Answer:
2a) -2
b) 8
Step-by-step explanation:
<u>Equation of a parabola in vertex form</u>
f(x) = a(x - h)² + k
where (h, k) is the vertex and the axis of symmetry is x = h
2 a)
Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):
f(x) = a(x - 2)² - 6
If one of the x-axis intercepts is 6, then
f(6) = 0
⇒ a(6 - 2)² - 6 = 0
⇒ 16a - 6 = 0
⇒ 16a = 6
⇒ a = 6/16 = 3/8
So f(x) = 3/8(x - 2)² - 6
To find the other intercept, set f(x) = 0 and solve for x:
f(x) = 0
⇒ 3/8(x - 2)² - 6 = 0
⇒ 3/8(x - 2)² = 6
⇒ (x - 2)² = 16
⇒ x - 2 = ±4
⇒ x = 6, -2
Therefore, the other x-axis intercept is -2
b)
Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):
f(x) = a(x - 2)² - 6
If one of the x-axis intercepts is -4, then
f(-4) = 0
⇒ a(-4 - 2)² - 6 = 0
⇒ 36a - 6 = 0
⇒ 36a = 6
⇒ a = 6/36 = 1/6
So f(x) = 1/6(x - 2)² - 6
To find the other intercept, set f(x) = 0 and solve for x:
f(x) = 0
⇒ 1/6(x - 2)² - 6 = 0
⇒ 1/6(x - 2)² = 6
⇒ (x - 2)² = 36
⇒ x - 2 = ±6
⇒ x = 8, -4
Therefore, the other x-axis intercept is 8
3,3,2 these are the primes of 18
To do this problem, add up all the numbers and divide by the amount of numbers:
1.01+1.03+.98+.99+1.01+1.02+.98+1.05+.97+.98
10.02
Now divide by 10 (the amount of samples)
10.02/10
1.002
The Mean of the Data Set is 1.002
Hope this helps!
Answer:
Step-by-step explanation:
In this question, it appears that you need to solve this equation in terms of x.
Beginning with the equation a = x(1 + bc), we must isolate the 'x' variable and make an equation equivalent to 'x'. This can be done by:
a = x(1 + bc)
Divide (1 + bc) from both sides, giving you:
Answer:The pool must have been the same depth at the start of the interval as it was at the end of the interval.
Step-by-step explanation:
The average rate of change is calculated as:
[final value - initial value] / time interval.
Then, the average rate of change does not take into account intermediates values, and you cannot draw any conclusion about such intermediate values.
In the given case you have:
average rate of change in depth = [final depth - initial depth] / 2 weeks.
0 = [final depth - initial depth] / 2 weeks.
⇒ 0 = final depth - initial depth
⇒ final depth = initial depth.
That is why the conclusion is the second statement of the answer choices: the pool must have been the same depth at the start of the interval as it was at the end of the interval.
In between the pool might have been deeper, more shallow, empty or change in any form, since the average rate of change does not tell the full history but only the net change.
