Answer:
x = 78 degrees
Step-by-step explanation:
Let y represent the last angle in the triangle containing 79 degrees and x degrees.
Since the top and bottom lines are parallel, then angle y and angle 23 are alternate angles. Alternate angles are equal. Therefore,
Angle y = 23 degrees
The sum of the angles in a triangle is 180 degrees. It means that
Angle x + angle y + 79 degrees = 180 degrees. Therefore
x + 23 + 79 = 180
x + 102 = 180
Subtracting 102 from the left hand side of the equation and the right hand side of the equation, it becomes
x + 102 - 102 = 180 - 102
x = 78 degrees
Assuming the vertex of the triangle shown is the center of the pentagon, and the line segment shown is an altitude of the triangle:
If we join the center of (the circumscribed circle and of) the pentagon to the 5 vertices, 5 isosceles triangles are formed, all congruent to the one shown in the figure. It is clear that these triangles are congruent, so to find the area of the pentagon, we find the area of one of these triangles and multiply by 5.
The base of the triangle is 22.3 in, and the height is 15.4 ins, thus the area of the pentagon is:
5(Area triangle)=5*[(22.3*15.4)/2]=<span>858.55 (square inches).
Answer: </span>858.55 (square inches).
According to the empirical rule, approximately 68% of data fall within 1 standard deviation of the mean.
9514 1404 393
Answer:
A. Nonlinear function
Step-by-step explanation:
No vertical line intersects the graph in more than one place, so it is a function (not a "relation").
The graph is not a straight line, so is not a linear function. It is a nonlinear function.
Answer:
45.6° (1 d.p)
Step-by-step explanation:
Using the cosine rule;
c = √( a² + b² - 2ab Cosx)
11 =√(8² + 15² - 2 (8) (15) Cosx)
11² = 8² + 15² - 240 Cosx
11² - 8² - 15² = - 240 Cosx
-168 = -240 cosx
cosx = 0.7
x = cos⁻¹ (0.7) = 45.57 ≈ 45.6°