Answer:
Step-by-step explanation:
Given
Equations are
and 
take 

Put the value of y in another equation

Put the value of x in y

Hence,
Answer:
x^4 + 8x^3 + 15x^2
Step-by-step explanation:
Answer:
a) 4/25, or 0.16, or 16%
b) 1/5, or 0.2, or 20%
c) The first option - the theoretical and experimental values should become closer the more trials that are performed.
Step-by-step explanation:
a) 4 of Tammy's 25 spins landed on black, so the experimental probability is 4/25, or 0.16, or 16%.
b) The spinner is split into 5 equal sections. Assuming it is fair, the chance of landing in any given section for a single spin is 1/5, or 0.2, or 20%.
c) The theoretical and experimental values should get closers the more trials you do.
For example, consider 1 coin flip vs 100. The theoretical probability of landing on a given side of a coin is 1/2, or 0.5, or 50%. With a single flip, your experimental probability will either be 0% or 100%, both off of the theoretical probability by 50%. After 100 flips however, the experimental and theoretical probabilities will be much closer to each other.
Answer:
x = - 2.5
Step-by-step explanation:
Given that the sketch represents
y = x² + bx + c
The graph crosses the y- axis at (0 , - 14), thus c = - 14
y = x² + bx - 14
Given the graph crosses the x- axis at (2, 0), then
0 = 2² + 2b - 14
0 = 4 + 2b - 14 = 2b - 10 ( add 10 to both sides )
10 = 2b ( divide both sides by 2 )
b = 5
y = x² + 5x - 14 ← represents the graph
let y = 0 , then
x² + 5x - 14 = 0 ← in standard form
(x + 7)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 7 = 0 ⇒ x = - 7
x - 2 = 0 ⇒ x = 2
The x- intercepts are x = - 7 and x = 2
The vertex lies on the axis of symmetry which is midway between the x- intercepts, thus
the x- coordinate of the turning point is
=
= - 2.5