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Stella [2.4K]
3 years ago
8

The length of the rectangle is 3 meters more than the width. The perimeter is 26 meters. Write and solve a system of equations t

hat represents this situation. What are the dimensions of the rectangle?
Mathematics
2 answers:
krok68 [10]3 years ago
6 0
X = Width
2X = Length
2X + 2(2X) = 26 (Perimeter)
6X = 26
X = 4.33333...

Note, the .3333 is repeating, and should be written as .33 with a line over it (can't do it on a keyboard).... It could also be written as 1/3
raketka [301]3 years ago
4 0
Width is 5
length is 8
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Soulotion to equation if y is =15 when x=2 ,find y when x=8
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Answer:

The value of y for x = 8 is 60  .

Step-by-step explanation:

Given expression as :

For x = 2  , y = 15

Let the equation be written with constant k'

So, y = k x

Or, k = \dfrac{y}{x}

∴   k =  \dfrac{15}{2}

<u>Now, again </u>

For x = 8

equation can be written as

   y = k x

Or,  y =  \dfrac{15}{2} × 8

Or,  y = \frac{15\times 8}{2}

∴    y = 15 × 4

I.e  y = 60

Hence The value of y for x = 8 is 60  . Answer

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Step-by-step explanation:

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3. Han has a fish tank that has a length of 14 inches and a width of 7 inches. Han puts in
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The height of the tank is 12 inches
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How do I solve: 2 sin (2x) - 2 sin x + 2√3 cos x - √3 = 0
ziro4ka [17]

Answer:

\displaystyle x = \frac{\pi}{3} +k\, \pi or \displaystyle x =- \frac{\pi}{3} +2\,k\, \pi, where k is an integer.

There are three such angles between 0 and 2\pi: \displaystyle \frac{\pi}{3}, \displaystyle \frac{2\, \pi}{3}, and \displaystyle \frac{4\,\pi}{3}.

Step-by-step explanation:

By the double angle identity of sines:

\sin(2\, x) = 2\, \sin x \cdot \cos x.

Rewrite the original equation with this identity:

2\, (2\, \sin x \cdot \cos x) - 2\, \sin x + 2\sqrt{3}\, \cos x - \sqrt{3} = 0.

Note, that 2\, (2\, \sin x \cdot \cos x) and (-2\, \sin x) share the common factor (2\, \sin x). On the other hand, 2\sqrt{3}\, \cos x and (-\sqrt{3}) share the common factor \sqrt[3}. Combine these terms pairwise using the two common factors:

(2\, \sin x) \cdot (2\, \cos x - 1) + \left(\sqrt{3}\right)\, (2\, \cos x - 1) = 0.

Note the new common factor (2\, \cos x - 1). Therefore:

\left(2\, \sin x + \sqrt{3}\right) \cdot (2\, \cos x - 1) = 0.

This equation holds as long as either \left(2\, \sin x + \sqrt{3}\right) or (2\, \cos x - 1) is zero. Let k be an integer. Accordingly:

  • \displaystyle \sin x = -\frac{\sqrt{3}}{2}, which corresponds to \displaystyle x = -\frac{\pi}{3} + 2\, k\, \pi and \displaystyle x = -\frac{2\, \pi}{3} + 2\, k\, \pi.
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Any x that fits into at least one of these patterns will satisfy the equation. These pattern can be further combined:

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  • \displaystyle x =- \frac{\pi}{3} +2\,k\, \pi.
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