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3 years ago

How do I solve this operation

Mathematics

1 answer:

ivann1987 [24]3 years ago

6 0

4 / ( 3 + 5i ) = [ 4( 3 - 5i)] / [ 3^2 - (5i)^2 ] = [ 4( 3 - 5i)] / 34 = [ 2( 3 - 5i)] / 17 =
6 / 17 - 10i / 17;

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A small garden measures 9 ft by 13 ft. A uniform border around the garden increases the total area to 192 ft square. What is the

victus00 [196]

The width of border is 1.5 feet

<h3><u>Solution:</u></h3>

Given that small garden measures 9 ft by 13 ft

A uniform border around the garden increases the total area to 192 ft square

To find: width of border

Let the width of border be "x"

Then the new measures of garden are (9 + 2x) feet and (13 + 2x) feet

The total area of garden = 192 square feet

$(9 + 2x)(13 + 2x) =192$

$117 + 18x + 26x + 4x^2 = 192\\\\4x^2 + 44x - 75 = 0$

<em><u>Let us solve the above equation by quadratic formula</u></em>

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Using the above formula,

For $4x^2 + 44x - 75 = 0$ , we have a = 4 ; b = 44 ; c = -75

Substituting the values of a = 4 ; b = 44 ; c = -75 in above quadratic formula we get,

$\begin{aligned}&x=\frac{-44 \pm \sqrt{44^{2}-4(4)(-75)}}{2 \times 4}\\\\&x=\frac{-44 \pm \sqrt{1936-1200}}{8}\\\\&x=\frac{-44 \pm \sqrt{3136}}{8}\\\\&x=\frac{-44 \pm 56}{8}\end{aligned}$

$\begin{aligned}&x=\frac{-44+56}{8} \text { or } x=\frac{-44-56}{8}\\\\&x=\frac{12}{8} \text { or } x=\frac{-100}{8}\\\\&x=1.5 \text { or } x=-12.5\end{aligned}$

Since "x" cannot be negative,

we get x = 1.5

Thus width of border is 1.5 feet

4 0

3 years ago

Which statement describes how to determine if a relation given in a table is a function?

Ahat [919]

I believe the answer is “If none of the input values are repeated, the relation is a function” because one input must have one output.

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3 years ago

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What is the area of a triangle whose vertices are G(−1, 2), H(5, 2) and K(8, −3)

bogdanovich [222]

the area is 15

steps:

a=1/2bh

a=1/2(5)(6)

a=1/2(30)

a=15

5 0

3 years ago

Find x & y so that quadrilateral is a parallelogram. (Look at image)

Pachacha [2.7K]

Answer:

x = 20° and y = 12°

Step-by-step explanation:

3y + 15° = 5y - 9° ( being opposite angles of parallelogram)

5y - 3y = 15° + 9°

2y = 24°

y = 24° / 2

y = 12°

Now

5x + 29° = 7x - 11° ( being opposite angles of parallelogram)

7x - 5x = 29° + 11°

2x = 40°

x = 40° / 2

x = 20°

Hope it will help :)❤

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3 years ago

What are the coordinates for this point? <br><br><br> Point D

TEA [102]

(0,-4) is the coordinate for point D

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