The reciprocal of the complex number 8-3i is found by dividing its complex conjugate (8+3i) by the modulus squared of 8-3i, which is 73. The result is 8/73 + 3i/73.
Explanation:The reciprocal of a complex number is the complex conjugate of that number divided by the modulus squared of the original number. In the case of the complex number 8-3i, its complex conjugate is 8+3i. To find the reciprocal of 8-3i, you would divide this complex conjugate by the modulus squared of 8-3i.
First, calculate the modulus squared of 8-3i:
Modulus of 8-3i = sqrt(82 + (-3)2) = sqrt(64 + 9) = sqrt(73).Modulus squared = (sqrt(73))2 = 73.Then, divide the complex conjugate by this modulus squared to get the reciprocal:
Reciprocal of 8-3i = (8+3i) / 73 = 8/73 + 3i/73.
The volume of a rectangular prism varies jointly with the length and width of the figure when the height remains constant. The volume of a rectangular prism is 672 cubic centimeters. The figure has a length of 8 centimeters and a width of 14 centimeters. A second prism has a length of 12 centimeters and a width of 8 centimeters. What is the volume of the second prism? 576 cubic centimeters 768 cubic centimeters 784 cubic centimeters 1,344 cubic centimeters
1st Prism = 8*14 = 112
672/112 = 6
2nd prism = 8*12=96
96*6 = 576 cubic cm
answer is 576 cubic centimeters
Answer:
The correct option is 1.
Step-by-step explanation:
The volume of a rectangular prism varies jointly with the length and width of the figure when the height remains constant.
Let the height of both rectangular prism be h cm.
The volume of a prism is
[tex]V=l\times b\times h[/tex]
Where, l is length, b is breadth or width and h is height.
The volume of a rectangular prism is 672 cubic centimeters. The figure has a length of 8 centimeters and a width of 14 centimeters.
[tex]672=8\times 14\times h[/tex]
[tex]672=112h[/tex]
Divide both sides by 112.
[tex]\frac{672}{112}=h[/tex]
[tex]6=h[/tex]
The value of h is 6 cm. It means the height of both prism is 6 cm.
A second prism has a length of 12 centimeters and a width of 8 centimeters. So, the volume of second prism is
[tex]V=12 \times 8\times 6[/tex]
[tex]V=576[/tex]
The volume of second prism is 576 cubic centimeters. Therefore the correct option is 1.
Mind helping a brother here! 20 points! Thanks!
y = 7x - 53 y = -4x + 35 a. ( -3, -8) c. ( -8, 3) b. ( 8, 3) d. No solution
Gina mixed paint to make her favorite shade of purple. She filled up one third of the container with red paint. Then she filled the remaining space with 4 Liters of blue paint.How many milliliters of paint did Gina mix
Need help fast!
The table shows the relationship between the number of drops of food color added to different number of cups of cake frosting. Look at the first picture.
Which point below shows an equivalent ratio in this situation? Look at the second picture.
A. Point B, because if cups of frosting are 50, then drops of food coloring will be 200
B. Point B, because if drops of food coloring are 50, then cups of frosting will be 200
C. Point J, because if cups of frosting are 40, then drops of food coloring will be 10
D. Point J, because if drops of food coloring are 40, then cups of frosting will be 10
Answer:
Option A. will be the answer.
Step-by-step explanation:
From the given table we will find the relation first and the we will try to find the point with the same relation in the graph.
From the given table ratio of Cups of frosting and Drops of food color is = [tex]\frac{\text{Cups of frosting}}{\text{Drops of food color}}[/tex]
= [tex]\frac{2}{8}[/tex]
= [tex]\frac{1}{4}[/tex]
Or 1 : 4
Now the point B shows the ratio between food color and frosting = [tex]\frac{\text{Cups of frosting}}{\text{Drops of food color}}[/tex]
= [tex]\frac{\text{x-coordinates}}{\text{y-coordinates}}[/tex]
= [tex]\frac{50}{200}[/tex]
= [tex]\frac{1}{4}[/tex]
The same ratio 1 : 4
Option A. will be the answer.
How many times bigger is a metric ton than a kilogram?
literal equations, please help! this one is confusing to me.
