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3 years ago

What is the length of DF? Round to the nearest hundredth.

Mathematics

1 answer:

OlgaM077 [116]3 years ago

3 0

Answer:

7.06

Step-by-step explanation:

This triangle can be solved a couple of ways. In the end, they amount to the same thing.

1) The area is ...

A = 1/2bh = 1/2(8)(15) = 60 . . . using DG as the base

Using GE as the base, the height (DF) is ...

A = (1/2)(17)(DF)

2(60)/17 = DF = 120/17

DF ≈ 7.06

2) Using similar triangles, we can find the ratio of the long side to the hypotenuse as ...

(long side)/(hypotenuse) = DE/GE = DF/DG

DF = DG(DE/GE) = 8(15/17) = 120/17

DF ≈ 7.06

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3 years ago

ANSWER ASAP ITS FOR FINALS

Roman55 [17]

Answer:

9. 66°

10. 44°

11. $2\sqrt{7}$

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Step-by-step explanation:

9. Add 120 + 80 (equals 200) and subtract that from 360 (Because all angles in a quadrilteral add to 360°), this equals 160. Plug the same number in for both variables in the two other angle equations until the two angles add to 160. For shown work on #9, write:

120 + 80 = 200

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10. Because the two sides are marked as congruent, the two angles are as well. This means the unlabeled angle is also 68°. The interior angles of a triangle always add to 180°, so add 68+68 (equals 136) and subtract that from 180, this equals 44. For shown work on #10, write:

68 x 2 = 136

180 - 136 = 44

11. Use the Pythagorean theorem (a² + b² = c²) (Make sure to plug in the hypotenuse for c). Solve the equation. For shown work on #10, write:

a² + b² = c²

a² + 6² = 8²

a² + 36 = 64

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12. (Same steps as #11) Use the Pythagorean theorem (a² + b² = c²) (Make sure to plug in the hypotenuse for c). Solve the equation. For shown work on #11, write:

a² + b² = c²

a² + 2² = 4²

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14. Use SOH CAH TOA and solve with a scientific calculator. For shown work on #14, write:

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15. Use SOH CAH TOA and solve with a scientific calculator. For shown work on #15, write:

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16. (Same steps as #15) Use SOH CAH TOA and solve with a scientific calculator. For shown work on #16, write:

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3 years ago

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Step two:
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Quadratic formula:
$x = \frac{ - b + - \sqrt{(b) ^{2} - 4(a)(c)} }{2(a)}$
Then you would plug in the information.
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The solve for what is underneath the square root ONLY.
$x = \frac{ - 9 + - \sqrt{73} }{2}$
Since you cannot solve this any further, your final two answers are...
$x = \frac{ - 9 + \sqrt{73} }{2}$
$x = \frac{ - 9 - \sqrt{73} }{2}$

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