Two distinct roots means two real solutions for x (the parabola needs to cross the x-axis twice)
Vertex form of a quadratic equation: (h,k) is vertex
y = a(x-h)^2 + k
The x of the vertex needs to equal 3
y = a(x-3)^2 + k
In order to have two distinct roots the parabola must be (+a) upward facing with vertex below the x-axis or (-a) downward facing with vertex above the x-axis. Parabolas are symmetrical so for an easy factorable equation make "a" 1 or -1 depending on if you want the upward/downward facing one.
y = (x-3)^2 - 1
Vertex (3,-1) upwards facing with two distinct roots 4 and 2
y = x^2 -6x + 9 - 1
y = x^2 -6x + 8
y = (x - 4)(x - 2)
Conditional probability is a measure of probability of an event given that another event has occurred.
P ( A\ B ) = P ( A ∩ B ) / P ( B ) - the conditional probability of A given B
P ( A ∩ B ) = 0.41; P ( B ) = 0.59
P ( A \ B ) = 0.41 / 0.59 = 0.6949152 ≈ 0.69
Answer: B ) 0.69
14 inch document....it is reduced to 0.6 times as long...
14 * 0.6 = 8.4 inches long
it is too small, so he enlarges it 1.4 times...
8.4 * 1.4 = 11.76 inches <===
The greatest common factor, or GCF, is the greatest factor
that divides two numbers. To find the GCF of two expression
<span>1.
</span>List the prime factors of each number.
<span>2.
</span>Multiply those factors both numbers
have in common. If there are no common prime factors, the GCF is 1.
16x^4y^3 = ( 4*4)(x*x*x*x)(y*y*y)
12x^2y^7 = (4*3)(x*x)(y*y*y*y*y*y*y)
<span>So common to them is 4x^2y^3 </span>
Answer:
Option B. 
Step-by-step explanation:
we know that
The area of a square is equal to
where
x is the length side of the square
In this problem we have
substitute and solve for x
suqre root both sides
