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Genrish500 [490]

3 years ago

14

A colony of bacteria starts with 50 organisms and quadruples each day. Write an exponential function, P(t), that represents the

population of the bacteria after t days.

1 answer:

Doss [256]3 years ago

5 0

P(t) = 50 x (4)^t ; 51200 bacteria

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Question 14 of 25What is the complete factorization of the polynomial below?x³+x² + 4x+4O A. (x-1)(x+2)(x+2)B. (x + 1)(x + 2)(x

mote1985 [20]

GIVEN:

We are given the following polynomial;

$x^3+x^2+4x+4$

Required;

We are required to factorize this polynomial completely.

Step-by-step explanation;

To factorize this polynomial, we start by grouping;

$(x^3+x^2)+(4x+4)$

We now take the common factor in each group;

$\begin{gathered} x^2(x+1)+4(x+1) \\ \\ (x^2+4)(x+1) \end{gathered}$

Next, we factorize the first parenthesis. To do this we set the equation equal to zero and solve for x as follows;

$\begin{gathered} x^2+4=0 \\ \\ Subtract\text{ }4\text{ }from\text{ }both\text{ }sides: \\ \\ x^2=-4 \\ \\ Take\text{ }the\text{ }square\text{ }root\text{ }of\text{ }both\text{ }sides: \\ \\ x=\pm\sqrt{-4} \\ \\ x=(\pm\sqrt{-1}\times\sqrt{4}) \\ \\ x=\pm2i \end{gathered}$

Therefore, the factors of the other parenthesis are;

$(x+2i)(x-2i)$

Therefore, the complete factorization of the polynomial is;

ANSWER:

$(x+1)(x+2i)(x-2i)$

Option C is the correct answer.

4 0

1 year ago

THERE ARE 3 BAGS OF APPLES WEIGHING A TOTAL OF 22 1/2 POUNDS. TWO OF THE BAGS WEIGH 6 3/8 POUNDS AND 3 1/4 POUNDS. HOW MUCH DOES

Mkey [24]

I wasn't going to click on this one, but the all-caps enthralled me and hypnotized me.

first off, let's change all the mixed fractions to "improper" and proceed from there, keep in mind that if we subtract the two bags' weight from the total, what's leftover is the 3rd bag's weight.

$\bf \stackrel{mixed}{22\frac{1}{2}}\implies \cfrac{22\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{45}{2}}
\\\\\\
\stackrel{mixed}{6\frac{3}{8}}\implies \cfrac{6\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{51}{8}}
\\\\\\
\stackrel{mixed}{3\frac{1}{4}}\implies \cfrac{3\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{13}{4}}\\\\
-------------------------------\\\\$

$\bf \stackrel{\textit{sum of the two bags}}{\cfrac{51}{8}+\cfrac{13}{4}}\impliedby \textit{our LCD is 8}\implies \cfrac{(1)51+(2)13}{8}
\\\\\\
\cfrac{51+26}{8}\implies \cfrac{77}{8}\\\\
-------------------------------\\\\
\stackrel{total}{\cfrac{45}{2}}~-~\stackrel{two~bags}{\cfrac{77}{8}}\impliedby \textit{our LCD is again 8}\implies \cfrac{(4)45-(1)77}{8}
\\\\\\
\cfrac{180~~-~~77}{8}\implies \cfrac{103}{8}\implies \stackrel{third~bag}{12\frac{7}{8}}$

3 0

4 years ago

A cylinder has a height of 14 centimeters and a radius of 11 centimeters. What is its

IRISSAK [1]

V≈5321.86
Sine the cylinder volume formula is pi*r^2*h.

4 0

3 years ago

Please need help ASAP!!!

Anarel [89]

The range of a function is the value of y where it is defined
Note the coordinates of the 3 points:

A(-2,0)
B(2,4)
C(3,-3)
As described the range (values of y) are 0,4 & -3
Hence Range ={ y ∈ -3 ≤ y ≤ 4}

4 0

3 years ago

Jasmine bought 6.4 pounds of chewy candy from the local confectionary store. If she gave 2.06 pounds of the candy to her little

lord [1]

Answer:

4.34 lbs

Step-by-step explanation:

6.4-2.06= 4.34

6 0

3 years ago

Read 2 more answers