Answer:
18 is it
Step-by-step explanation:
Which expressions are equivalent to the given complex number? 45 + 2i A. (2 + 8i) + 2(9 + 6i)(1 - i) B. (9 + 4i) + 2(4 + 7i)(1 - 2i) C. (13 + 4i) + 2(7 + 2i)(2 - i) D. (2 + 8i) + (30 - 6i) E. (9 + 4i) + (36 - 2i) F. (13 + 4i) + (32 - 6i)
The expressions which are equivalent to the complex number 45 + 2i is E. (9 + 4i) + (36 - 2i)
D. (2 + 8i) + (30 - 6i)
To determine which expressions are equivalent to the complex number 45 + 2i, we can simplify each expression and check if it matches the given number.
Let's evaluate each option:
A. (2 + 8i) + 2(9 + 6i)(1 - i) = 2 + 8i + 2(9 + 6i - 9i - 6i^2) = 2 + 8i + 2(9 + 6i - 9i + 6) = 2 + 8i + 2(15 - 3i) = 2 + 8i + 30 - 6i = 32 + 2i
B. (9 + 4i) + 2(4 + 7i)(1 - 2i) = 9 + 4i + 2(4 + 7i - 8i - 14i^2) = 9 + 4i + 2(4 + 7i - 8i + 14) = 9 + 4i + 2(23 - i) = 9 + 4i + 46 - 2i = 55 + 2i
C. (13 + 4i) + 2(7 + 2i)(2 - i) = 13 + 4i + 2(7 + 2i - 14i - 4i^2) = 13 + 4i + 2(7 + 2i - 14i + 4) = 13 + 4i + 2(24 - 12i) = 13 + 4i + 48 - 24i = 61 - 20i
D. (2 + 8i) + (30 - 6i) = 2 + 8i + 30 - 6i = 32 + 2i
E. (9 + 4i) + (36 - 2i) = 9 + 4i + 36 - 2i = 45 + 2i
F. (13 + 4i) + (32 - 6i) = 13 + 4i + 32 - 6i = 45 - 2i
From the evaluations above, we can see that options E and D are equivalent to the given complex number 45 + 2i.
The correct options are:
E. (9 + 4i) + (36 - 2i)
D. (2 + 8i) + (30 - 6i)
For more such questions on complex number
https://brainly.com/question/29747482
#SPJ8
The expressions that are equivalent to the given complex number 45 + 2i are: (9 + 4i) + (36 - 2i) and (2 + 8i) + (30 - 6i).
Thus, option (D) and (E) are correct.
Given complex number 45 + 2i.
A. (2 + 8i) + 2(9 + 6i)(1 - i)
Simplifying: (2 + 8i) + 2(9 + 6i - 9i - 6)
= (2 + 8i) + 2(3 + 3i)
= 2 + 8i + 6 + 6i
= 8 + 14i
B. (9 + 4i) + 2(4 + 7i)(1 - 2i)
Simplifying: (9 + 4i) + 2(4 + 7i - 8i - 14)
= (9 + 4i) + 2(-10 - i)
= 9 + 4i - 20 - 2i
= -11 + 2i
C. (13 + 4i) + 2(7 + 2i)(2 - i)
Simplifying: (13 + 4i) + 2(14 + 4i - 7i - 2)
= (13 + 4i) + 2(12 - 3i)
= 13 + 4i + 24 - 6i
= 37 - 2i
D. (2 + 8i) + (30 - 6i)
Simplifying: 2 + 8i + 30 - 6i
= 32 + 2i
E. (9 + 4i) + (36 - 2i)
Simplifying: 9 + 4i + 36 - 2i
= 45 + 2i
F. (13 + 4i) + (32 - 6i)
Simplifying: 13 + 4i + 32 - 6i
= 45 - 2i
Thus, option (D) and (E) are correct.
Learn more about Complex number here:
https://brainly.com/question/20566728
#SPJ6
HELP ASAP PLEASE WILL MARK BRAINIEST
Answer:
Step-by-step explanation:
the first one
Answer:
Its the first one W'Z||X'Y'
Step-by-step explanation:
The translation is just upwards meaning the points dont move other then the Y changing, the original has WZ parallel to XY so having it translated up will still have it be parallel
Find the equation of the line that runs through the points (1, 2) and (4, -1).
