In parallelogram, LMNO,
Because Opposite angles are equal:
Therefore, 2x = 3x -55
Or x= 55
Now, the sum of angles in a parallelogram is 360
2x+3x-55+5y+5y =360
5x +10y -55 = 360
5*55 -55 + 10y = 360
10y +220 = 360
10y = 140
y=14
Thus, x=55 and y= 14
Given,
The population of the county in 2000 is 844.
The population of the county in 2009 is 856.
The population of the county in 2015 is 810.
Here, the population of 2000 and 2009 is given.
As known, the value changes linearly between two points.
When the value changes linearly between two points, then value of point between given points can be obtained by interpolation.
Hence, to predict the population of county interpolation is used.
Answer:
y = (9/4)x + 2, given that I've assume the correct meaning of "-5x4."
Step-by-step explanation:
A parallel line has the same slope as the reference line,
The reference line is 9x-4y = -5x4, as written. I'm not sure the 4 belongs, but I'll assume it is written correctly. I'm not sure if the term -5x4 is meant to mean -5x^4, -20x or -20. I'll assume -20:
9x-4y = -20
Put the equation into standard slope-intercept form: Y = mx + b, where m is the slope and b is the y-intercept (the value of y when x = 0).
-4y = -9x - 20
y = (9/4)x + 5
This line has a slope of (9/4). The parallel line will have the same slope.
y = (9/4)x + b
We can find a value of b that would shift this line to include (4,7) by using this point in the equation:
y = (9/4)x + b
7 = (9/4)(4) + b
7 = 9 + b
b = 2
The equation of a line parallel to the reference line is y = (9/4)x + 2
Answer:
122 degrees, because x and z are alternate interior angles
122 degrees, because 58 degrees and z are same side interiors which add to 180
Step-by-step explanation:
1) we know that
m∠x=m∠z -----> by alternate interior angles
m∠x+58°=180° ----> by supplementary angles (form a linear pair)
m∠x=180°-58°=22°
therefore
m∠z=22°
2) m∠z+58°=180° ----> by same side interior angles
solve for z
m∠z=180°-58°=122°
therefore
122 degrees, because x and z are alternate interior angles
122 degrees, because 58 degrees and z are same side interiors which add to 180
The area:
Substitution: u = - 6 x
du = - 6 dx
dx = -1/6 du
∫ -1/6 e^(u) du = - 1/6 e^(u) = - 1/6 e^(-6x)
=
π / 3
