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GaryK [48]
3 years ago
8

The length of the longer leg of a right triangle is 6cm more than twice the length of the shorter leg. The length of the hypoten

use is 9cm more than twice the length of the shorter leg. Find the side lengths of the triangle.
Length of the shorter leg:
cm
Length of the longer leg:
cm
Length of the hypotenuse:
cm

Mathematics
1 answer:
pishuonlain [190]3 years ago
6 0
Same as the one before a few way back.... so...check the picture below, then we use the pythagorean theorem

\bf (2s+9)^2=s^2+(2s+6)^2
\\\\\\
4s^2+36s+81=s^2+4s^2+24s+36\implies 36s+81=s^2+24s+36
\\\\\\
0=s^2-12s-45\implies 0=(s-15)(s+3)\implies 
\begin{cases}
0=s-15\\
\boxed{15=s}\\
-----\\
0=s+3\\
-3=s
\end{cases}

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leonid [27]

Answer:

(1, -2)

Step-by-step explanation:

<u>Step 1:  Set the second equation into the first </u>

x + (-2x) = -1

x - 2x = -1

-x / -1 = -1 / -1

x = 1

<u>Step 2:  Solve the second equation </u>

y = -2(1)

y = -2

Answer:  (1, -2)

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Please help! I attached the question below.
kompoz [17]

Answer:

\frac{2(c+2)}{c(c-2)}

Step-by-step explanation:

\frac{c^{2}-4 }{6c^{4}+15c^{3}}=\frac{(c-2)(c+2)}{c(6c^{3}+15c^{2}) }

Identity used:

a^{2}-b^{2}=(a-b)(a+b)

\frac{c^{2}-4c+4}{12c^{3}+30c^{2}}=\frac{(c-2)^{2}}{2(6c^{3}+15c^{2}) }

Now let us divide the modified expressions:

\frac{(c-2)(c+2)}{c(6c^{3}+15c^{2})} ÷ \frac{(c-2)^2}{2(6c^{3}+15c^{2}) }

we get:

\frac{2(c+2)}{c(c-2)}

5 0
3 years ago
Find 2 common angles that sum to (17pi/12) 2. Evaluate tan(17pi/12) using the sum identity for tangent.
Dmitry [639]
Note that
\frac{17 \pi }{12} = \frac{3 \pi }{12} + \frac{14 \pi }{12} = \frac{ \pi }{4} + \frac{7 \pi }{6}

Note that
x= \frac{ \pi }{4}:\,\, sin(x) =cos(x)= \frac{1}{ \sqrt{2} },\,tan(x)=1\\x= \frac{7 \pi }{6} :\,\,sin(x)=- \frac{1}{2} ,\,\,cos(x)=- \frac{ \sqrt{3} }{2} ,\,\,tan(x)= \frac{1}{ \sqrt{3} }

Use the identity
tan(x+y)= \frac{tan(x)+tan(y)}{1-tan(x)tan(y)}

Therefore
tan( \frac{17 \pi }{12} )= \frac{1+ \frac{1}{ \sqrt{3} } }{1- \frac{1}{ \sqrt{3} } } = \frac{ \sqrt{3}+1 }{ \sqrt{3}-1} =  \frac{( \sqrt{3}+1 )^{2}}{( \sqrt{3}-1 )( \sqrt{3}+1 )}  = \frac{3+1+2 \sqrt{3}}{3-1} =2+ \sqrt{3}

Answer: 2 + √3
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3 years ago
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Let x = 0.25555…
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4 0
3 years ago
Consider the equation: x^2+10x+22=13<br> Need help asap!!!! <br> this is due in a hour!
klio [65]

Answer:

(x + 5)^2 = (5 - 3)^2

Step-by-step explanation:

Given the equation;

x^2 + 10x + 22 = 13

We have;

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Adding half of 10 to both sides and completing the square as usual, we have;

(x + 5)^2 = 5^2 + (-9)

(x + 5)^2 = (5 - 3)^2

7 0
3 years ago
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