Here is how to solve it with long division and synthetic division.
Answer:
$262.5
Step-by-step explanation:
Given data
Commission earned= 7.5%
Sales for last week= $3,500
Let us find the amount of the commission
=7.5/100* 3500
=0.075*3500
=$262.5
Hence the commission earned last week is
$262.5
Answer:
1/8, 1/4, 1/2, 1/2, 1/8 plus 1 tablespoon, 3/8, 1/16, 1/2, 1/8, 1/4
Step-by-step explanation:
multiply the denominator by 2 for each one because fractions are smaller as the number gets bigger.
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.
9514 1404 393
Answer:
70° (number in the blank at the bottom)
Step-by-step explanation:
You need to know the meaning of "complement of an angle."
Complementary angles have a sum of 90°. So, the complement of 20° is the angle that makes the total 90°. It is 70°.
The line at the bottom of the figure tells you how to work the problem. It says "the cosine of an angle is the sine of its complement." If you put numbers in this statement, it tells you ...
the cosine of 20° is the sine of 70°
So, the answer to the question at the top of the page is ...
look up the value of sin(70°) in the table
