Answer:
C) AB = BC = CD = DA = 2√5
Step-by-step explanation:
Given
A(1, 4)
B(3, 0)
C(1, −4)
D(−1, 0)
We get the distance between point A and point B
AB = √((3-1)²+(0-4)²) = √20 = 2√5
BC = √((1-3)²+(-4-0)²) = √20 = 2√5
CD = √((-1-1)²+(0-(-4))²) = √20 = 2√5
DA = √((1-(-1))²+(4-0)²) = √20 = 2√5
C) AB = BC = CD = DA = 2√5
A rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator
Answer:
x = 3 . . . or . . . x = 4
Step-by-step explanation:
The factored form is ...
(x -3)(x -4) = 0
The zero product rule tells you the solutions are the values of x that make the factors be zero:
x = 3
x = 4
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Comment on factoring
When the leading coefficient is 1, the coefficient of the x-term is the sum of the constants in the binomial factors, and the constant term is their product. You can see this by multiplying out the generic case:
(x +a)(x +b) = x^2 +(a+b)x + ab
What this means is that when you're factoring, you're looking for factors of the constant that add up to give the coefficient of the x-term. Here, the x-term is negative and the constant is positive, so both factors will be negative.
12 = -1×-12 = -2×-6 = -3×-4
The sums of these factor pairs are -13, -8, -7. Clearly, the last pair of factors of 12 will be useful to us, since that sum is -7. So, the binomial factors of our equation are ...
(x -3)(x -4) = 0
___
If the leading coefficient is not zero, the method of factoring is similar, but slightly different. Numerous videos and web sites discuss the method(s).
4(2) - 5 = 3
4(5) - 5 = 15
4(8) - 5 = 27
4(9) - 5 = 31
so the answers are 3, 15, 27, and 31
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