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zheka24 [161]
3 years ago
15

Identify the reflection of the figure with vertices E(8,4), F(-16,-8), and G(24,-16) across the y-axis.

Mathematics
1 answer:
Dafna1 [17]3 years ago
6 0

Answer:

\boxed{\text{E$'$(-8, 4), F$'$(16,-8), G$'$(-24,-16)}}

Step-by-step explanation:

When you reflect a point (x, y) in the y-axis, the y-coordinate remains the same, but the x-coordinate gets the opposite sign. Thus,

E (8,4) ⟶ E' (-8,4)

F (-16,-8) ⟶ F' (16,-8)

G (24,-16) ⟶ G' (-24,-16)

\text{The reflected figure has coordinates } \boxed{\textbf{E$'$(-8, 4), F$'$(16,-8), G$'$(-24,-16)}}

The figure EFG and its reflection E'F'G' are shown in the diagram below.

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Solve for x in the equation 3 x squared minus 18 x + 5 = 47.
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Answer:

x= 3 +\sqrt{23}, 3 -\sqrt{23}

Step-by-step explanation:

You use the quadratic formula to get x= \frac{18+6\sqrt{23} }{6} ,\frac{18-6\sqrt{23} }{6}

Then you simplify and get the answers x= 3 +\sqrt{23}, 3 -\sqrt{23}

​​  

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Step-by-step explanation:

(cos 10° − sin 10°) / (cos 10° + sin 10°)

Rewrite 10° as 45° − 35°.

(cos(45° − 35°) − sin(45° − 35°)) / (cos(45° − 35°) + sin(45° − 35°))

Use angle difference formulas.

(cos 45° cos 35° + sin 45° sin 35° − sin 45° cos 35° + cos 45° sin 35°) / (cos 45° cos 35° + sin 45° sin 35° + sin 45° cos 35° − cos 45° sin 35°)

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Combining like terms:

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Answer:

11). x = 25.8°

12). x = 67.3°

Step-by-step explanation:

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12). By applying tangent rule in the given triangle,

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    x = \text{tan}^{-1}(\frac{43}{18} )

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