The option D) x + x+2 + x+4 = 53 represents the exact equation of sum of three consecutive odd integers which is equal to 53.
<u>Step-by-step explanation:</u>
The sum of the three consecutive odd integers = 53
<u>To frame the equation :</u>
- Let us consider any of the three consecutive odd integers.
- Let us take 1,3,5 as the three consecutive odd integers.
Assume the first odd integer as 'x'. In this case, (x=1)
- The second consecutive odd integer is 3.
- The difference between 1 and 3 is 2.
Therefore, the second consecutive odd integer is x+2.
- The third consecutive odd integer is 5.
- The difference between 1 and 5 is 4.
Therefore, the third consecutive odd integer is x+4.
This means that, the sum of any three consecutive odd integers are given as x + x+2 + x+4.
Given that,
Sum of the three consecutive odd integers is 53.
The first odd integer + second odd integer + third odd integer = 53
x + x+2 + x+4 = 53.
The option D) x + x+2 + x+4 = 53 represents the exact equation of sum of three consecutive odd integers which is equal to 53.
Answer:
Step-by-step explanation:
As the statement is ‘‘if and only if’’ we need to prove two implications
is surjective implies there exists a function 
such that 
.- If there exists a function such that , then is surjective
Let us start by the first implication.
Our hypothesis is that the function is surjective. From this we know that for every 
there exist, at least, one 
such that 
.
Now, define the sets 
. Notice that the set 
is the pre-image of the element 
. Also, from the fact that 
is a function we deduce that 
, and because the sets are no empty.
From each set choose only one element 
, and notice that 
.
So, we can define the function 
as 
. It is no difficult to conclude that 
. With this we have that 
, and the prove is complete.
Now, let us prove the second implication.
We have that there exists a function such that .
Take an element , then 
. Now, write 
and notice that . Also, with this we have that 
.
So, for every element we have found that an element (recall that ) such that , which is equivalent to the fact that is surjective. Therefore, the prove is complete.
Answer:
Step-by-step explanation:
<u>The two angles of the triangle ADB are:</u>
- m∠A/2 and m∠B/2 or
- α/2 and β/2
<u>The three interior angles add to 180°, so the missing angle is:</u>
- m∠ADB = 180° - 1/2(α + β)
Aight let's answer this step by step
What you need to know is if two values are equal either one will be similar to the other it's only the format that's different if you calculate each of the fractions you'll see each pair is equal except for the last option
Where if calculated
8/3=2.67 but
5/4.8=1.04
Therefore values aren't equal to each other
Answer:
.
Step-by-step explanation:
3x - y = 17 .......A
10 × [x/5 + y/2] = 10 × 0
2x + 5y = 0 .......B
......A× 5 both 2 sides of equation
15x - 5y = 85 .....C
......B + ........C
2x + 15x = 0 + 85
17x = 85
x = 85/17
x = 5
put x value in ........A or .......B or ......C
you will receive y = -2
