Given:
[tex]\dfrac{5}{6+2i}[/tex]
To find:
The quotient in the form a + bi.
Solution:
We have,
[tex]\dfrac{5}{6+2i}[/tex]
Multiply numerator and denominator by 6-2i.
[tex]=\dfrac{5\times (6-2i)}{(6+2i)\times (6-2i)}[/tex]
[tex]=\dfrac{5(6)+5(-2i)}{6^2+(2i)^2}[/tex]
[tex]=\dfrac{30-10i}{36+4i^2}[/tex]
[tex]=\dfrac{30-10i}{36+4(-1)}[/tex] [tex][\because i^2=-1][/tex]
On further simplification, we get
[tex]=\dfrac{30-10i}{36-4}[/tex]
[tex]=\dfrac{30-10i}{32}[/tex]
[tex]=\dfrac{30}{32}-\dfrac{10i}{32}[/tex]
[tex]=\dfrac{15}{16}+(-\dfrac{5}{16})i[/tex]
Therefore, the form a+bi is [tex]\dfrac{15}{16}+(-\dfrac{5}{16})i[/tex], where, [tex]a=\dfrac{15}{16}[/tex] and [tex]b=(-\dfrac{5}{16})[/tex].
John has $190 in his savings account. He earns 10% in interest per year.
What will John’s saving account balance be at the end of the year?
Answer:
1,900
Step-by-step explanation:
Need help due in a few minutes. Plzzzzzz
Answer:
7 seconds
Step-by-step explanation:
set the equation to 0 because the water is the 0 point, and solve, you will get 7 and -5. It is not possible to have negative seconds so 7
Solve: |11x + 10| = 22
To solve the equation |11x + 10| = 22, we need to consider two cases: one where the expression inside the absolute value is positive and one where it is negative.
Case 1: (11x + 10) is positive:
In this case, the equation becomes 11x + 10 = 22. Solving for x, we subtract 10 from both sides, resulting in 11x = 12. Dividing by 11 gives x = 12/11.
Case 2: (11x + 10) is negative:
Here, the equation becomes -(11x + 10) = 22. Simplifying, we have -11x - 10 = 22. Adding 10 to both sides gives -11x = 32. Dividing by -11 yields x = -32/11.
Thus, the solution set for the given equation is x = 12/11 and x = -32/11, representing the two possible values of x that satisfy the equation |11x + 10| = 22.
For more such questions on equation
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what is the x-coordinate of R' ?
Answer:
3
Step-by-step explanation:
Answer:
12
The x-axis is the horizontal one. The full coordinate is (12, 0), which the x-coordinate (or x-intercept) is 12.
Eva paid $16 for some notebooks and a backpack . She paid $1.25 for 5 notebooks.how much did she pay for her backpack ?write the equation
Answer:
10 dollars ALSO CAN SOMEONE PLEASE ANSWER MY QUESTION
Step-by-step explanation:
1.25 times 5=6
16-6=10
Answer:
$9.75
Step-by-step explanation:
Notebooks - $1.25 each
Number of notebooks bought - 5
Total money spent - $16
5 * 1.25 = 6.25
16 - 6.25 = 9.75
$9.75
solve 2x^2+9x-7=0
Give your solutions correct to 3 significant figures.
Answer:
X = -1 or X = -3.5
Step-by-step explanation:
2x^2 + 9x + 7 = 0
ac = 14
b = 9
find a two numbers which when you multiply you get 14 and add you get 9.
so it will 2 and 7. (they replace b which is 9x)
therefore: 2x^2 + 2x + 7x + 7 = 0
find common factors using each 2 from the four.
2x( x + 1) + 7 (x+1) = 0
so it will be (2x + 7) (x+1) = 0
find x,
i) 2x +7 = 0
x= -3.5
ii) x + 1 = 0
x = -1
Whoever helps gets BRAINLIEST
The answer D. 275
Hope this helps :)
Help please your guys are smart
help plz i rely need help with this question
Answer:
It gets smaller which is B
Step-by-step explanation:
multiplying by a number less than 1 will make a fraction smaller like 1/2 (4) which is basilcally asking ou half of 4 which makes the final answer smaller.
2. If f(x) = 2(x - 3)2 find f(-8).
Answer:
-44
Step-by-step explanation:
help> ?????? pleaes asdfdfffffffff
Answer:
37.9701
Step-by-step explanation:
I only know the first one?? I'm really sorry cacsknak ik i said id help, but :( it's hard, and i never learned how to do the bottom two.
