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Marina CMI [18]
2 years ago
11

Find the roots of the equation x^2 +7= 2x express your answer in simplest a +bi form

Mathematics
1 answer:
Fittoniya [83]2 years ago
7 0

x^2+7=2x\\\\\implies x^2 -2x +7 =0\\\\\text{Apply quadratic formula,}~ x =\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{in this case,}~ a = 1, b= -2 ~\text{and}~ c = 7\\\\\\x= \dfrac{-(-2) \pm \sqrt{(-2)^2 -4\cdot 1 \cdot 7}}{2\cdot 1}\\\\\\\implies x =\dfrac{2 \pm \sqrt{-24}}{2}\\\\\\\implies x = \dfrac{2 \pm i\sqrt{24}}2\\\\\implies x =\dfrac{2 \pm i2\sqrt{6}}2\\\\\implies x = \dfrac{2\left(1 \pm i  \sqrt 6\right)}2\\\\\implies x = 1 \pm i\sqrt 6\\\\

\text{Hence,}~ x = 1-i\sqrt 6 ~\text{or}~ x = 1+i\sqrt 6

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2 t-shirts and 3 hats costs £12.
Mariana [72]

Answer:

Cost of tshirt = £7.29

Cost of what = £0.86

Step-by-step explanation:

2t +3h = 12; 10t + 15h = 60

5t + 4h =33; 10t + 8h = 66

15h -8h = -6

7h = -6; h = -6/7; h = 0.86

2t +3(-6/7) =12

14t -18 = 84

14t = 102; t = 102/ 14; t=7.29

6 0
3 years ago
The Rodriquez family is donating
laiz [17]

Subtract the blue caps:

25-11 = 14 caps are either white or green.

Let green = X

white = X +2

Green +  white = 14:

x + x +2 = 14

Combine like terms:

2x +2 = 14

Subtract 2 from both sides:

2x = 12

Divide both sides by 2:

x = 6

There are 11 blue caps, 6 green caps and 8 white caps.

5 0
3 years ago
The cable provider's "triple play" package offers a land line, internet service, and cable TV for one fixed price. If you alread
cupoosta [38]

Answer:

$166.16, you would have to subtract 132 by 12% or .12 and would get 166.16 :)

5 0
3 years ago
Read 2 more answers
The quotient of (x⁴+ 5x³ 3x - 15) and (x³ - 3) is a polynomial. What is the quotient?
lesya [120]

Answer:

x+5 (under assumption you meant to do -3x

Step-by-step explanation:

you can use long division.

Take the leading coefficient x^4 and divide it by x^3. This results in x which is going to be the first part of you quotient. Now take that x and multiply it by the divisor (x^3 - 3). This gives you x(x^3 - 3) = x^4 - 3x. Now subtract that x^4 - 3x from the original polynomial and repeat this until you can't divide anymore

x^4+5x^3-3x-15 - (x^4-3x) = 5x^3-15\\x^3/5x^3=5\\5(x^3-3) = 5x^3-15\\5x^3-15-(5x^3-15) = 0\\\\x+5

6 0
2 years ago
Y=2x. 1x=-y+6<br> Solve this system of equations
Allushta [10]

Answer:

y=2

x=1

Step-by-step explanation:

check the image attached

6 0
3 years ago
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