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balu736 [363]
3 years ago
10

Alphonsus went shopping for new school clothes. He bought 4 t-shirts and 3 pairs of pants.

Mathematics
1 answer:
tia_tia [17]3 years ago
5 0
E. 12
You take 4 shirts times 3 pairs of pants
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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

Rounded to the nearest tenth = 4.5 miles

That is the distance between the helicopter and the high school.
5 0
3 years ago
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What is the range of the data set? <br><br> 61<br> 40<br> 41<br> 55
antoniya [11.8K]

Answer:

40

Step-by-step explanation:

The range is the difference between the largest value and the smallest value in the data set.

minimum value = 21 and maximum value = 61

range = 61 - 21 = 40

6 0
3 years ago
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Topic Test
ladessa [460]

Answer:

B part Rate the 0ercent that interest is paif anually as a decimal

7 0
3 years ago
Find the length and width of a rectangle with an area of 2x^2+x-3
nasty-shy [4]
2x^2 + x -3 can be factorised 

<span>[2x + 3][x - 1] </span>

<span>As length times width = area </span>

<span>one possible set of measurements are </span>

<span>length = [2x + 3] </span>
<span>width = [x-1] </span>
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What is 4 divided by2/5
Minchanka [31]

Answer:

10

Step-by-step explanation:

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