Answer: 3.75 g
Step-by-step explanation:
Assume the weight of the square is x.
The hanger is in balance so the left side is equal to the right side.
Equation therefore is:
Triangle + Square + 3 * circle = 5* square + circle
3 + x + (3 * 6) = 5x + 6
3 + x + 18 = 5x + 6
5x - x = 3 + 18 - 6
4x = 15
x = 15/4
x = 3.75 g
Answer:
16. Angle C is approximately 13.0 degrees.
17. The length of segment BC is approximately 45.0.
18. Angle B is approximately 26.0 degrees.
15. The length of segment DF "e" is approximately 12.9.
Step-by-step explanation:
<h3>16</h3>
By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.
For triangle ABC:
,- The opposite side of angle A
, - The angle C is to be found, and
- The length of the side opposite to angle C
.
.
.
.
Note that the inverse sine function here
is also known as arcsin.
<h3>17</h3>
By the law of cosine,
,
where
,
, and
are the lengths of sides of triangle ABC, and
is the cosine of angle C.
For triangle ABC:
,
, - The length of
(segment BC) is to be found, and - The cosine of angle A is
.
Therefore, replace C in the equation with A, and the law of cosine will become:
.
.
<h3>18</h3>
For triangle ABC:
,
,
, and- Angle B is to be found.
Start by finding the cosine of angle B. Apply the law of cosine.
.
.
.
<h3>15</h3>
For triangle DEF:
- The length of segment DF is to be found,
- The length of segment EF is 9,
- The sine of angle E is
, and - The sine of angle D is
.
Apply the law of sine:

.
3/4 of a mile until he reaches the end of the path.
Hope this helps.
Answer:
y=3/2x+5
The slope is 3/2 and the y-intercept is 5
Step-by-step explanation:
Solving for y will give us the slope and y-intercept
Isolate y
2y/2=10+3x/2
y=5+3/2x
The slope is 3/2 and the y-intercept is 5
Graph it by graphing (0,5) and using the slope (up 3 over 2) to put other points
Answer:
The radius is: 
Step-by-step explanation:
The equation of a circle in center-radius form is:

Where the center is at the point (h, k) and the radius is "r".
So, given the equation of the circle:

You can identify that:

Then, solving for "r", you get that the radius of this circle is:
