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3 years ago

Can someone help me out with my math homework my grades are ba

Mathematics

1 answer:

kupik [55]3 years ago

7 0

<h3>Answer: 18</h3>

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Explanation:

2 cm on paper (or on screen) represents 3 meters in real life.

The backyard is 2 cm horizontally across on the screen, so it's 3 meters across in real life. This is the shorter dimension.

The longer dimension is 6 meters. We can think of it like this

2 cm : 3 meters

2*2 cm : 2*3 meters .... multiply both sides by 2

4 cm : 6 meters

The real backyard is 6 meters by 3 meters to give an area of 6*3 = 18 square meters.

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3 years ago

What are the solutions of x^2-2x+5=0

sweet [91]

The solution of $x^{2}-2 x+5=0$ are 1 + 2i and 1 – 2i

<u>Solution:</u>

Given, equation is $x^{2}-2 x+5=0$

We have to find the roots of the given quadratic equation

Now, let us use the quadratic formula

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ --- (1)

<em><u>Let us determine the nature of roots:</u></em>

Here in $x^{2}-2 x+5=0$ a = 1 ; b = -2 ; c = 5

$b^2 - 4ac = 2^2 - 4(1)(5) = 4 - 20 = -16$

Since $b^2 - 4ac < 0$ , the roots obtained will be complex conjugates.

Now plug in values in eqn 1, we get,

$x=\frac{-(-2) \pm \sqrt{(-2)^{2}-4 \times 1 \times 5}}{2 \times 1}$

On solving we get,

$x=\frac{2 \pm \sqrt{4-20}}{2}$

$x=\frac{2 \pm \sqrt{-16}}{2}$

$x=\frac{2 \pm \sqrt{16} \times \sqrt{-1}}{2}$

we know that square root of -1 is "i" which is a complex number

$\begin{array}{l}{\mathrm{x}=\frac{2 \pm 4 i}{2}} \\\\ {\mathrm{x}=1 \pm 2 i}\end{array}$

Hence, the roots of the given quadratic equation are 1 + 2i and 1 – 2i

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3 years ago

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