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Gelneren [198K]
3 years ago
7

The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments 3cm and 27cm long. Find the length of th

e altitude to the hypotenuse.

Mathematics
1 answer:
marissa [1.9K]3 years ago
3 0
To find the length of the altitude, we have to use the ratios of the similar sides.
Let the length of altitude=x
Ratio of sides:
\frac{x}{3} = \frac{27}{x}  \\
Cross \ multiply \\
 x^{2} =81 \\
Take \ square \ root.\\
 \sqrt{x^2}= \sqrt{81} \\
x=9 \\
So length of altitude is 9 cm.

Answer: 9 cm

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Miya is picking up two friends to go the beach. She drives from her house to
Serga [27]

Answer:

Option (C)

Step-by-step explanation:

Coordinates of the point representing the location of Miya → (1, 10)

Coordinates of the point representing the location of Drea → (13, 1)

Coordinates of the point representing the location of Francine → (16, 1)

Coordinates of the point representing the location of Beach → (19, 4)

Distance between Miya and Drea = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

                                                        = \sqrt{(13-1)^2+(1-10)^2}

                                                        = \sqrt{144+81}

                                                         = 15 miles

Distance between Drea and Francine = \sqrt{(16-13)^2+(1-1)^2}

                                                               = 3 miles

Distance between Francine and Beach = \sqrt{(19-16)^2+(4-1)^2}

                                                                  = \sqrt{9+9}

                                                                  ≈ 4.2 miles

Total distance between Miya and the beach = 15 + 3 + 4.2

                                                                          = 22.2 miles

Option (C) is the answer.

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3 years ago
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\sin ^4 x \tan ^2 x = \dfrac{\sin ^4 x\ \sin ^2 x }{\cos ^2 x} = \dfrac{\sin^6 x}{\cos ^2 x} = \dfrac{(\sin ^2 x)^3}{\cos^2 x}=\dfrac{(1-\cos^2 x)^3}{\cos^2 x}
7 0
3 years ago
Please help with this question
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Answer:

sin( -∅ )

- 1 / csc ( ∅ )

1 / csc ( -∅ )

Step-by-step explanation:

Since sin(x) is and odd function (a function where f(-a) = f(a) ).

-sin( ∅ ) = sin( -∅ )

On the other hand, we know that sin( ∅ ) = 1 / csc ( ∅ )

Another odd function, so the same as before applies.

-sin( ∅ ) = -1 / csc ( ∅ )

-sin( ∅ ) = 1 / csc ( -∅ )

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2 years ago
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2 years ago
Read 2 more answers
Find the standard equation of the circle with center (5, -3
Mrac [35]

Answer:

○ C

Explanation:

Accourding to one of the circle equations, \displaystyle (x - h)^2 + (y - k)^2 = r^2,the centre of the circle is represented by \displaystyle (h, k).Moreover, all negative symbols give you the OPPOCITE TERMS OF WHAT THEY <em>REALLY</em> ARE, so you must pay cloce attention to which term gets which symbol. Another thing you need to know is that the radius will ALWAYS be squared, so no matter how your equation comes about, make sure that the radius is squared. Now, in case you did not know how to define the radius, you can choose between either method:

Pythagorean Theorem

\displaystyle a^2 + b^2 = c^2 \\ \\ 6^2 + 8^2 = r^2 \hookrightarrow 36 + 64 = r^2 \hookrightarrow \sqrt{100} = \sqrt{r^2} \\ \\ \boxed{10 = r}

Sinse we are dealing with <em>length</em>, we only desire the NON-NEGATIVE root.

Distanse Equation

\displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = d \\ \\ \sqrt{[-5 - 3]^2 + [3 + 3]^2} = r \hookrightarrow \sqrt{[-8]^2 + 6^2} = r \hookrightarrow \sqrt{64 + 36} = r; \sqrt{100} = r \\ \\ \boxed{10 = r}

Sinse we are dealing with <em>distanse</em>, we only desire the NON-NEGATIVE root.

I am joyous to assist you at any time.

5 0
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