Answer:
y+1 = -(x-4)
Step-by-step explanation:
find slope: (-1-2)/(4-1) = -1
y+1 = -(x-4)
What is the rotation of triangle ABC? B 3. C
k=1/3 and k=3/2 which line would be steeper
Answer:
k = 3/2
Step-by-step explanation:
assuming k is your slope
rise/run = y/x
k = 1/3 therefore, (3,1) is your (x,y) points
k=3/2 therefore, (2,3) is your (x,y) points
as you can see, you move 2 more units up on the y-axis with k =3/2. Therefore, it is steeper.
A backpack is on sale for 30% off. If the sale price is $15.75, what is the original price to the nearest cent?
Answer:
$22.50
Step-by-step explanation:
As it is 30% off, $15.75 is 70% of the full price. You can then divide 15.75 by 70 [= 0.225] to get 1% of the full price. Multiply 0.225 by 100 to get the full price. 0.225 x 100 = 22.5
We can check that this answer is correct by multiplying 22.50 by 0.7. If you get 15.75 you know the answer is correct as 15.75 is 70% of the full price.
Whats the answer for number 3?
Answer:
B. There are no discounts or charges per month.
Step-by-step explanation:
Hope this helps. Pls give brainliest.
Janet has 7 albums. She divides 42 pictures evenly between the albums, Which expression helps us find out how many pictures are in each album? Choose 1 answer:
Answer:
6 check how I did to understand it
Step-by-step explanation:
42:7=6
6.
Solve the equation *x + 3 ={x +3
Answer:
x=4
Step-by-step explanation:
Vanessa has 23 coins in nickels and dimes and has $1.50 in all. Which equation could
be used to find the number of
nickels, n?
A. 5n + 10 (23) = 1.50
B.5n + 10 (23 – n) = 1.50
C. 0.05%+0.10 (23 – 1) = 1.50
D. 0.05m+0.10 (m - 23) = 1.50
Answer:
a
Step-by-step explanation:
what is the value of Z in degrees, in the figure shown?
Answer: 69.2
Step-by-step explanation:
What is ⅓ divided by ¼? Use the model if needed. Answer should be in simplest form. Explain your answer
Answer:
The answer to the expression in simplest form is:
[tex]\frac{\frac{1}{3}}{\frac{1}{4}}=\frac{4}{3}[/tex]
Step-by-step explanation:
Given the function
[tex]\frac{\frac{1}{3}}{\frac{1}{4}}[/tex]
solving to get the simplest form
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}[/tex]
[tex]\frac{\frac{1}{3}}{\frac{1}{4}}=\frac{1\cdot \:4}{3\cdot \:1}[/tex]
[tex]\mathrm{Apply\:rule}\:a\cdot 1=a[/tex]
[tex]=\frac{4}{3}[/tex]
Thus, the answer to the expression in simplest form is:
[tex]\frac{\frac{1}{3}}{\frac{1}{4}}=\frac{4}{3}[/tex]
Find the equation of the line that is perpendicular to Y= -2/3x and contains the point (4,-8)
Answer:
Y=-3/5x
Step-by-step explanation:
Answer:
y = 3/2x -14
Step-by-step explanation:
y = -2/3 x
has a slope of -2/3
We want a line perpendicular
Take the negative reciprocal to find the slope
- (1 / -2/3)
3/2
The slope of a line perpendicular is 3/2
Using the slope intercept form of a line
y = mx+b where m is the slope and b is the y intercept
y = 3/2x +b
Substitute a point into the equation
-8 = 3/2(4) +b
-8= 6+b
Subtract 6 from each side
-8-6 = b
y = 3/2x -14
Find the slope that passes through (-1, -3) and (-2, 2).
A
-5
С
-2
B
-1/5
D
1/3
Answer:
A.-5
Step-by-step explanation:
I have used an online calculator to check my answer against so this answer is 100% correct. I used "Slope Calculator" by Omni.
PLEASAE MARK BRAINLIEST
Find the value of x (Round to the nearest tenth)
Help plssssssssss
Answer:
bbhwhehwyayyquqysyegegegsgsgsgsusus
Step-by-step explanation:
vgsgahah z z zb
perpendicular to the line 4x - 6y + 7 = 0 , passing through (3, 4) .
