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# Find the multiplicative inverse of 6 + 2i.

The solution to the problem is as follows:

First thing to do is get rid of the i. Multiplying by 6 - 2i will do this

( 6 + 2i)(6 - 2i) = 6^2 - (2i)^2 = 36 - 4(-1) = 36 + 4 = 40

Dividing by 40 gets you 1

(6 + 2i) (6-2i)/40 = 1

The answer is (6 - 2i)/40 = (3 - i)/20

I hope my answer has come to your help. God bless and have a nice day ahead!

## Related Questions

Posted in Mathematics

What is the range of the function f(x) = 3x2 + 6x – 9

I have a solution here however with a slight change in the equation:

f(x)=3x^2-6x+1

My solution is:

The domain is all real numbers--there are no restrictions like a square root or variable in the denominator

this is a U shape parabola and you want to find the bottom point, it is at the vertex

x=-b/2a =- (-6) /2 (3) =1
f(1) =3(1)^2 -6(1) +1 =3-6+1 =-2
the minimum is (1, -2)
so the range is all real numbers >= -2

By examining my solution, you could just answer the problem on your own! I hope it helps!

Posted in Mathematics

Solve the equation for y 2x+6y=13

So here is how we are going to solve for y for the given equation above:
2x+6y=13
Next, transfer 2x to the right side and it will look like this:
6y=13-2x
Now, divide both sides by 6, and it will look like this:
y=13-2x
--------
6
So, this is the final answer for y.

Posted in Mathematics

The price of a cup of coffee was $2.65 yesterday. today, the price fell to$2.50 . find the percentage decrease. round your answer to the nearest tenth of a percent.

