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2 years ago

What is the greatest common factor of 15 and 42

Mathematics

2 answers:

lukranit [14]2 years ago

8 0

Answer:

Step-by-step explanation:

The factors of 15 are: 1, 3, 5, 15

The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42

Then the greatest common factor is 3.

guajiro [1.7K]2 years ago

5 0

Answer:

Step-by-step explanation:

You might be interested in

When 5 is subtracted from the square of a number, the result is 4 times the number. Find the negative solution.

wariber [46]

Answer:

-1

Step-by-step explanation:

You can write it as...

$x^{2} -5=4x$

Carry the 4x

$x^{2} -4x-5=0$

Then use the quadratic formula to solve, since you want to find the negative solution, you don't need to find the positive solution, so we will have

$(4-\sqrt{16+20}) /2=\frac{4-6}{2}=\frac{-2}{2} =-1$

Therefore our answer is -1

8 0

3 years ago

Juanita bought 6 lemons. she used 2/3 of them to make lemonade. how many lemons did she used?

ivanzaharov [21]

6 times 2/3 equal to 4
Juanita ues 4 lemons to make lemonade

4 0

3 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

12n^2+48n = -n^3-64 factoring polynomial equations

xxTIMURxx [149]

Answer:

Step-by-step explanation:

12n2+48n=−n3−64

Step 1: Subtract -n^3-64 from both sides.

12n2+48n−(−n3−64)=−n3−64−(−n3−64)

n3+12n2+48n+64=0

Step 2: Factor left side of equation.

(n+4)(n+4)(n+4)=0

Step 3: Set factors equal to 0.

n+4=0

n=−4

4 0

3 years ago

What will be the coordinates

svlad2 [7]

N=(-1,-4)
hmm, a 270 counterclockwise rotation is the same as a 90 degree clockwise

so that would become (-4,1)
N'=(-4,1)

6 0

3 years ago