Answer:
B. The maximum occurs at the function's x-intercept.
Step-by-step explanation:
Given table:
![\large\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} x & -5 & -4 & -3 & -2 & -1 & 0\\\cline{1-7} g(x) & -1 & 0 & -1 & -4 & -9 & -16\\\cline{1-7}\end{array}](https://tex.z-dn.net/?f=%5Clarge%5Cbegin%7Barray%7D%7B%7C%20c%20%7C%20c%20%7C%20c%20%7C%20c%20%7C%20c%20%7C%20c%20%7C%20c%20%7C%7D%5Ccline%7B1-7%7D%20x%20%26%20-5%20%26%20-4%20%26%20-3%20%26%20-2%20%26%20-1%20%26%200%5C%5C%5Ccline%7B1-7%7D%20g%28x%29%20%26%20-1%20%26%200%20%26%20-1%20%26%20-4%20%26%20-9%20%26%20-16%5C%5C%5Ccline%7B1-7%7D%5Cend%7Barray%7D)
From inspection of the table, we can see that:
and![g(-3) = -1](https://tex.z-dn.net/?f=g%28-3%29%20%3D%20-1)
This indicates <u>symmetry</u>.
The line of symmetry is the mid-point between the two x-values.
Therefore, the <u>line of symmetry</u> is x = -4
The vertex (minima/maxima) is on the line of symmetry, therefore the vertex is at (-4, 0). As the function decreases as x → 0, the vertex is a <u>maximum</u>.
As the y-value of the vertex is 0, the maximum occurs at the function's <u>x-intercept</u>.
Answer:
5
Step-by-step explanation:
29÷7=4.14
Well you can't have 4.14 boxes so you'll need 5 boxes
We know that:
Mean = 82 mm and SD = 10 mm ( standard deviation )
82 - 3 * SD = 82 - 3 * 10 = 82 - 30 = 52 mm
82 + 3 * SD = 82 + 3 * 10 = 82 + 30 = 112 mm
Population between 52 and 112 mm is within +/- 3 standard deviations from the mean.
By the 66- 95 - 99.7 % rule it is: 99.7% of the test group.
0.977 * 500 = 498.5
Answer:
99.7 % of the test group have a diastolic pressure between 52 and 112 mm, or 498 men.
Answer:
The quotient is : x+9
The remainder is : 13
Step-by-step explanation:
The question requires you to perform the long division method;
This will be;
![x-2\sqrt{x^2+7x-5}](https://tex.z-dn.net/?f=x-2%5Csqrt%7Bx%5E2%2B7x-5%7D)
start with the x term in x-2 and the first term in the function, x², to get x then multiply the x with x-2 to get x²-2x and perform the operation below;
x-2√x²+7x-5 -----------to first get x and then multiply x*[x-2]⇒x²-2x
- x²-2x+0 ------------perform subtraction of like terms
---------------------
9x-5 ----now divide this answer by x-2 ,starting with x and 9x
----------------------This will give , 9 then multiply 9 by x-2 to get 9x-18 and perform the subtraction operation as;
9x-5
- 9x-18
------------------------
13
So the answer will be; x+9 remainder 13
Answer:
The population be after 15 years is 171376.
Step-by-step explanation:
Given : A population of 110,000 grows 3% per years 15 years.
To find : How much will the population be after 15 years?
Solution :
Exponential growth population model is given by,
![P(t)=P_o(1+r)^t](https://tex.z-dn.net/?f=P%28t%29%3DP_o%281%2Br%29%5Et)
Where,
P(t) is the population at time (t)
is the initial value of the population
r=3%=0.03 is the annual rate of growth
t=15 is the time in years.
Substitute the value,
![P(t)=110000(1+0.03)^{15}](https://tex.z-dn.net/?f=P%28t%29%3D110000%281%2B0.03%29%5E%7B15%7D)
![P(t)=110000(1.03)^{15}](https://tex.z-dn.net/?f=P%28t%29%3D110000%281.03%29%5E%7B15%7D)
![P(t)=110000\times 1.5579](https://tex.z-dn.net/?f=P%28t%29%3D110000%5Ctimes%201.5579)
![P(t)=171376.41](https://tex.z-dn.net/?f=P%28t%29%3D171376.41)
Therefore, the population be after 15 years is 171376.