(x-8) ^ 2 = 121
(x-8) = + / - root (121)
x = 8 +/- root (121)
The solutions are:
x1 = 8 + root (121)
x2 = 8 - root (121)
2a ^ 2 = 8a-6
2a ^ 2-8a + 6 = 0
a ^ 2-4a + 3 = 0
(a-1) (a-3) = 0
The solutions are:
a1 = 1
a2 = 3
x ^ 2 + 12x + 36 = 4
x ^ 2 + 12x + 36-4 = 0
x ^ 2 + 12x + 32 = 0
(x + 4) (x + 8) = 0
The solutions are:
x1 = -8
x2 = -4
x ^ 2-x + 30 = 0
x = (- b +/- root (b ^ 2 - 4 * a * c)) / 2 * a
x = (- (- 1) +/- root ((- 1) ^ 2 - 4 * (1) * (30))) / 2 * (1)
x = (1 +/- root (1 - 120))) / 2
x = (1 +/- root (-119))) / 2
x = (1 +/- root (119) * i)) / 2
The solutions are:
x1 = (1 + root (119) * i)) / 2
x2 = (1 - root (119) * i)) / 2
Answer:
5 and 1/2
Step-by-step explanation: 2 goes into 11 5 times without passing it. That one that is left over would be the numerator and 2 as the demonator.
Answer:
Since the plane if cutting through the prism to make 5 sides, than the original shape needs to have less than 5.
A prism, is a 3D shape, so you can't have a 2 sided shape.
Now you have a choice of 3+or 4 sides.
A 3 sides shape is a triangle, which also can't be cut into a 5 sided prism, so the answer would need to be 4.
Step-by-step explanation:
Answer:
The sides of the rectangle can then be divided into parts to reveal partial products that make up the total product. This helps students develop the flexibility and conceptual understanding required to build fluency with basic facts and strategies for multiplication of larger numbers.
Step-by-step explanation:
Answer:
There are (63) combinations. The notation means "six choose three". Out of six items (flavors) choose three.
(nk)=n!k!(n−k)!.
(63)=6!3!3!.
Think of it this way. There are 6 ways to choose a flavor. Once you choose, there are 5 ways to choose the next. After that, there are 4 flavors left. which is 6!/3!=6⋅5⋅4⋅3⋅2⋅13⋅2⋅1=6⋅5⋅4=120.
But, you could have chosen {chocolate,vanilla,strawberry} and you get the same combination as {vanilla, strawberry, chocolate} so we have to divide by 3!=3⋅2⋅1=6 to account for the order of choosing.
So the number of combinations of flavors is (63)=1206=20.
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