angle AOB = 132 and is also the sum of angles AOD and
DOB. Hence
angle AOD + angle DOB = 132° ---> 1
angle COD = 141 and is also the sum of angles COB and BOD. Hence
angle COB + angle DOB = 141° ---> 2
Now we add the left sides together and the right sides of equations 1 and 2
together to form a new equation.
angle AOD + angle DOB + angle COB + angle DOB = 132 + 141 ---> 3
We should also note that:
angle AOD + angle DOB + angle COB = 180°
Therefore substituting angle AOD + angle DOB + angle COB in equation 3 by 180
and solving for angle DOB:
180 + angle DOB = 132 + 141
angle DOB = 273 - 180 = 93°
180-2(55)-x=0
180-110-x=0
70-x=0
-x=-70
x=70°
The number is 66.
Solution:
Let the number be x.
To find the number x using given conditions.
Start with the last condition.
It is less than 7 times 8 + 23 = 7 × 8 + 23 = 79
So, the number is less than 79 which implies x < 79.
Using condition (4),
It is greater than 5 times 4 = 5 × 4 = 20
So, the number is greater than 79 which implies x > 20.
Combining condition (4) and (7), we get 20 < x < 79.
Using condition (3) and (5),
The number is a multiple of 11 and 6.
The number which is multiplied by both 11 and 6 is 66, 132, ...
But here x lies between 20 < x < 79.
So x = 66.
66 is not odd number and the sum of the digits is divisible by 2.
Therefore condition (1) and (2) also satisfied.
Hence the number is 66.
The domain of the function is D ∈ R or (-∞, ∞) and the range of the function is R ∈ (591.39, ∞)
<h3>What is a function?</h3>
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = -4.92x² + 17.96x + 575
The above function is a quadratic function and we know,
The quadratic function domain is all real numbers.
The domain of the function is all real numbers or
D ∈ R or (-∞, ∞)
The range:
From the graph of a function:
The maximum value of the graph:
f(1.825) = 591.39
So the range of the function:
R ∈ (591.39, ∞)
Thus, the domain of the function is D ∈ R or (-∞, ∞) and the range of the function is R ∈ (591.39, ∞)
Learn more about the function here:
brainly.com/question/5245372
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