Answer:
Step-by-step explanation:
<u>Let the functions be</u>
- f(x)= ax + b
- g(x) = cx + d
<u>Their sum</u>
<u>Their product</u>
<h3>The answer options</h3>
<u>A. When added, the sum of the y-intercepts must be 1.
</u>
- Correct. We see point (0,1) of j(x) on the graph. b+d = 1
<u>B. When multiplied, the product of the y-intercepts must be –15.
</u>
- Incorrect. -15 is the vertex of k(x). The vertex of ax^2 + bx + c is -b/2a. So it has no relation to constants of the functions f(x) and g(x)
<u>C. Either f(x) or g(x) has a positive rate of change and the other has a negative rate of change.
</u>
- Incorrect. It refers to the value of ac. If one of a or c has opposite sign it makes k(x) to open down but it is not as per graph.
<u>D. f(x) could have a rate of change equal to 1 and g(x) could have a rate of change of 2.
</u>
- Correct. As per above statement, both linear equations could be positive as their sum and product is positive from the graphs of j(x) and k(x)
<u>E. f(x) could have a rate of change equal to 2 and g(x) could have a rate of change of –6.</u>
- Incorrect. It should result in decreasing function of j(x) with slope of -4 but it is increasing as per graph.
Answer:
2.083 < µ1 - µ2 < 5.917
Step-by-step explanation:
We will need to construct a 90% confidence interval for the difference of 2 means where the populations are normally distributed, and their variances are equal.
The calculations of the sample means and standard deviations are done for us.
Sample 1: Catalyst 1
n = 12, x = 85, s = 4
Sample 2: Catalyst 2
n = 10, x = 81, s = 5
See attached photo for the construction of the confidence interval...
Answer:
(x+9) (x+4)
Step-by-step explanation:
x²+13x+36
x²+9x+4x+36
x(x+9) +4(x+9)
(x+4) (x+9)