Answer:
a) x = 69°
b) y = 69°
Step-by-step explanation:
a. Given that AB and CD are parallel lines, therefore:
x = 69° (alternate interior angles are congruent to each other)
b. y + 111° = 180° (consecutive interior angles are supplementary)
y = 180° - 111° (substraction property of equality)
y = 69°
We can see values of angles in degrees first
= 150°
Similarly
= 300°
Now reference angle means positive acute angle they will have
As we can see in attachment 150° lies in second quadrant so its reference angle will be 180°-150° = 30° from x axis line as shown.
Where as angle 300° lies in fourth quadrant so its reference angle will be 360° - 300° = 60° from x axis as shown. So clearly both reference angles are different . So 1st choice " angles donot have same reference angle" best explains it
Choice (2) and (3) are incorrect as tan is positive only in first and third quadrants and angle 300° is in fourth quadrant.
since angle 150° is in second quadrant and 300° is in fourth quadrant so both will have same negative sign so choice (4) is not correct.
So final ansewr is choice (1) "the angles donot have same reference angle"
Answer:
Width of lawn = 35 ft
Dimensions of factory = length: 210 ft, width: 140 ft
Step-by-step explanation:
The total area of the lot can be calculated as:

Since, the area of factory should be equal to area of lawn:

Now, let 'x' be the width of lawn, the dimensions of factory can be written as:

Since, area is equal to length x width:

Divide whole equation by 4,

Solving above quadratic equation, we get,

x = 35 seems realistic width of the lawn.
Now, finding the dimension of factory:

We can also reconfirm the area of factory by multiplying the above two lengths:
140 * 210 = 29400 ft
Answer:
1). Increases
2). Slope = 4
3). Slope = -1
4). y = 4 when x = 5
Step-by-step explanation:
1). Initially, as x increases, y also increases. (Linear growth has been shown in the graph initially).
2). Afterward, the slope of the graph of the function is equal to 4 for all x between x = 3 and x = 5.
[Slope of the line passing through two points (3, 0) and (5, 4)
m = \frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}
(x
2
−x
1
)
(y
2
−y
1
)
= \frac{4-0}{5-3}
5−3
4−0
= \frac{4}{1}
1
4
= 4 ]
3). The slope of the graph is equal to -1 for x between x = 5 and x = 9.
[Slope of the line passing through two points (5, 4) and (9, 0),
Slope = \frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}
(x
2
−x
1
)
(y
2
−y
1
)
= \frac{4-0}{5-9}
5−9
4−0
= -\frac{4}{4}
4
4
= -1 ]
4). The greatest value of y is y = 4, and it occurs when x = 5. (From the given graph)