Answer:
a. Domain : All Real Numbers
b. Range: y≥ -1
c. The x-intercepts are (0,0) and (-4,0)
d. The y-intercept is (0,0).
e. f(2)=3
f(-2)=-1
Step-by-step explanation:
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Answer:
4000 ft
Step-by-step explanation:
There is 3280.84 foot in km.
So, that makes the 4000 ft the longest.
if we have a number like say hmm 4, and we say hmmm √4 is ±2, it simply means, that if we multiply that number twice by itself, we get what's inside the root, we get the 4, so (+2)(+2) = 4, and (-2)(-2) = 4, recall that <u>minus times minus = plus</u>.
so, any when we're referring to even roots like
, the positive number, that can multiply itself an even amount of times, will produce a valid value, BUT the negative number that multiply itself an even amount of times, will also produce a valid value.
now, that's is not true for odd roots like
, because the multiplication of the negative number will not produce a valid value, let's put two examples on that.
![\bf \sqrt[3]{27}\implies \sqrt[3]{3^3}\implies 3\qquad because\qquad (3)(3)(3)=27 \\\\\\ however\qquad (-3)(-3)(-3)\ne 27~\hspace{8em}(-3)(-3)(-3)=-27 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \sqrt[3]{-125}\implies \sqrt[3]{-5^3}\implies -5\qquad because\qquad (-5)(-5)(-5)=-125 \\\\\\ however\qquad (5)(5)(5)\ne -125~\hspace{10em}(5)(5)(5)=125](https://tex.z-dn.net/?f=%5Cbf%20%5Csqrt%5B3%5D%7B27%7D%5Cimplies%20%5Csqrt%5B3%5D%7B3%5E3%7D%5Cimplies%203%5Cqquad%20because%5Cqquad%20%283%29%283%29%283%29%3D27%0A%5C%5C%5C%5C%5C%5C%0Ahowever%5Cqquad%20%28-3%29%28-3%29%28-3%29%5Cne%2027~%5Chspace%7B8em%7D%28-3%29%28-3%29%28-3%29%3D-27%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0A%5Csqrt%5B3%5D%7B-125%7D%5Cimplies%20%5Csqrt%5B3%5D%7B-5%5E3%7D%5Cimplies%20-5%5Cqquad%20because%5Cqquad%20%28-5%29%28-5%29%28-5%29%3D-125%0A%5C%5C%5C%5C%5C%5C%0Ahowever%5Cqquad%20%285%29%285%29%285%29%5Cne%20-125~%5Chspace%7B10em%7D%285%29%285%29%285%29%3D125)
so, when the root is an odd root, you will always get only one number that will produce the radicand.
The growth factor for the mass of bacteria is 2.8 in 1 week.
Step-by-step explanation:
Step 1:
It is given that the bacteria in the culture increase by 260% per week. Now we assign values to get a better understanding. If there were 1,000 bacteria in the culture at the start of the week there would be 1,000 + 260% at the week's end = 1,000 + 2,600 = 3,600 at the week's end.
Step 2:
To calculate the growth factor, we calculate the difference between the present value and the past value and divide it by the past value.
Here the past value is 1,000 and the present value is 2,600.
Growth factor = 
So the growth factor is 2.6 per week.
Answer:
y^2 +8y + 16
Step-by-step explanation:
6y^2 +2y +5 - (5y^2 -6y -11)
I distribute the minus sign
6y^2 +2y +5 - 5y^2 +6y +11
Then I put them vertical.
6y^2 +2y +5
-5y^2 +6y +11
------------------------
y^2 +8y + 16
This is in standard from since the exponential decreases.