We must find the difference between prices. $2.65 -$2.50 = $0.15. Now we need to calculate what percent$0.15 is of $2.65. It is 5.7%! The price decreased, so it is a 5.7% decrease! Posted in Mathematics What interval includes all possible values of x, where –3(6 – 2x) ≥ 4x + 12? (–∞, –3] [–3, ∞) (–∞, 15] [15, ∞) The solution to the problem is as follows: solve for x : −3(6−2x)≥4x+12 −18+6x≥4x+12 2x≥30 x≥15 So the answer is D ) 15 to +infinity I hope my answer has come to your help. God bless and have a nice day ahead! Posted in Mathematics Algebraic terms are separated by ______. Choose all that apply. 1)= 2)+ 3)x 4)÷ 5)- Answer 1)= 2)+ 5)- Explanation When letter or numbers are separated by multiplication or division can be combined to make one term. In an algebra equation, terms are separated by an addition sign, subtraction sign or an equal sign. For example, 3a + 7b = 21. This equation have 3 terms. ## Use our writing service to score better and meet your deadlines No matter what kind of academic paper you need, it is simple and secure to hire a writer for a price you can afford at StudyHawks. Save more time for yourself. Posted in Mathematics When simplified and written in standard form, which quadratic function is equivalent to the polynomial shown? 2 + 7c – 4c2 – 3c + 4 –4c2 + 4c + 6 –7c2 + 10c + 6 –4c2 + 4c + 8 –7c2 + 7c + 6 Answer: A) -4c^2 + 4c + 6 Step-by-step explanation: The given polynomial is 2 + 7c – 4c^2 – 3c + 4 Add the like terms. 2 + 4 + 7c - 3c -4c^2 = 6 + 4c - 4c^2 Write it in a standard form = -4c^2 + 4c + 6 Answer is A) -4c^2 + 4c + 6 Hope this will helpful. Thank you. Posted in Mathematics What is the ratio of the area of the inner square to the area of the outer square? (a−b)²+b²/a² a²−b²/a² (a−b)²/(a+b)² (ab)²/(a+b)² The answer is (a−b)²+b²/a² proof if A is the area of the inner squared, so A= c², and c²= (a−b)²+b² so the side of the outer must be a-b +b=a, its area is a² Posted in Mathematics Arrange the following polynomial into descending order for x, then interpret the degree of the 2nd term. 7x3y3 + 4 − 11x5y2 − 3x2y For the answer to the question above, the power of "y" doesn't influence descending order for x even if it is higher than power of x. Unordered polynomial is 7x3y3 + 4 - 11x5y2 - 3x2y Polynomial in descending order looks like this -11x5y2 + 7x3y3 - 3x2y + 4 Degree of the second term is 5 ( because of x5 ) Posted in Mathematics Which of the following is a factor of 2x4 + 22x3 + 60x2? 2x3 x4 x + 4 x + 5 The correct answer is Option D, or X+5. I hope I answered this question to your satisfaction Have a nice day! Posted in Mathematics The discriminant of a quadratic equation is negative. One solution is 3+4i . What is the other solution? A.4-3i B.3-4i C.4+3i D.-3+4i The way you stated the problem, there is an infinity of possibilities for the other solution. ► For instance, the quadratic equation: x² – (6 + 4i)x + (9 + 12i) = 0 has for discriminant: Δ = (6 + 4i)² – 4(9 + 12i) = 36 – 16 + 48i – 36 – 48i = -16 which is indeed negative. Its solutions will then be: x₁ = [(6 + 4i) + 4i]/2 = 3 + 4i x₂ = [(6 + 4i) – 4i]/2 = 3 And the other solution here is 3. ► If you are not convinced, the quadratic equation: x² – (6 + 5i)x + (5 + 15i) = 0 has for discriminant: Δ = (6 + 5i)² – 4(5 + 15i) = 36 – 25 + 60i – 20 – 60i = -9 which is indeed negative. Its solutions will then be: x₁ = [(6 + 5i) + 3i]/2 = 3 + 4i x₂ = [(6 + 5i) – 3i]/2 = 3 + i And the other solution here is 3+i. ► In fact, every quadratic equation of the form: x² – [6 + (4 + α)i]x + (3 + 4i)(3 + αi) = 0 where α is any real, has for discriminant: Δ = [6 + (4 + α)i]² – 4(3 + 4i)(3 + αi) = 36 – (4 + α)² + 12(4 + α)i – 36 + 16α – 12(4 + α)i = 16α – (4 + α)² = 16α – 16 – 8α – α² = -16 + 8α – α² = -(α – 4)² WILL be negative. Their solutions will then be: x₁ = [ [6 + (4 + α)i] – (α – 4)i ]/2 = 3 + 4i x₂ = [ [6 + (4 + α)i] + (α – 4)i ]/2 = 3 + αi And the other solution will then be is 3+αi. Since α can take any real value, you'll obtain an infinity of solutions of the form 3+αi. ► So conclusively: If the discriminant of a quadratic is negative AND one of the solutions is 3+4i, the only thing we can say about the other solution is that its real part must be 3. ## Use our writing service to score better and meet your deadlines No matter what kind of academic paper you need, it is simple and secure to hire a writer for a price you can afford at StudyHawks. Save more time for yourself. Posted in Mathematics Let P be a point between points S and T on 2004-01-01-02-00_files/i0120000.jpg. If ST = 21, SP = 3b – 11, and PT = b + 4, solve for b. A. –7 B. 7 C. 14 D. 32 The best and most correct answer among the choices provided by your question is the third choice or letter C. If ST = 21, SP = 3b – 11, and PT = b + 4, the value of b would be 14. I hope my answer has come to your help. God bless and have a nice day ahead! Posted in Mathematics Which polynomial expression represents the area of the outermost square tile, shown below? A square shaped tile with length x plus three is shown x2 + 6x + 6 x2 + 9x + 6 x2 + 6x + 9 x2 − 6x + 9 I believe the correct answer from the choices listed above is the third option. The polynomial expression that represents the area of the outermost square tile would be x^2 + 6x + 9. The area of a square is calculated by the square of its side and the side of this square is given as x+3. A = (x+3)^2 = x^2+6x+9 Posted in Mathematics What is the additive inverse of the polynomial 9xy^2 + 6x^2y – 5x^3? A.9xy2 – 6x2y + 5x3 B. 9xy2 – 6x2y – 5x3 C. 9xy2 + 6x2y + 5x3 D. 9xy2 – 6x2y + 5x3 Are you sure that you wrote all your choices right? Because for so solving the additive inverse of 9xy² + 6x²y - 5x³ -1(9xy² + 6x²y - 5x³) then it will turn to this ⇒ (-1)(9xy²) + (-1)(6x²y) + (-1)(-5x³) -9xy² - 6x²y + 5x³ is the additive inverse of the given polynomial. Posted in Mathematics A car travel 90 Km in 2 1/2 hours. How much time is required to cover 30 Km and find the distance cover in 2 hours 90:2 1/2 90/3 : (2 1/2)/3 30 : (2 1/2)/3 30 : (5/2)/(3/1) 30 : 5/2*1/3 30 : 5/6 30km in 50 mins 90 : 2 1/2 90/(2 1/2) : (2 1/2) / (2 1/2) 90/(2 1/2) : 1 (90/1)/(5/2) : 1 (90/1)*(2/5) : 1 180/5 :1 36:1 Multiply each side by 2: 72:2 72 km in 2 hours Hope this helps :) ## Use our writing service to score better and meet your deadlines No matter what kind of academic paper you need, it is simple and secure to hire a writer for a price you can afford at StudyHawks. Save more time for yourself. Posted in Mathematics Sophia is saving money for a new bicycle. The bicycle will cost at least$623. Sophia makes $8.22 per hour. Which inequality could be used find the number of hours Sophia needs to work to make enough money to buy a new bicycle?$8.22h > $623$8.22h ≤ $623$8.22h ≥ $623$8.22h < $623 Answer: C.$ 623

Step-by-step explanation:

We are given that Sophia is saving money for a new bicycle.