Answer:
The equation of line perpendicular to given line passing through (3,4) is:
[tex]y = -\frac{3}{2}x+\frac{17}{2}[/tex]
Step-by-step explanation:
Given equation of line is:
[tex]4x - 6y + 7 = 0[/tex]
Given equation is in standard form. It has to be converted into slope-intercept form to extract slope from the equation.
So,
[tex]4x+7 = 6y\\6y=4x+7\\\frac{6y}{6} = \frac{4x+7}{6}\\y = \frac{4}{6}x+\frac{7}{6}\\y=\frac{2}{3}x+\frac{7}{6}[/tex]
The standard form of slope-intercept form of equation is:
[tex]y=mx+b[/tex]
Here, the co-efficient of x is the slope of the line.
So the slope of given line is: 2/3
m = 2/3
The product of slopes of two perpendicular lines is -1
Let m1 be the slope of line perpendicular to given line
Then
[tex]m.m_1 = -1\\\frac{2}{3} . m_1 = -1\\m_1 = -1*\frac{3}{2}\\m_1 = -\frac{3}{2}[/tex]
The equation of perpendicular will be:
[tex]y = m_1x+b[/tex]
Putting the value of slope
[tex]y = -\frac{3}{2}x+b[/tex]
To find the value of b, putting (3,4) in the equation
[tex]4 = -\frac{3}{2}(3)+b\\4 = -\frac{9}{2}+b\\b = 4+\frac{9}{2}\\b= \frac{8+9}{2}\\b=\frac{17}{2}[/tex]
So the equation of line perpendicular to given line passing through (3,4) is:
[tex]y = -\frac{3}{2}x+\frac{17}{2}[/tex]
At a department store kendra has a debt greater than $25.00 which could be kendras balance? A-$32.00 B-$22.00 C -$19.00 D-$11.00
Answer: A
Step-by-step explanation: 22.00, 19.00 and 11.00 are all less than 25. $32.00 is the only logical explanation.
Answer:
A. -$32.00
Step-by-step explanation:
This is because it is a greater debt than 25 and all the other choices are greater than $25.
Whats the answer to number 9?
Answer:
B and D
Step-by-step explanation:
Because only those two equations on the graphs are straight. and are increasing or decreasing in a constant pace.
A kite string is 220 feet in length. It makes a 450 angle with the ground. How high is the kite off of the ground?
Sasha is selling t-shirts. She uses the function f(x) = 2x + 8 to determine her sales, where
x represents the number of shirts and f(x) represents the sales in dollars. What would
her sales be if she sells 24 t-shirts?
Answer:
f(x)=56
Step-by-step explanation:
2(24)+8=56
I need to know the minus 2 ounces
Answer:
Step-by-step explanation:
10 is your answer
A) What are the coordinates of the image of vertex G after a reflection across the line y = x?
B) What is the rule when reflecting across the line y = x
Answer:
b. (-5, 4)
Step-by-step explanation:
edge2020
find the value of the question
Answer:
0
Step-by-step explanation:
3x^2−18x+12=0 by completing the square
Answer:
mark me brailist if it helped
my and Stephanie were playing a number game. Amy picked a number and told Stephanie that if she added 8 to the number and multiplied the sum by 3, it would equal 9. Which equation could Stephanie use to find the number, x?
A.
3 + (x + 8) = 9
B.
8(x + 3) = 9
C.
3(x + 8) = 9
D.
3(x) + 8 = 9
The fourth graders are going on a field trip to the Zoo. There are 83 students in the fourth grade. If tickets cost $26 each, how much will the field trip cost?
Answer:
Total trip cost = $2,158
Step-by-step explanation:
Given:
Cost of each ticket = $26
Number of student = 83
Find:
Total trip cost
Computation:
Total trip cost = Cost of each ticket x Number of student
Total trip cost = $26 x 83
Total trip cost = $2,158
A bag has 7 red marbles, 8 blue marbles and 5 purple marbles
Answer:
you didnt put anything like the full question but it equals 20
Step-by-step explanation:
so yea 2000
What's on your Christmas List? Santas Listening~
Step-by-step explanation:
ps5
gaming pc
and many more
divisible rules what is divisible by 4518
Answer:
where are the options
Step-by-step explanation:
Michelle ran 3,168 meters at a constant speed over 11 minutes. What was Michelle's pace?
A.
288 meters per minute
B.
864 meters per minute
C.
290 meters per minute
D.
11 meters per minute