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3 years ago

Is the square root of 12 rational or irrational?

Mathematics

1 answer:

Andreyy893 years ago

5 0

<h3>Answer: Irrational</h3>

We cannot write sqrt(12) as a fraction of two whole numbers

Note how sqrt(12) = 3.464 and the decimal portion goes on forever without any known pattern (and it doesnt repeat either).

Compare this to something like sqrt(16) = 4 which can be written as a fraction 4/1, so sqrt(16) is rational

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Describe a sequence of transformations that maps ABC to A'B'C'.

Sphinxa [80]

The correct answer is " (1) Reflect ABC across the x-axis and call this new triangle A'B'C'. (2) Translate A'B'C' 2 units right and 6 units up so that its image is A''B''C''. "

It is assumed that the points are

A in ABC is (1,9), B in ABC is (3,12), and C in ABC is (4,4).

A'' in A''B''C'' is (3,-3), B'' in A''B''C'' is (5,-6), and C'' in A''B''C'' is (6,2).

Both triangles are congruent. Since they are congruent, there are no contractions nor dilations occured. After rotating clockwise, we get A"C"B". So we need to reflect it to get A"B"C"

hope this helped :D

7 0

2 years ago

Solve the equation on the interval [0,2π]

WARRIOR [948]

$\bf 16sin^5(x)+2sin(x)=12sin^3(x)
\\\\\\
16sin^5(x)+2sin(x)-12sin^3(x)=0
\\\\\\
\stackrel{common~factor}{2sin(x)}[8sin^4(x)+1-6sin^2(x)]=0\\\\
-------------------------------\\\\
2sin(x)=0\implies sin(x)=0\implies \measuredangle x=sin^{-1}(0)\implies \measuredangle x=
\begin{cases}
0\\
\pi \\
2\pi 
\end{cases}\\\\
-------------------------------$

$\bf 8sin^4(x)+1-6sin^2(x)=0\implies 8sin^4(x)-6sin^2(x)+1=0$

now, this is a quadratic equation, but the roots do not come out as integers, however it does have them, the discriminant, b² - 4ac, is positive, so it has 2 roots, so we'll plug it in the quadratic formula,

$\bf 8sin^4(x)-6sin^2(x)+1=0\implies 8[~[sin(x)]^2~]^2-6[sin(x)]^2+1=0
\\\\\\
~~~~~~~~~~~~\textit{quadratic formula}
\\\\
\begin{array}{lcccl}
& 8 sin^4& -6 sin^2(x)& +1\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array} 
\qquad \qquad 
sin(x)= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}
\\\\\\
sin(x)=\cfrac{-(-6)\pm\sqrt{(-6)^2-4(8)(1)}}{2(8)}\implies sin(x)=\cfrac{6\pm\sqrt{4}}{16}
\\\\\\
sin(x)=\cfrac{6\pm 2}{16}\implies sin(x)=
\begin{cases}
\frac{1}{2}\\\\
\frac{1}{4}
\end{cases}$

$\bf \measuredangle x=
\begin{cases}
sin^{-1}\left( \frac{1}{2} \right)
sin^{-1}\left( \frac{1}{4} \right)
\end{cases}\implies \measuredangle x=
\begin{cases}
\frac{\pi }{6}~,~\frac{5\pi }{6}\\
----------\\
\approx~0.252680~radians\\
\qquad or\\
\approx~14.47751~de grees\\
----------\\
\pi -0.252680\\
\approx 2.88891~radians\\
\qquad or\\
180-14.47751\\
\approx 165.52249~de grees
\end{cases}$

3 0

3 years ago

What is the probability that a randomly dropped marker will fall in the unshaded region?

statuscvo [17]

The correct answer is 14 by 15

7 0

3 years ago

Read 2 more answers

What is 6,400 in scientific notation

ch4aika [34]

The answer is 64*10^2

7 0

3 years ago

Read 2 more answers

(2,4) is perpendicular to y:2x

Luda [366]

Answer:

is a Step-by-step explanation:

combination

A selection in which order has no importance.A mathematical symbol, or combination of symbols, representing a value, or relation. Example:

.equation

A mathematical statement that says two expressions have the same value; any number sentence with an

ordered pair

Set of two numbers in which the order has an agreed-upon meaning, such as the Cartesian coordinates

(

)

, where the first coordinate represents the horizontal position, and the second coordinate represents the vertical position.

solution

1. The value of a variable that makes an equation true.

2. In chemistry, a solution is a homogeneous mixture composed of only one phase.

4 0

2 years ago