Please help and thank you

Which of the side lengths could form a triangle? A) 2 cm, 2 cm, 4 cm B) 3 cm, 5 cm, 10 cm C) 3 cm, 4 cm, 5 cm D) 4 cm, 8 cm, 15

Deffense [45]

The correct answer for USATesprep is

C) 3 cm, 4 cm, 5 cm

7 0

3 years ago

Read 2 more answers

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

I need the the unknown angle measures

Valentin [98]

Answer: Mark brainliest if satisfied

m<B=72 degrees

m<C= 36 degrees

Step-by-step explanation:

m<B is congruent to m<A

72 times 2 equals 144

180 minus 144 equals 36

6 0

3 years ago

How to multiply 523 × 73

hichkok12 [17]

Line them up
3x3= 9, 3x2= 6, 3x5= 15

Add a 0 under the 9, 7x3= 21, leave the 1 and carry the 2, 7x2= 14+2= 16 leave the 6 and carry the 1, 7x5= 35+1= 36

9+0= 9, 6+1= 7, 5+6= 11 leave 1 carry 1, 1+6= 7+1= 8, 0+3= 3

523
x 73
———
1,569
+ 36,610
———
38,179

4 0

3 years ago

Which logarithmic equation is equivalent to this exponential equation? <br><br> 12=5^x

Brut [27]

Given:

The equation is:

$12=5^x$