(1) From the information given, if we want to choose 5 colors from 8 distinct colors and the order in which the selection is made is relevant, then what we have is a permutation.
The formula is given as;
This formula means we need to select/arrange r items out of a total of n items and the anwer derived would be the total number of arrangements possible.
Therefore, we would have;
Therefore, if the order is relevant, this selection can be done in 6,720 ways.
(2) If the order is NOT relevant, then what we need to calculate is a combination and the formula is;
The formula can now be applied as follows;
If the order is not relevant, then the selection can be done in 56 ways.
Answer:
424 cm²
Step-by-step explanation:
The figure is composed of a square and a trapezium on top
A of square = 18² = 324 cm²
A of trapezium = 
h (b₁ + b₂ )
where h is the perpendicular height and b₁, b₂ the parallel bases
Here h = 8, b₁ = 18 and b₂ = 7 , then
A = 0.5 × 8 × (18 + 7) = 4 × 25 = 100 cm²
Area of hexagonal park = 324 + 100 = 424 cm²
We have to find the value of x from the given equation.
- (x - 2)(x² - 2x + 2) = 0 is a quadratic equation, so it will have two values.
Step: Write the equation in simplest form.
Step: Solve the problem by spiltting method.
- (x-2)(x² - x -x + 1) = 0
- (x - 2)(x²-x - x + 1) = 0
- (x - 2) [x(x - 1) -1(x -1)]
- (x - 2)[(x-1)(x-1)]
Step: Solve the problem with using algebraic formula.
{x-1](x-1)
Step : We have used a²-b² to solve the problem.
(x-2)(x² - x -x + 1) = 0
(x - 2)(x²-x - x + 1) = 0
(x - 2) [x(x - 1) -1(x -1)]
(x - 2)[(x-1)(x-1)]
Therefore, the possible factorization is (x - 2)[(x-1)(x-1)].
Answer:
D' = ( -3, -2)
Step-by-step explanation:
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That is the vertex form of a quadratic equation
