Carry out the mult.: f(x) = -[x^2 - 21x + 9x - 189]
Combine like terms: f(x) = -[x^2 - 12x - 189]
Eliminate the brackets [ ]: f(x) = -x^2 + 12x + 189
Identify coefficients a, b and c: a= -1, b=12, c=189
The equation of the axis of symmetry is x = -b/(2a), which here equals
x = -(12)/[2(-1)], or x = 6
This is also the x-coordinate of the vertex. Plug x=6 into the original equation to calculate the y-coordinate.
Answer:
You can use Pythagoras theorem to calculate x:
12² + 14² = x²
144 + 196 = x²
x² = 340
x = √340 ≈ 18,44
The vertex form of a quadratic function is:
f(x) = a(x - h)² + k
The coordinate (h, k) represents a parabola's vertex.
In order to convert a quadratic function in standard form to the vertex form, we can complete the square.
y = 2x² - 5x + 13
Move the constant, 13, to the other side of the equation by subtracting it from both sides of the equation.
y - 13 = 2x² - 5x
Factor out 2 on the right side of the equation.
y - 13 = 2(x² - 2.5x)
Add (b/2)² to both sides of the equation, but remember that since we factored 2 out on the right side of the equation we have to multiply (b/2)² by 2 again on the left side.
y - 13 + 2(2.5/2)² = 2(x² - 2.5x + (2.5/2)²)
y - 13 + 3.125 = 2(x² - 2.5x + 1.5625)
Add the constants on the left and factor the expression on the right to a perfect square.
y - 9.875 = 2(x - 1.25)²
Now, we need y to be by itself again so add 9.875 back to both sides of the equation to move it back to the right side.
y = 2(x - 1.25)² + 9.875
Vertex: (1.25, 9.875)
Solution: y = 2(x - 1.25)² + 9.875
Or if you prefer fractions
y = 2(x - 5/4)² + 79/8
Answer: (a)
P - Value = 0.0981 is high, this indicates stronger evidence that we should fail to reject the null hypothesis: H0: pD = pR (There is no significant difference between the proportion of Democrats who plan to vote for the Democratic candidate in the upcoming election and the proportion of Republicans who plan to vote for the Republican candidate in the upcoming election). P - Value = 0.0981 is the probability of obtaining results at least as extreme as the observed results of the Hypothesis Test, assuming that the null hypothesis is correct.
(b)
Since P - Value = 0.0981 is greater than \alpha = 0.05, the difference is not significant. Fail to reject null hypothesis.
(c)
Since in the Hypothesis Test, we have failed to reject null hypothesis, we could have made: Type II Error: Failure to reject a false null hypothesis. One potential consequence of this error is as follows:
Suppose in reality there is significant difference between the proportion of Democrats who plan to vote for the Democratic candidate in the upcoming election and the proportion of Republicans who plan to vote for the Republican candidate in the upcoming election. But the political pollster wrongly concludes that there is no significant difference between the proportion of Democrats who plan to vote for the Democratic candidate in the upcoming election and the proportion of Republicans who plan to vote for the Republican candidate in the upcoming election. Type II Error is committed in this situation. The consequence of this Type II Error is that the political pollstar will that the political parties are loyal and will not do any follow up work whereas in reality it is not so.
Step-by-step explanation:
got this from chegg!!!
Answer:
1/2x-5=13
Step-by-step explanation:
Let x= Frankie’s mother’s age
Half his mother’s age= 1/2x
5 less than that=1/2x-5
We know that Frankie is 13 so that equation is equal to Frankie’s age, which is 13.
Hope this helps.
