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leonid [27]
4 years ago
5

Nicole has 17 nickels n and dimes d. If the value of her coins is $1.30, how many of each coin does she have?

Mathematics
1 answer:
denis-greek [22]4 years ago
7 0

Answer:

  8 nickels and 9 dimes

Step-by-step explanation:

If all were dimes, the value would be $1.70. It is $0.40 less than that. Changing a dime for a nickel reduces the value by $0.05, so there must have been $0.40/$0.05 = 8 such changes.

There are 8 nickels and 9 dimes.

_____

<em>Check</em>

8 · 0.05 + 9 · 0.10 = 0.40 + 0.90 = 1.30 . . . the answer checks OK

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620,000 rounded to the nearest thousand is:

620,000 because 2 is less than 5

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Multiply 4 and 7. Then, divide by q.
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3 years ago
A helicopter is flying above a town. the local high school is directly to the east of the helicopter at a 20° angle of depressio
guapka [62]
Answer: 4.5 miles

Explanation:

When you draw the situation you find two triangles.

1) Triangle to the east of the helicopter

a) elevation angle from the high school to the helicopter = depression angle from the helicopter to the high school = 20°

b) hypotensue = distance between the high school and the helicopter

c) opposite-leg to angle 20° = heigth of the helicopter

d) adyacent leg to the angle 20° = horizontal distance between the high school and the helicopter = x

2) triangle to the west of the helicopter

a) elevation angle from elementary school to the helicopter = depression angle from helicopter to the elementary school = 62°

b)  distance between the helicopter and the elementary school = hypotenuse

c) opposite-leg to angle 62° = height of the helicopter

d) adyacent-leg to angle 62° = horizontal distance between the elementary school and the helicopter = 5 - x

3) tangent ratios

a) triangle with the helicpoter and the high school

tan 20° = Height / x ⇒ height = x tan 20°

b) triangle with the helicopter and the elementary school

tan 62° = Height / (5 - x) ⇒ height = (5 - x) tan 62°

c) equal the height from both triangles:

x tan 20° = (5 - x) tan 62°

x tan 20° = 5 tan 62° - x tan 62°

x tan 20° + x tan 62° = 5 tan 62°

x  (tan 20° + tan 62°) = 5 tan 62°

⇒ x = 5 tant 62° / ( tan 20° + tan 62°)

⇒ x = 4,19 miles

=> height = x tan 20° = 4,19 tan 20° = 1,525 miles

4) Calculate the hypotenuse of this triangle:

hipotenuese ² = x² + height ² = (4.19)² + (1.525)² = 19.88 miles²

hipotenuse = 4.46 miles

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