Which number is a solution of the inequality?
12<y(8-y)
a. 0
b. 1
c. 2****
d. 3
Oh lord, I will take one for the team and report back on what I get!
it is D 100%
explanation: 12<3(8-3) gives u 12<15 and this is a true statement.
12 < 8 y - y^2
or
8 y - y^2 > 12
now is
8*2 - 4 > 12 I think not
but
8*3 - 9 = 24 - 9 = 15 which is
so is my answer right?
No
has to be greater than, not equal to
so d
are you sure???
To find out which number is a solution of the inequality 12 < y(8-y), we need to solve the inequality and check if each given answer choice satisfies the inequality.
Let's go step by step:
1. Rearrange the inequality:
12 < y(8-y)
2. Expand the expression on the right side:
12 < 8y - y^2
3. Rewrite the inequality in standard quadratic form:
y^2 - 8y + 12 > 0
4. Factor the quadratic equation:
(y - 6)(y - 2) > 0
5. Determine the critical points:
Set each factor equal to 0 and solve:
y - 6 = 0 => y = 6
y - 2 = 0 => y = 2
6. Create a number line and mark the critical points:
-inf <======[2]======[6]======> inf
7. Test intervals to determine where the inequality holds true:
- Test values in the intervals (-inf, 2), (2, 6), and (6, inf).
- Test a value less than 2, for example, y = 0:
Substitute y = 0 into the inequality:
(0 - 6)(0 - 2) > 0
(-6)(-2) > 0
12 > 0
Since the inequality holds true, y = 0 is a solution.
- Test a value between 2 and 6, for example, y = 4:
Substitute y = 4 into the inequality:
(4 - 6)(4 - 2) > 0
(-2)(2) > 0
-4 > 0
Since the inequality does not hold true, y = 4 is NOT a solution.
- Test a value greater than 6, for example, y = 7:
Substitute y = 7 into the inequality:
(7 - 6)(7 - 2) > 0
(1)(5) > 0
5 > 0
Since the inequality holds true, y = 7 is a solution.
8. Based on the intervals where the inequality is true, we can conclude that the number 7 is the only solution.
Therefore, the correct answer is c. 2.
no
1. a
2. d
3. d
4. d
5. c
6. a
7. d
8. not sure :(
9. b
10. a
11. also not sure :(
12. d
13. b
14. c
15. d
16. c
17. a
18. b
19. d
20. d
21. a
22. a
23. word problem answer (reword please)
c >/= 325 - 135 - 89
c >/= 101
so 101 or more
(credit to damon)
(this is 100% besides the 2 problems i didnt give. sorry)