Answer:
37.68 inches
Step-by-step explanation:
Circumference = 12 x 3.14
Circumference = 37.68
Hope that helps!
Answer:
x = -1
Step-by-step explanation:
1/3(6x-3)+2(x-1) = -7
Distribute
2x-1 +2x-2 = -7
Combine like terms
4x -3 = -7
Add 3 to each side
4x-3+3 = -7+3
4x = -4
Divide by 4
4x/4 = -4/4
x = -1
Answer:
The length of the shadow is decreasing 8 metres per second.
Step-by-step explanation:
In the attached figure, we draw the situation of the bear approaching the tree.
We can use the Tales to make some calculations.
The proportion between the height of the bear (h) and his shadow (S) is equal to the proportion between the height of the flashlight (H) and the sum of the distance of the bear (d) and the bear shadow.
This can be written as:
If we clear S we have:
We know that the distance is a function of time and it is reduced, as the bear approaches the tree, as a rate of 6 m/s.
We can express then the rate of variation of the shadow S as:
The length of the shadow is decreasing 8 metres per second.
Answer:
Please check the explanation.
Step-by-step explanation:
The general quadratic equation is
ax²+bx+c=0
The discriminant = D = b² - 4ac
When b² - 4ac = 0 there is one real root.
When b² - 4ac > 0 there are two real roots.
When b² - 4ac < 0 there are two complex roots.
1) x² -6x + 9=0
On comparing with given quadratic equation x² -6x + 9=0
a = 1, b=-6, c=9
D = b² - 4ac
= (-6)² - 4(1)(9)
= 36 - 36
= 0
D = 0
Thus, there is one real root of quadratic equation x² -6x + 9=0.
2) x² -4x + 3=0
On comparing with given quadratic equation x² -4x + 3=0
a = 1, b=-4, c=3
D = b² - 4ac
= (-4)² - 4(1)(3)
= 16 - 12
= 4
D > 0
Thus, there are two real roots of quadratic equation x² -4x + 3=0.
3) x² -7x - 4=0
On comparing with given quadratic equation x² -7x - 4=0
a = 1, b=-7, c=-4
D = b² - 4ac
= (-7)² - 4(1)(-4)
= 49 + 16
= 65
D > 0
Thus, there are two real roots of quadratic equation x² -7x - 4=0
4) 2x² +3x +5=0
On comparing with given quadratic equation 2x² +3x +5=0
a = 2, b=3, c=5
D = b² - 4ac
= (3)² - 4(2)(5)
= 9 - 40
= -31
D < 0
Thus, there are two complex roots of quadratic equation 2x² +3x +5=0
Answer:
The ratio between Roberto and David is 3:11
Step-by-step explanation:
If Roberto were to have 18 cards when we start, then David would have 24. Roberto has 3/4 the amount that David has. Then Roberto gives half of his cards (9) to David. Roberto now has 9 cards and David has 33.