Help please! In the figure line a and line b are parallel based on the figure match each given angle with its congruent angles
Answer: copy the guy on top of me but the last one for PLATO users is <3,<6,<2 is angles congruent to <7
Step-by-step explanation: bec I said so
the answers are
A. 15
B. 14
C. 16
D. 19
Factor out the greatest common factor of 5ab^2+10ab
Answer: 5ab
Step-by-step explanation:
The given polynomial : [tex]5ab^2+10ab[/tex]
The prime factorization of [tex]5ab^2= 5\times a\times b\times b[/tex]
The prime factorization of [tex]10ab= 5\times2\times a\times b[/tex]
We can see that the greatest common factor of [tex]5ab^2\text{ and }10ab[/tex] is [tex]5\times a\times b[/tex]
Hence, the greatest common factor of [tex]5ab^2+10ab[/tex] = 5ab
Bret is starting a business selling handmade necklaces. He has decided to invest and initial amount of $387 for advertising and materials cost seven dollars for each necklace he makes. Bret can sell his creations for $10 per necklace.once he makes and sells a certain number of necklaces he will break even with identical expenses and sales. How many necklaces would that take? What would the total expenses and sales be then?
To break even, Bret would need to make and sell 40 necklaces, with a total expense of $15,760 and total sales of $400.
Explanation:To determine the number of necklaces Bret needs to make and sell to break even, we need to consider his initial investment and the expenses and sales associated with each necklace.
First, let's calculate the total expenses for each necklace: $7 (materials cost) + $387 (initial investment) = $394.
Next, let's calculate the total sales for each necklace: $10 (selling price).
To break even, the total expenses and total sales need to be equal.
Let n represent the number of necklaces:
Total expenses = $394 * n
Total sales = $10 * n
Setting the two equations equal to each other, we have: $394 * n = $10 * n.
Now, let's solve for n:
$394 * n = $10 * n
$394 = $10
n = 394 / 10
n = 39.4
Since we cannot sell a fraction of a necklace, Bret would need to make and sell 40 necklaces to break even.
The total expenses for 40 necklaces would be $394 * 40 = $15,760, and the total sales would be $10 * 40 = $400.
What is the range of the function y=2sin x
Answer:
Range: [-2, 2] {y | -2 ≤ y ≤ 2}
Step-by-step explanation:
The given function is y = 2sinx
We have to find the range of the given function.
Since at y-axis sine function has the variance between -1 to 1 so range of y = sinx is [-1, 1]
and if the amplitude of sine function is 2 then sine function will vary from -2 to 2 which implies that range of y = 2 sinx will be [-2, 2]
So range of y = 2sinx is [-2, 2]
The range of the function y=2sin x is mathematically given as
dy=(-2,2)
What is the range of the function y=2sin x?Question Parameter(s):
function y=2sin x
Generally, the equation for the wave is mathematically given as
[tex]y(x,t)=Asin(kx−wt+\phi)[/tex]
Therefore, Comparing both equations
y(x,t)=Asin(kx−wt+\phi)
y=2sin x
We have
A=2
In conclusion, The range of a function y=2sin x is simply defined as the probable outcomes, with x values as independent factors.
Hence, with sinx having min and max values at (-1,1)
The y value range will be
dy=(2(-1),2(1))
dy=(-2,2)
Read more about Wave
https://brainly.com/question/23271222
Given the parent function of f(x) = x3, what is the value of k in the translated graph of f(x − h) + k?
we have
[tex]f(x)=x^{3}[/tex]
we know that
The point [tex](0,0)[/tex] in the graph of f(x) is the point [tex](3,2)[/tex] in the translated graph
so
The rule of the translation is
[tex](x,y)----> (x+3,y+2)[/tex]
That means
The translation is [tex]3[/tex] units to the right and [tex]2[/tex] units up
The equation of the translated graph is equal to
[tex]f(x)=(x-3)^{3}+2[/tex]
therefore
The answer is
the value of k is equal to
[tex]k=2[/tex]
see the attached figure to better understand the problem
Answer:
k=2
Step-by-step explanation:
I just did the assignment
Which function below has the following domain and range?
Domain:
{−9,−5,2,6,10}
Range:
{−2,0,8}
Select one:
a.
{(−2,−5),(8,10),(0,6),(−2,−9),(0,2)}
{(−2,−5),(8,10),(0,6),(−2,−9),(0,2)}
b.
{(−9,10),(−2,8)}
{(−9,10),(−2,8)}
c.
{(−9,−2),(−5,0),(2,8),(6,5),(10,9)}
{(−9,−2),(−5,0),(2,8),(6,5),(10,9)}
d.
