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Digiron [165]
3 years ago
8

7. What is the solution to x2 + 10x + 27 = 0 when written in the form a ± bi? (1 point)

Mathematics
2 answers:
son4ous [18]3 years ago
7 0

Answer:

<u>The correct answer is D. -5 +/- i√2</u>

Step-by-step explanation:

Let's solve for x, the equation given to us, this way, using the quadratic formula:

x = (- b +/- √b² - 4ac)/2a

Replacing with the real values, we have:

x = (-10 +/- √10² - 4 * 1 * 27)/2

x = (-10 +/- √100 -108)/2

x = (-10 +/- √-8)/2

x = (-10 +/- √-1 * 4 * 2)/2 Let's recall that √-1 = i

x = (-10 +/- 2i√2)/2

x = 2 (-5 +/- i√2)/2 (Dividing by 2 both the numerator and the denominator)

<u>x₁ = -5 + i√2</u>

<u>x₂ = -5 - i√2</u>

<u>The correct answer is D. -5 +/- i√2</u>

Lena [83]3 years ago
6 0

Answer:

The solution is -5(+-)1.4i

Step-by-step explanation:

  • To calculate the roots of  a quadratic equation , you should remember the well known formula : \frac{-b(+-)\sqrt{b^2-4ac} }{2a}, where "a" is the term linked to  the squared term, "b" is the term linked to the linear term, and "c" is the constant term.
  • In this case, a=1, b=10 and c=27. Then, applying this formula means doing the following calulations: \frac{-10(+-)\sqrt{10^2-4\times1\times27} }{2\times1} =\frac{-10(+-)\sqrt{100-108} }{2} =\frac{-10(+-)\sqrt{-8} }{2}.
  • Because we know that the imaginary unit is i=\sqrt{-1}, or alternatively, i^2=-1, we can express the previous expression as follows: \frac{-10(+-)\sqrt{8\times(-1)} }{2}.
  • We can now apply distributive property of the radical of a product , and obtain the following:\frac{-10(+-)\sqrt{8}\times\sqrt{-1}}{2} =\frac{-10(+-) 2.83i}{2} =-5(+-)1.41i, which is our final expression.
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harkovskaia [24]
G(X)=6X-3
Y=6X-3
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6 0
3 years ago
Question 3 options: lily is building a picture frame. the larger rectangle represents the frame. the smaller rectangle represent
Finger [1]

The area of the shaded region of this figure which can be calculated by the difference of the larger region from the smaller region would be 104 in.²

<h3>What is the area of the rectangle?</h3>

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Area of a larger rectangle

= Length × Width

= 18 × 12

= 216 in.²

Area of the smaller rectangle

Length = 12 - 2 - 2 = 8 in.

Width = 18 - 2 - 2 = 14 in.

= Length × Width

= 8 × 14

= 112 in.²

Area of the shaded region = Area of a larger rectangle - Area of the smaller rectangle

= 216 - 112

= 104 in.²

Hence, the area of the shaded region of this figure is 104 in.²

Learn more about the area;

brainly.com/question/2289492

5 0
2 years ago
When I'm with my factor 5 , my product is 20 . what number am I ? explain ..<br> plzz helpp !
jekas [21]
The answer is 4.

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7 0
2 years ago
Read 2 more answers
Find the equation of the graphed line.
belka [17]
<h3><u>Answer:</u></h3>

\boxed{\boxed{\pink{\bf \leadsto Hence \ option\ [d]\ \bigg(y =  \dfrac{5}{2}x + 5\bigg) \ is \ correct  }}}

<h3><u>Step-by-step explanation:</u></h3>

Here from the given graph we can see that the graph the graph intersects x axis at (2,0) and y axis at (5,0). On seeing options it's clear that we have to use Slope intercept form . Which is :-

\large\boxed{\orange{\bf y = mx + c} }

We know that slope is \tan\theta. So here slope will be ,

\red{\implies slope = \tan\theta} \\\\\implies slope =\dfrac{PERPENDICULAR}{BASE} \\\\\bf \implies slope =\dfrac{5}{2}

Hence the slope is 5/2 . And here value of c will be 5 since it cuts y axis at (5,0).

\purple{\implies y = mx + c }\\\\\implies y = \dfrac{5}{2}x + 5 \\\\\underline{\boxed{\red{\tt \implies y = \dfrac{5}{2}x + 5 }}}

<h3><u>Hence</u><u> </u><u>option</u><u> </u><u>[</u><u> </u><u>d</u><u> </u><u>]</u><u> </u><u>is</u><u> </u><u>corre</u><u>ct</u><u> </u><u>.</u><u> </u></h3>
4 0
2 years ago
Tim install 50 square feet of his floor in 45 mins. At this rate how long does it take him to install 495 square feet. Is that 9
Nimfa-mama [501]

Answer:

the answer is 445.5

Step-by-step explanation:

what I did was divide 50 by 495 and got 9.9 then since it took 45 minutes every 50 square feet of floor i multiplied 45 x 9.9 and got 445.5  

6 0
3 years ago
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