The GCF of two numbers is 850 neither number is divisible by the other what is the smallest these two numbers can be?
1 answer:
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In the class, there is a total of 42 students.
25 take biology.
15 take history.
18 take biology but not history.
There are four situations that you have to include in the Venn diagram:
"The students take only biology"
"The students take only history"
"The students take biology and history"
"The students take neither classes"
To draw the Venn diagram, you have to make one circle for each subject, i.e. one circle for biology and one for history, and label them.
Then you have to enter the similarities between both subjects, this means, where the circles overlap, you will find the students that take both subjects.
Finally, outside the circles, you will find the students that take neither subject:
Now, you have to determine how many students are included in each part of the Venn Diagram.
1) You know that 25 students take biology and that 18 take biology but not history, to determine the number of students that take both subjects, you have to calculate the difference between both values:
7 students take biology and history.
2) 15 students take history out of these you know that 7 take also biology. To determine the number of students that take only history, you have to calculate the difference between both values:
8 students take history but not biology.
3) To determine the number of students that take neither class, you have to subtract to the total number of students, those who take only biology plus those who take only history plus those who take both classes:
9 Students of the class take neither class.
Finally, you can write each value in the corresponding part of the Venn diagram:
• Inside the green circle, you have to include the 18 students that take only biology.
,• Inside the blue circle, you have to include the 8 students that take only history.
,• Where both circles overlap, you have to include the 7 students that take both classes.
,• Outside the circles, you have to include the students that take neither.
2A) C is correct.
2B) If x + 13 = 28, solve.
If x = 15 and x + 13 = 28, you can solve it two ways:
1. Plug x into 4x + 26 to get a perimeter of 86, or
2. Redo the equation:
3a. Since the 6z is negative, you want an expression the has 5z - (11z). Answers A and D have that in their answer.
But since the 13 is positive, you want the answer that subtracts the smaller number from the larger. Thus, D is your answer since it subtracts 2 from 15.
3b) You think about this question the same way; 6z is positive, so the smaller number is being subtracted from the larger, meaning that 11z - 5z is what you look for. C and D are the two that have that, so now let's look at the second term.
The 13 is negative, so you want the answer that has 2 - 15. The answer that has that is D.
Hope this helps :D
2B) If x + 13 = 28, solve.
If x = 15 and x + 13 = 28, you can solve it two ways:
1. Plug x into 4x + 26 to get a perimeter of 86, or
2. Redo the equation:
3a. Since the 6z is negative, you want an expression the has 5z - (11z). Answers A and D have that in their answer.
But since the 13 is positive, you want the answer that subtracts the smaller number from the larger. Thus, D is your answer since it subtracts 2 from 15.
3b) You think about this question the same way; 6z is positive, so the smaller number is being subtracted from the larger, meaning that 11z - 5z is what you look for. C and D are the two that have that, so now let's look at the second term.
The 13 is negative, so you want the answer that has 2 - 15. The answer that has that is D.
Hope this helps :D