The bicycle will  cost atleast $623. Sophia makes$8.22 per hour.

We have to find the inequality that could be used to find the number of hours Sophia needs to work to make enough money to buy a new bicycle.

Let Sophia works h hours to make enough money to buy a new bicycle.

Sophia makes money per hour =$8.22 Total money made by Sophia in h hours = According to question$623

Hence, option C is true.

Posted in Mathematics

Solve for x. round to nearest tenth if needed. 1. 7r-7=2r+18 a.r=-5 b.r=5 c.r=2.2 d.r=1.2 2. 2x+12=18-x a.x=3 b.x=10 c.x=6 d.x=2 3. 8x-3=15x+18 a.x=-3 b.x=3 c.x=2.1 d.x=0.9 4. 6y-6=4y+16 a.y=2.2 b.y=-2.2 c.y=11 d.y=5 5. 3(x-4)=5(x+2) a.x=11 b.x=-11 c.x=1 d.x=-1

1)  The answer is: [B]: r = 5 .
__________________________
Explanation:
__________________________
Given: 7r − 7 = 2r + 18 ; Round your answer to the nearest tenth, if necessary.
____________________________
Since "r" is the only variable given, let us assume we want to solve for "r" (instead of "x").
___________________________
→ Subtract "2r" from EACH SIDE of the equation; and & add "7" to EACH SIDE of the equation:
_____________
→ 7r − 7 − 2r + 7 = 2r + 18 − 2r + 7 ;  to get: → 5r = 25 ;
_____________
→ Now, divide EACH SIDE of the equation by "5"; to isolate "r" on one side of the equation; and to solve for "r" :
______________
→ 5r / 5 = 25 / 5 → r = 5 → which is: "Answer choice: [B]".
_________________
Let us check our answer, by plugging in "5" for "r" in the original equation:
_________________
→ 7r − 7 = 2r + 18 ;  →  7(5) − 7 =? 2(5) + 18? ;
______________________
→ 35 − 7 =? 10 + 18 ?;     → 28 =? 28? Yes!
______________________
2) The answer is: [D]: x = 2 .
_____________
Explanation:
_____________
Given: 2x + 12 = 18 − x ; Solve for "x" (round to nearest tenth, if necessary).
_______________
→ Add "x" to EACH SIDE of the equation, & subtract "12" from EACH SIDE of the equation:  → 2x + 12 + x − 12 = 18 − x + x − 12 ;
______________
→ To get: 3x = 6 ;  → Divide EACH SIDE of the equation by "3";
to isolate "x" on one side of the equation; and to solve for "x":
_____________
→ 3x / 3 = 6 / 3 ; → x = 2 ; which is: "Answer choice: [D]".
______________
Let us check our answer, by plugging in "2" for "x" in the original equation:
________________
→ 2x + 12 = 18 − x ; → 2(2) + 12 =? 18 − 2 ?
________________
→ 4 + 12 =? 18 − 2 ? ;   → 16 =? 16?  Yes!
________________________________
3)  The answer is: [A]: x = -3 .
_____________
Explanation:
________________
Given:  8x − 3 = 15x + 18 ; Solve for "x". Round your answer to the nearest tenth, if necessary.
_________________
→ Subtract "8x" from EACH SIDE of the equation, & add "3" to EACH SIDE of the equation:
_______________
→ 8x − 3 − 8x + 3 = 15x + 18 − 8x + 3 ; to get:
_______________
→ 0 = 7x + 21 ; → Subtract "21" from EACH SIDE of the equation;
_______________
→ 0 − 21 = 7x + 21 − 21 ; to get:
_______________
→  -21 = 7x ; Now divide EACH SIDE of the equation by "7";
to isolate "x" on one side of the equation; & to solve for "x":
_______________
→ = -21 / 7 = 7x / 7 ; →  -3 = x ; which is "Answer choice: [A]."
_________________
Let us check our answer, by plugging in "-3" for "x" in the original equation:
________________
→  8x − 3 = 15x + 18 ;  → 8(-3) − 3 =?  15(-3) + 18 ?;
________________________
→ -24 − 3 =?  -45 + 18 ? ;   →  -27 =? -27?  Yes!
___________________________
4)  The answer is: [C]: y = 11 .
_____________
Explanation:
____________
Given: 6y − 6 = 4y + 16 ; Solve for "y"; Round to the nearest tenth, if necessary.
____________
(Note: Since "y" is the only variable given; assume we are to solve for "y" instead of "x").
____________
→ Subtract "4y" from EACH SIDE of the equation, & add "6" to EACH SIDE of the equation; → 6y − 6 − 4y + 6 = 4y + 16 − 4y + 6 ; to get:
_______________
→ 2y  = 22 ; Now, divide EACH SIDE of the equation by "2"; to isolate "y" one side of the equation; and to solve for "y" ;
_______________
→ 2y / 2 = 22 / 2 ; →  y = 11 → which is "Answer choice: [C]".
_______________________________
Let us check our answer, by plugging in "11" for "y" in the original equation:
___________________
→  6y − 6 = 4y + 16 ; → 6(11) − 6 =? 4(11) + 16 ?
_______________________
→ 66 − 6  =? 44 + 16 ?  → 60 =? 60 ?  Yes!
__________________
5)  The answer is: [B]: x = -11 .
_____________________
Explanation:
_________________
Given: 3(x − 4) = 5(x + 2) ; Solve for "x". Round to the nearest tenth, if necessary.
___________
→Note the "distributive property of multiplication":
_____________
a*(b + c) = ab + ac ;  and: a*(b − c) = ab − ac ;
_______________
→ Let us expand EACH SIDE of our given equation.
____________
3(x − 4) = (3*x)  − (3*4) = 3x − 12;
______________________________
→Now let us expand the "right-hand side" of the given equation:
____________
→  5(x + 2) = (5*x) + (5*2) = 5x + 10 ;
______________
→Now, we can rewrite the original equation:
_______________
→ 3(x − 4) = 5(x + 2) ; by substituting the expanded values for EACH SIDE of the question:   →  3x − 12 = 5x + 10 ;
__________________
→ Subtract "3x" from EACH SIDE of the equation; and add "12" to EACH SIDE of the equation: →  3x − 12 − 3x + 12 = 5x + 10 − 3x + 12 ; to get:
________________
→  0 = 2x + 22;  → Now subtract "22" from EACH SIDE of the equation:
______________
→  0 − 22 = 2x + 22 − 22 ; to get:  →  -22 = 2x ;
__________
→ Divide EACH SIDE of the equation by "2"; to isolate "x" on one side of the equation; & to solve for "x" ;
_____________
→  -22 / 2 = 2x /2 ;  →  -11 = x ; which is "Answer choice: [B]".
______________
Let us check our answer, by plugging in "-11" for "x" in the original equation:
___________
→ 3(x − 4) = 5(x + 2) ; →  3(-11 − 4) =? 5(-11 + 2) ? ;
_______________________
→3(-15) =? 5(-9) ? ; → -45 =? -45 ?  Yes!
_____________________________________________

