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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°
For rate you do the amount of mins dived by the number of posters so 40/5 so the answer is 8
A polynomial is an equation/expression that contains one or more terms. Generally speaking, it applies to 3 or more.
<span>Integral of sqrt(36 + x^2)dx = 1/2sqrt(36 + x^2)x + 18sinh^1 (x/6) + c </span>