X + y = 7
xy = -30
x + y = 7
x - x + y = -x + 7
y = -x + 7
xy = -30
x(-x + 7) = -30
x(-x) + x(7) = 30
-x² + 7x = -30
-x² + 7x + 30 = 0
-1(x²) - 1(-7x) - 1(-30) = 0
-1(x² - 7x - 30) = 0
-1 -1
x² - 7x - 30 = 0
x² - 10x + 3x - 30 = 0
x(x) - x(10) + 3(x) - 3(10) = 0
x(x - 10) + 3(x - 10) = 0
(x + 3)(x - 10) = 0
x + 3 = 0 or x - 10 = 0
- 3 - 3 + 10 + 10
x = -3 or x = 10
x + y = 7 or x + y = 7
-3 + y = 7 or 10 + y = 7
+ 3 + 3 - 10 - 10
y = 10 or y = -3
(x, y) = (-3, 10) or (x, y) = (10, -3)
The two numbers that add up to 7 and multiply to 30 are -3 and 10.
Answer:
0.231
Step-by-step explanation:
Let the Probability of students that knew the correct answer be: P(A)
P(A) = 60% = 0.6
Let the Probability that the student picked the wrong answer even if he/she knows the right answer be: P(B)
P(B) = 15% =0.15
Let the Probability of the student that do not knew the correct answer Be P(C)
P(C) = 1 - P(A)
P(C) = 1 - 0.6
P(C) = 0.4
Let the Probability that the student does not know the right answer but guessed it correctly be: P(D)
P(D) = 25% = 0.25
Let the Probability that the student picked the right answer even if he/she knows the right answer be: P(E)
P(E) = 1 - P(B)
P(E) = 1 - 0.15
P(E) = 0.85
Probability that the student got the answer wrong = (0.60 X 0.15) + (0.40 X 0.75) = 0.39
P( Student knew answer given he answered wrong) =
=
=
= 0.23076923077
= 0.231
It's very easy to come up with linear functions if all you have to do is make sure that your slope is more than -1 and less than 0. The easier slope to choose would be -0.5. To rest of the equation (b) can be filled out as you choose:
y = -0.5x + b
b = any constant value (ex. 1, 3, 7)
Step-by-step explanation:
v=1/3nr2h for h
3(v)=3(1/3nr2h)
3v/2nrh=2nrh/2nr
3v/2nrh=h
h = 3v/2nrh