Posted in Mathematics

Which expression represents the sum of 2/3m - 1 1/6 and 5/6 - 1 1/3?a. 1 1/2m + 2 1/2b.1/6m - 1/3c.1 1/2m - 2 1/2d.1/6m + 1/3

The answer to "which expression represents the sum of 2/3m - 1 1/6 and 5/6 - 1 1/3?a. 1 1/2m + 2 1/2b.1/6m - 1/3c.1 1/2m - 2 1/2d.1/6m + 1/3" is B.

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Posted in Mathematics

Find the value of 3x + 2 when 7+ x = 5

I hope this helps you

x= 5-7

x= -2

3.(-2)+2

-6+2

-4

Posted in Mathematics

Find all the zeros of the function y=x^3+6x^2+x+6

one more thing X= not real solution

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Posted in Mathematics

WILL UPVOTE! Which equation is related to 89 = x + 61? A. x = 150 B. 61 = 89 + x C. x = 28 D. x = 18

C! x = 28. If you use simplification, and then you find the answer and use it in the equation, it would be correct.

Posted in Mathematics

What is the radius of a circle whose equation is (x – 7)2 + (y – 10)2 = 4? 2 units 4 units 8 units 16 units

Option (a) is correct.

The radius of circle with equation is 2 units.

Step-by-step explanation:

Given : The equation of circle as

We haave to determine the radiusof th circle whose equation is given as .

Consider the gicen equation

The standard equation of circle with centre (h, k) and radius r is given by

Thus, Comparing the gicen equation h = 7 , k = 10 and r = 2

Thus, The radius of circle with equation is 2 units.

Posted in Mathematics