the length of a side of the
original square. Help me! From: Jessie
Answers
The length of the original square must be equal to 3 inches.
Length of the Original SquareTo find the length of the original square, we have to first assume the unknown length is equal x and then use formula of area of a square to determine it's length.
Since the new length is stretched by 5in, the new length would be.
[tex]l = (x + 5)in[/tex]
The area of a square is given as
[tex]A = l^2[/tex]
But the area is equal 64 squared inches; let's use substitute the value of l into the equation above.
[tex]A = l^2\\l = x + 5\\A = 64\\64 = (x+5)^2\\64 = x^2 + 10x + 25\\x^2 + 10x - 39 = 0\\[/tex]
Solving the quadratic equation above;
[tex]x^2 + 10x - 39 = 0\\x = 3 or x = -13[/tex]
Taking the positive root only, x = 3.
The side length of the original square is equal to 3 inches.
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Find the x- and y-intercepts for the following equation. Then use the intercepts to graph the equation.
4x + 2y = 8
Answers
Answer:
Step-by-step explanation:
x int=2
y int=4
graph 2,0 and 0,4 as two points
help ! it may or may not have multiple answers
Answers
From the given problem, there are 3 computer labs and each lab has "s" computer stations.
So the total number of computers is :
[tex]3\times s=3s[/tex]Mr. Baxter is ordering a new keyboard and a mouse for each computer, since the cost of a keyboard is $13.50 and the cost of a mouse is $6.50.
Each computer has 1 keyboard and 1 mouse, so the total cost needed for 1 computer is :
[tex]\$13.50+\$6.50[/tex]Since you now have the cost for 1 computer, multiply this to the total number of computers which is 3s to get the total cost needed by Mr. Brax :
[tex]3s\times(13.50+6.50)[/tex]Using distributive property :
[tex]a(b+c)=(ab+ac)[/tex]Distribute s inside the parenthesis :
[tex]3(13.50s+6.50s)[/tex]One answer is 1st Option 3(13.50s + 6.50s)
Simplifying the expression further :
[tex]\begin{gathered} 3(13.50s+6.50s) \\ =3(20.00s) \end{gathered}[/tex]Another answer is 4th Option 3(20.00s)
Find f(x) • g(x) if f(x) = x2 – 7 and g(x) = x2 + 3x + 7
Answers
Given the functions:
[tex]\begin{gathered} f(x)=x^2-7 \\ g(x)=x^2+3x+7 \end{gathered}[/tex]We will find: f(x) • g(x)
So, we will find the product of the functions
We will use the distributive property to get the result of the multiplications
So,
[tex]\begin{gathered} f\mleft(x\mright)•g\mleft(x\mright)=(x^2-7)\cdot(x^2+3x+7) \\ f\mleft(x\mright)•g\mleft(x\mright)=x^2\cdot(x^2+3x+7)-7\cdot(x^2+3x+7) \\ f\mleft(x\mright)•g\mleft(x\mright)=x^4+3x^3+7x^2-7x^2-21x-49 \\ f\mleft(x\mright)•g\mleft(x\mright)=x^4+3x^3-21x-49 \end{gathered}[/tex]so, the answer will be:
[tex]f\mleft(x\mright)•g\mleft(x\mright)=x^4+3x^3-21x-49[/tex]What type of number is - Choose all answers that apply:AWhole numberBIntegerRationalDIrratio
Answers
It is whole, integer, rational
2.) On the first night of a concert, Fish Ticket Outlet collected $67,200 on the sale of 1600 lawn
seats and 2400 reserved seats. On the second night, the outlet collected $73,200 by selling
2000 lawn seats and 2400 reserved seats. Solve the system of equations to determine the cost
of each type of seat.
Answers
Answer:
L=$15
R=$18
Step-by-step explanation:
i cant really explain the work
Find 8 3/4 ÷ 1 2/7. Write the answer in simplest form.
Answers
Problem: Find 8 3/4 ÷ 1 2/7. Write the answer in the simplest form.
Solution:
[tex](8+\frac{3}{4}\text{ )}\div(1\text{ + }\frac{2}{3})[/tex]this is equivalent to:
[tex](\frac{32+3}{4}\text{ )}\div(\text{ }\frac{3+2}{3})\text{ = }(\frac{35}{4}\text{ )}\div(\text{ }\frac{5}{3})\text{ }[/tex]Now, we do cross multiplication:
[tex]=(\frac{35}{4}\text{ )}\div(\text{ }\frac{5}{3})=\frac{35\text{ x 3}}{5\text{ x 4}}\text{ =}\frac{105}{20}[/tex]then, the correct answer would be:
[tex]=\frac{105}{20}[/tex]When we use function notation, f(x)=# is asking you to find the input when the output is the given number. We can also consider that an ordered pair can be written as (x,#). With this is mind, explain why f(x)=0 is special.
Answers
Notice that f(x)=0 is special because is the intercept of the graph with the x-axis and if f(x) corresponds to a function, the x-intercepts are the roots of the function.
The ordered pair can be written as (x,0), where x is such that f(x)=0.
According to the Florida Agency for Workforce, the monthly average number of unemployment claims in a certain county is given by () = 22.16^2 − 238.5 + 2005, where t is the number of years after 1990. a) During what years did the number of claims decrease? b) Find the relative extrema and interpret it.
Answers
SOLUTION
(a) Now from the question, we want to find during what years the number of claims decrease. Let us make the graph of the function to help us answer this
[tex]N(t)=22.16^2-238.5t+2005[/tex]We have
From the graph above, we can see that the function decreased at between x = 0 to x = 5.381
Hence the number of claims decreased between 1990 to 1995, that is 1990, 1991, 1992, 1993, 1994 and 1995
Note that 1990 was taken as zero
(b) The relative extrema from the graph is at 5.381, which represents 1995.
Hence the interpretation is that it is at 1995 that the minimum number of claims is approximately 1363.
Note that 1363 is approximately the y-value 1363.278