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drek231 [11]
3 years ago
11

Find the point, M, that divides segment AB into a ratio of 5:6 if A is at (0, 22) and B is at (11, 0). A) (5, 12) B) (5, 11) C)

(6, 12) D) (6, 11)
Mathematics
2 answers:
amid [387]3 years ago
6 0
\bf \left. \qquad  \right.\textit{internal division of a line segment}
\\\\\\
A(0,22)\qquad B(11,0)\qquad
\qquad 5:6\quad \textit{from A to B}
\\\\\\
\cfrac{AM}{MB} = \cfrac{5}{6}\implies \cfrac{A}{B} = \cfrac{5}{6}\implies 6A=5B\implies 6(0,22)=5(11,0)\\\\
-------------------------------\\\\

\bf { M=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}\\\\
-------------------------------\\\\
M=\left(\cfrac{(6\cdot 0)+(5\cdot 11)}{5+6}\quad ,\quad \cfrac{(6\cdot 22)+(5\cdot 0)}{5+6}\right)
\\\\\\
M=\left( \cfrac{55}{11}~~,~~\cfrac{132}{11} \right)

and surely you know what that is.
lozanna [386]3 years ago
4 0

Answer:

Answer is (5,12) if anyone wanted to know

Step-by-step explanation:


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Answer:

144 un^2

Step-by-step explanation:

Base: 4 × 11 = 44

Left-most face: 3 × 11 = 33

Top face: 5 × 11 = 55

Triangular faces: 3 × 4 = 12

Add: 44 + 33 + 55 + 12 = 144

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3 years ago
Need help with math problems A-C. Please?
dolphi86 [110]
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In order to solve the equation below, you need to change it around so that n is by itself. Write this new equation. Do not inclu
ale4655 [162]
N/6=30
Multiply both sides by 6
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6 0
2 years ago
How to show these 2 problems are inverses
nataly862011 [7]
\bf \begin{cases}
f(x)=\sqrt[3]{7x-2}\\\\
g(x)=\cfrac{x^3+2}{7}
\end{cases}\\\\
-----------------------------\\\\
now
\\\\
f[\ g(x)\ ]\implies f\left[ \frac{x^3+2}{7} \right]\implies \sqrt[3]{7\left[ \frac{x^3+2}{7} \right]-2}\implies \sqrt[3]{x^3+2-2}
\\\\\\
\sqrt[3]{x^3}\implies x\\\\
-----------------------------\\\\
or
\\\\
g[\ f(x)\ ]\implies g\left[\sqrt[3]{7x-2}\right]\implies \cfrac{\left[\sqrt[3]{7x-2}\right]^3+2}{7}
\\\\\\
\cfrac{7x-2+2}{7}\implies \cfrac{7x}{7}\implies x

thus f[ g(x) ] = x indeed, or g[ f(x) ] =x, thus they're indeed inverse of each other
8 0
3 years ago
A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is ce
lubasha [3.4K]
<h2>Answer:</h2>

\boxed{(5(-\sqrt{2}+\sqrt{6}),5(\sqrt{2}+\sqrt{6}))}

<h2>Step-by-step explanation:</h2>

The origin of the coordinate system is the center of the circle. So we have an angle that measures 5\pi/12=75^{\circ}. so the x-coordinate and y-coordinate can be found, by using trigonometry as follows:

x=20cos(5\pi/12)=5\sqrt{6}-5\sqrt{2} \\ \\ Arranging:\\ \\x=5(-\sqrt{2}+\sqrt{6}) \\ \\y=20sin(5\pi/12)=5\sqrt(6)+5\sqrt{2} \\ \\ Arranging:\\ \\y=5(\sqrt{2}+\sqrt{6})

Finally, the exact value of the position of the rider after the carousel rotates 5\pi/12 radians is:

\boxed{(5(-\sqrt{2}+\sqrt{6}),5(\sqrt{2}+\sqrt{6}))}

3 0
3 years ago
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