Whats The Answer Marking Brainliest, Please explain your answer:D...
.
Answer:
C. 12x
Each box has 12 envelopes.
The number of total envelopes will be the number of envelopes in a box multiplied by the number of boxes. The number of boxes is unknown, so it is replaced by the variable. This gives us 12x
The clock below shows what time mason mom drops him off for practice . what time did mason mom drop him off
Answer:
where is the clock?
Step-by-step explanation:
simplify 6(2x + 4) – 2x + 15 – y
Please help me on this one I'm tripping on it.
Answer:
10x + 39 - y
Step-by-step explanation:
Answer:
10x - y +39
Step-by-step explanation:
2. Use the distributive property to evaluate the expression.
A) 4(x-2)
B) 3(y+9)
C) -2(3-r)
Answer:
a) 4x-8
b) 3y + 27
c) -6 + 2r
Step-by-step explanation:
Here, we want to use the distributive property to evaluate the given expressions
Mathematically, the distributive property is;
(a + b) * c = (a * c) + (b * c)
So we use this on each of our questions;
a) 4(x-2)
= (4 * x) - (4 * 2) = 4x-8
b) 3(y + 9)
= (3 * y) + (3 * 9)
= 3y + 27
c) -2(3-r)
= (-2 * 3) - (-2 * r)
= -6 + 2r
Which statement can help build a person’s self-esteem? A. I am really proud of you B. You really disappointed me with your presentation. C. You should strive to do better next time. D. Your work was lacking and uninspiring.
Answer:
A. I am really proud of you
Step-by-step explanation:
3. The sum of Ben and Jerry's ages are 47. Jerry is 9 years older than Ben How old are Ben
and Jerry?
(HELP ME!!!)
Answer:
Ben has 38 years older and jerry is 9 years old
Determine the quadrant point
Answer:
I think b
Step-by-step explanation:
Determine the intercepts of the line
Answer:
Step-by-step explanation:
y-intercept: (0 , 2.5)
x-intercept: (3.5 , 0)
you
are studying bacteria; the
population originally started with 6000
bacteria. After
28,000 cells.
a.) Find the exponential model (equation)
2 hours,
tiere
were
Cells expected after 4
b.) How
many
hours?
* algebra 2*
Answer:
I think it's b I hope I help
Pls help me ill give me brainliest
Do all 3 for brainliest pls
Write and solve an equation for seven less than fou
times a number is 29.
Jerry is purchasing books online. The books cost $65.00. There is a shipping and handling fee of 6%. How much will the books cost him including the shipping and handling fee?
Answer:
$68.9
Step-by-step explanation:
65*0.06 is 3.9
65+3.9 is 68.9
Hope this helps!
Merry Christmas!
solve each system of equation by elimination
{y=-x+1
{y= 4x-14
Answer:
(3, -2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = -x + 1
y = 4x - 14
Step 2: Rewrite Systems
y = 4x - 14
Multiply everything by -1: -y = -4x + 14Step 3: Redefine Systems
y = -x + 1
-y = -4x + 14
Step 4: Solve for x
Elimination
Combine equations: 0 = -5x + 15Isolate x term: -15 = -5xIsolate x: 3 = xRewrite: x = 3Step 5: Check
Define equation: y = -x + 1Substitute in x: y = -3 + 1Add: y = -2PLSSSS HELP END OF GRADING PERIOD IS TODAY
Answer:
18,750
Step-by-step explanation:
If you add up all of the expenses you get 18,750. I hope this helps!
Do you give brainliest?
what is the slope of the line that contains the points (-1,2) and (2,2)
Answer:
the equation to find the slope is (y2-y1)/(x2-x1)
the points are (-1,2) and (2,2) so plug it in and you get
(2-2)/(2-(-1))
0/ (2+1)
0/3
whenever the numerator is 0, that means the slope is 0. the line is just a horizontal line.
I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!!
Choose one of the following.
Parallel lines have ____________________.
A. one solution
B. 10 solutions
C. infinitely many solutions
D. no solution
D. no solution
Because they never found each other, the point they cross on is the solution.
Answer: D
Step-by-step explanation: it just is
what is 0.42 10 times as much?
Answer:
Answer is 4.2
Step-by-step explanation:
420 presents in 15 hours at this rate how many presents does Santa deliver in 5 hours
Answer:31500
Step-by-step explanation:hope it helps!
Answer:
140
Step-by-step explanation:
420/15=28
28x5=140
help plz :(((((((((((((
Answer: ITS A! I HAVE THE SAME TEST!
Step-by-step explanation: