Hello!
This is a problem about relating values of the Unit Circle.
First, we need to figure out the specific "points" of each angle measure of 30 and 60.
For the angle measure 30, the point will be 
.
For the angle measure 60, the point will be 
.
The tangent value of a point will be its 
value over its 
value.
The cotangent value of a point will be the reciprocal of the tangent value, which we found previously.
The sine value of a point will be the value of the point.
So the values we have so far are 
Now we have to find the LCD to add these together, which in this case would be 6.
Which adds up to 
, which is in simplest radical form.
Hope this helps!
d(x) = { (x,y): y = sqrt(x) and y >=0 }
since sqrt function requires x to be >=0 so
<u>x >= 0</u>
Find the value of x using substitution
(x-1)=-x+7
2x-1=7
2x=6
x=4
plug your x value into one of the equations to find y
y=(4)-1
y=3
your coordinate is (4,3) you would plot that point.
Answer:
3.) m < 7 = 155°, m < 8 = 25°
4.) m < 5 = 30°
m < 6 = 30°
m < 7 = 60°
m < 8 = 60°
Step-by-step explanation:
3.) By definition, angles that do not share a common side are called nonadjacent angles. Two nonadjacent angles formed by two intersecting lines are called vertical angles.
- Given that < PQT + < TQR = 180°
- Then it also means that the sum of <em>m</em> < 7 and <em>m</em> < 8 will also equal 180°.
- Also, < PQT ≅ < SQR because they are <u>vertical angles,</u> therefore, their measurements must also be congruent.
- Similarly, < PQS ≅ < TQR because they are <u>vertical angles</u>, and their measurements must also be congruent.
m < 7 = 5x + 5
m < 8 = x - 5
m < 7 + m < 8 = 180°
Substitute the values of m < 7 and m < 8 into the equation:
5x + 5 + x - 5 = 180°
6x + 0 = 180°
6x = 180°
Divide 6 on both sides of the equation to solve for x:
x = 30°
Plug in x = 30° to find the value of m< 7 and m< 8:
m < 7 = 5x + 5 = 5(30) + 5 = 150 + 5 = 155°
m < 8 = x - 5 = 30 - 5 = 25°
4.) This problem is an example of angles on a straight line. By definition, the sum of angles on a straight line is equal to 180°.
Therefore, the measurements of the following angles add up to 180°:
- < UVX + < XVY + < YVZ + <ZVW = 180°
- <em>m </em>< 5 + <em>m</em> < 6 + <em>m </em>< 7 + <em>m</em> < 8 = 180°
m < 5 = 5x
m < 6 = 4x + 6
m < 7 = 10x
m < 8 = 12x - 12
Substitute the values of each measurement onto the following equation:
5x + 4x + 6 + 10x + 12x - 12 = 180°
Combine like terms:
31x - 6 = 180°
Add 6 on both sides of the equation:
31x - 6 + 6 = 180° + 6
31x = 186
Solve for x:
x = 6
Plug in x = 6° to find the values of <em>m</em> < 5, <em>m</em> < 6, <em>m</em> < 7, and <em>m</em> < 8:
5(6) + 4(6) + 6 + 10(6) + 12(6) - 12 = 180°
180° = 180°
Therefore:
m < 5 = 5(6) = 30°
m < 6 = 4(6) + 6 = 30°
m < 7 = 10(6) = 60°
m < 8 = 12(6) - 12 = 60°
