The value of <em>x</em> where by exterior angles theorem, ∠DCO equals 2·x, 69° equals the sum of ∠DCO and x° is <em>x </em>= 23°
<h3>What is the exterior angles theorem?</h3>
The exterior angles theorem states that the exterior angle of a triangle is equal to the sum of the opposite interior angles.
The given parameters are;
Points on the circle are; ABCD
Straight lines = AOBE and DCE
Segment CO = Segment CE
∠AOD = 69°
∠CEO = x°
∠OCD = ∠ODC base angles of isosceles triangle
69° = ∠x° + ∠ODC exterior angle of a triangle
∠DOC = 180 - 2×∠ODC (Angle sum property of a triangle)
180 - 2×∠ODC + x° + 69° = 180° (Sum of angles on a straight line are supplementary)
x° + 69° - 2×∠ODC = 0
∠ODC = 2·x° (exterior angle of a triangle is equal to the sum of the opposite interior angles)
69° = x° + ∠ODC = x° + 2·x° = 3·x° (substitution property of equality)
69° = 3·x°
x = 69° ÷ 3 = 23°
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Answer:
3x - y = 1
Step-by-step explanation:
This will be the same equation written in a different way'
The original equation is:
y = 3x - 1
0 = 3x - y - 1
3x - y = 1.
Answer:
X ∪ Y = {0, 10, 100, 1000}
Step-by-step explanation:
Y is a subset of X, so the union of the two sets is the same as set X:
{0, 10, 100, 1000}
Input is the same as the x-term and output is the same as the y-term.
For example, take a look at the image provided with thee table.
Looking at the first box of our table, notice that if we subtract 5 from 1, we get -4 and if we subtract 5 from 2 we get -3 and if we subtract 5 from 3, we get -2. Notice that in each case, we're subtracting 5 from the input to get the output.
I attached a table so you can practice if you'd like to. All you have to do is subtract 5 from each input and you will end up with the output. The first few are done for you. I also provided an answer key in the next image so you can check your work.
The last one might be a little trick. In the input, we have n which is a variable that represents any number. If we want to find the nth term, we simply subtract 5. So we have n - 5.
First image is practice if you'd like and the second is the key.
If you don't want to do it, no worries.
The remainder is 2 when 2n is divided by 4 if the whole number n which when divided by 4 gives 3 as the remainder.
<h3>What is an arithmetic operation?</h3>
It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
It is given that:
A whole number n which when divided by 4 gives 3 as the remainder.
Here n is the real number.
As we know,
The relationship:
Dividend = (Divisor×Quotient) + Remainder
From the question:
n = 4q + 3
2n = 8q + 6
= 4(2q + 1) + 2
When 2n is divided by 4, the remainder is 2.
Thus, the remainder is 2 when 2n is divided by 4 if the whole number n which when divided by 4 gives 3 as the remainder.
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