Find the first of three consecutive even integers if the sum of the first and second is 15 less than 3 times the third.
1 answer:
Answer:
<em>First even integer: 6</em>
Step-by-step explanation:
<u>Inequalities</u>
Assume x is the first even integer. The next integer is x+2, and the last integer ix x+4.
The condition states that the sum of the first and the second number is 15 less than three times the third. This takes us to the inequality:
Operating:
Subtracting 2 and 2x:
Simplifying:
Solving:
x>5
There are infinitely many solutions. For example, for x=6 (first even number into the solution interval):
First integer: 6
Second integer: 8
Third integer: 10
There are other solutions, like 20,22,24 but the first set is 6,8,10.
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Answer:
See below:
Step-by-step explanation:
Hello my name is Galaxy and I'll be helping you today. I hope you are having a nice day!
Simplification
To figure out how we can order them, we can first simplify the problems so that we can easily determine its place. We can put the fractions into decimal form so that they are are in one form and will be easy for us to comprehend.
We know that is equal to 0.20 because we know that 1.00 will be equal to 100 in this case and we can divide that by five to get 20 which will be divided back to get to 0.20.
As I've explained how I've simplified the first one, simplifying the others should be a quite similar process, feel free to comment below if you need any assistance with this.
(Everything simplified to decimal form.)
We can now proceed to ordering them.
Ordering
Ordering decimals doesn't have to be as hard as it looks, we know that as per the number line a number that is more negative (e.g. -37) will be less than (e.g. -5) as it is closer to the number 0.
Now that we know how to order the negative numbers, we can order them into order, and for ordering the positive numbers, we should already know how to do that.
So, now, in order from Greatest to Least. We can order them by what I said above.
We can convert the numbers back into their original form by looking at how we converted them in the Simplification section.
Final Answer
After converting them into a way that we can comprehend, we get our final answer in terms of greatest to least as:
Cheers!
Answer:
Total number of ways will be 209
Step-by-step explanation:
There are 6 boys and 4 girls in a group and 4 children are to be selected.
We have to find the number of ways that 4 children can be selected if at least one boy must be in the group of 4.
So the groups can be arranged as
(1 Boy + 3 girls), (2 Boy + 2 girls), (3 Boys + 1 girl), (4 boys)
Now we will find the combinations in which these arrangements can be done.
1 Boy and 3 girls = =24
2 Boy and 2 girls=
3 Boys and 1 girl =
4 Boys =
Now total number of ways = 24 + 90 + 80 + 15 = 209