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2 years ago

A. Are the length of a side of a square and the perimeter of the square related proportionally? Why or why not?

2 answers:

7 0

Yes, they are. A square has the same measurement for all four sides. Unlike a parallelogram which is slanted and uneven.

Yanka [14]2 years ago

7 0

Answer:

The answer is yes.

Step-by-step explanation:

Yes, the length of a side of a square and the perimeter of the square are related proportionally.

Let the side of the square be a.

So, perimeter is given as = $a+a+a+a=4a$

Or we can say = $4\times a=4a$

We can see, that the perimeter is always 4 times the side length of the square.

Example:

Suppose the side of the square is 4 cm.

So, perimeter = $4\times4=16$ cm

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Solve the equation for all real values of x.<br> cosxtanx - 2 cos x=-1

IceJOKER [234]

Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

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

Here we have , $cosxtanx - 2 cos^2 x=-1$ . Let's solve :

⇒ $cosxtanx - 2 cos^2 x=-1$

⇒ $cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1$

⇒ $sinx = 2 cos^2 x-1$

⇒ $sinx = 2 (1-sin^2x)-1$

⇒ $sinx = 1-2sin^2x$

⇒ $2sin^2x+sinx-1=0$

By quadratic formula :

⇒ $sinx = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

⇒ $sinx = \frac{-1 \pm \sqrt{1^2-4(2)(-1)} }{2(2)}$

⇒ $sinx = \frac{-1 \pm3}{4}$

⇒ $sinx = \frac{1}{2} , sinx =-1$

⇒ $sinx = sin\frac{\pi}{6} , sinx = sin\frac{3\pi}{2}$

⇒ $x=\frac{\pi}{6} , x=\frac{3\pi}{2}$

But at $x=\frac{3\pi}{2}$ we have equation undefined as $cos\frac{3\pi}{2}=0$ . Hence only solution is :

⇒ $x=\frac{\pi}{6}$

Since , $sin(\pi -x)=sinx$

⇒ $x=\pi -\frac{\pi}{6} = \frac{5\pi}{6}$

Now , General Solution is given by :

⇒ $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$

Therefore , Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

3 0

3 years ago

What is the perimeter of a triangle that has side measures of the following

defon

I got 3x^2 + 12x + 4. I recommend you verify my answer, so you have to combine like terms in the first expression then add all the expressions.

8 0

2 years ago

A system of equations consists of a line s of the equation y = x – 5 and a line t that passes through the points (0, 2) and (8,

GenaCL600 [577]

Answer:

$\text{The slope of the line t:}\ m=-\dfrac{3}{4}\\\\\text{The y-intercept of the line t:}\ b=2\\\\\text{The equation of a line t in the slope-intercept form:}\ y=-\dfrac{3}{4}x+2$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept → (0, b)

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have two points (8, -4) and (0, 2) → b = 2.

Calculate the slope:

$m=\dfrac{2-(-4)}{0-8}=\dfrac{6}{-8}=-\dfrac{3}{4}$

Therefore the equation of a line t in the slope-intercept form is:

$y=-\dfrac{3}{4}x+2$

5 0

3 years ago

Read 2 more answers

a triangle has a perimeter of 10x+2 . two sides have lengths of 5x and 2x+9 what is the length of the 3rd side

stiks02 [169]

Since all the sides add up to 10x+2, that means that 10x-2-<side1>-<side2>=<side3>. Plugging it in, we have 10x-2-5x-(2x+9)=side3, and 5x-2-(2x+9)=side3, then expanding it to 5x-2-2x-9=3x-11=side3

8 0

3 years ago

Please any help is necessary

Ugo [173]

Answer:

Option D. 50 ft

Step-by-step explanation:

we know that

The area of the figure is equal to the area of three rectangles

$A=18x+(48-36)(32-11)+(18)(32)$