{(2,0),(−5,−2),(10,8),(6,0),(−9,−2)}
{(2,0),(−5,−2),(10,8),(6,0),(−9,−2)}
Answer:
The correct option is d.
Step-by-step explanation:
Domain is the set of all possible inputs or the values of x and the range is value of output or y.
In option a,
The given function is
{(−2,−5),(8,10),(0,6),(−2,−9),(0,2)}
Domain = {-2,0,8}
Range = {-9,-5,2,6,10}
Therefore option a is incorrect.
In option b,
The given function is
{(−9,10),(−2,8)}
Domain = {-9,-2}
Range = {8,10}
Therefore option b is incorrect.
In option c,
The given function is
{(−9,−2),(−5,0),(2,8),(6,5),(10,9)}
Domain = {-9,-5,2,6,10}
Range = {-2,0,5,8,9}
Therefore option c is incorrect.
In option d,
The given function is
{(2,0),(−5,−2),(10,8),(6,0),(−9,−2)}
Domain = {-9,-5,2,6,10}
Range = {-2,0,8}
Therefore option d is correct.
The process of moving a figure to a different location is called:
mapping.
transformation.
isometry.
None of the choices are correct.
About 15% of the population of a large country is allergic to pollenallergic to pollen. if two people are randomly selected, what is the probability both are allergic to pollen? what is the probability at least one is allergic to pollenallergic to pollen?
Answer:
(a) 0.0225
(b) 0.225
Step-by-step explanation:
It is given that 15% of total population is allergic to pollenallergic to pollen.
Thus, Probability of an individual s/he has allergy is 0.15
Thus, The probability that two person is selected and both has allergy is 0.15 × 0.15 = 0.0225
And the Probability that at least one person is suffered from allergy from that two person = P(allergic and non-allergic) + P(non-allergic and allergic)
⇒ 0.15 × (1 - 0.15) + (1 - 0.15) × 0.15
⇒ 0.15 × 0.85 + 0.85 × 0.15 = 0.225
In a computer game, when choosing a character there are 5 choices for hair style, 3 choices for eye color, and 7 choices for outfits. How many different characters are possible if you were to choose 1 hair style, 1 eye color, and 1 outfit?
105
140
22
15
Which of the following indicates that the roots of a quadratic are irrational
a) discriminant is zero
b) discriminant is negative
c) discriminant is rational
d) discriminant is prime
f(x)=5x^2 + 9x-4 g(x)= -8x^2-3x-4 find (f+g)(x)
7x1,000,000+
3x100,000+
5x10,000+
6x1.00+
2x100+3x10+7+1
The perimeter of a rectangular field is 376 yards. if the width of the field is 89 yards, what is its length?
Answer:
Step-by-step explanation:
The length of the field will be calculated as:
P=2(L+W)
P=376
W=89
thus substituting the values in the equation we get;
376=2(L+89)
376/2=(L+89)
solving for L;
188=L+89
L=188-89
L=99 yards
therefore the length is 99 yards
Misha’s family bought a large cattle farm. The number of acres of the cattle farm is the cube of the acres they used to own plus 10 acres. If a represents the number of acres the family used to own, which expression represents the number of acres they own now?
When positive integer x is divided by 11, the quotient is y and the remainder is 4. when 2x is divided by 8, the quotient is 3y and the remainder is 2. what is the value of 13y – x ?
By the empirical rule, what percentage of the area under the normal curve lies to the left of mu, the average? put your answer as a percentage.
Which relationship is always true for the angles x, y, and z of triangle MNP?
A. x + z = y
B. y + z = x
C. x + y + z = 180 degrees
D. x + y + z = 90 degree
-the answer would be C: "x+y+z= 180 degrees"
-and here is proof so you know you won't get the answer wrong
- hope you do good on your test, have a good day :)
Evaluate the function rule to find the range of each function for the domain {-3, 0, 5}. f(x) = x² − 6x + 4
A. {-5, -4, -1}
B. {-5, -1, 4}
C. {-1, 4, 31}
D. {4, 31, 59}
Please I beg of you!
the discriminant of a quadratic equation is negative. one solution is 2+3i. what is the other solution?
Answer:
2-3i
Step-by-step explanation:
Factor the following.
If an eagle and a bumblebee are traveling at 8 km/hr, which has more momentum explain
The speed of light is about nine hundred eighty million feet per second. What is that speed in scientific notation?
Answer:
The answer is 9.8*10^8
i think
Step-by-step explanation: