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sertanlavr [38]
3 years ago
6

Lavania is studying the growth of a population of fruit flies in her laboratory. After 6 days she had nine more than five times

as many fruit flies as when she began the study. If she observes 20 fruit flies on the first day of the study, write and evaluate an expression to find the population of fruit flies Lavania observed after 6 days
Mathematics
1 answer:
MatroZZZ [7]3 years ago
5 0

Answer:

Lavania observed 39 fruit flies after 6 days of observation

Step-by-step explanation:

Let x be the number of fruit flies on the first day of Lavania's study.

After 6 days she had nine more than five times as many fruit flies as when she began the study.

Five times as many fruit flies as when she began the study = 5x

Nine more than five times as many fruit flies as when she began the study=5x+9

The expression to find the population of fruit flies Lavania observed after 6 days is 5x+9

If she observes 20 fruit flies on the first day of the study, then x=6, then

5x+9=5\cdot 6+9=30+9=39

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6 0
3 years ago
Read 2 more answers
P(x)= 3x^3-5x^2-14x-4
nexus9112 [7]
   
\displaystyle\\
P(x)=3x^3-5x^2-14x-4\\\\
D_{-4}=\{-4;~-2;~\underline{\bf -1};~1;~2;~4\}\\\\
\text{We observe that } \frac{-1}{3} \text{ is a solution of the equation:}\\
3x^3-5x^2-14x-4=0\\\\


\displaystyle\\
\text{Verification}\\\\
3x^3-5x^2-14x-4=\\\\
=3\times\Big(-\frac{1}{3}\Big)^3-5\times\Big(-\frac{1}{3}\Big)^2-14\times\Big(-\frac{1}{3}\Big)-4=\\\\
=-\frac{1}{9}-\frac{5}{9}+\frac{14}{3}-4=\\\\
=-\frac{6}{9}+\frac{14}{3}-4=\\\\
=-\frac{6}{9}+\frac{42}{9}- \frac{4\times 9}{9}=\\\\
 =-\frac{6}{9}+\frac{42}{9}- \frac{36}{9}= \frac{42-6-36}{9}=\frac{42-42}{9}=\frac{0}{9}=0\\\\
\Longrightarrow~~~P(x)~\vdots~\Big(x+ \frac{1}{3}\Big)\\\\
\Longrightarrow~~~P(x)~\vdots~(3x+1)


\displaystyle\\
3x^3-5x^2-14x-4=0\\
~~~~~-5x^2 = x^2 - 6x^2\\
~~~~~-14x =-2x-12x \\
3x^3+x^2 - 6x^2-2x-12x-4=0\\
x^2(3x+1)-2x(3x+1) -4(3x+1)=0\\
(3x+1)(x^2-2x -4)=0\\\\
\text{Solve: } x^2-2x -4=0\\\\
x_{12}= \frac{-b\pm  \sqrt{b^2-4ac}}{2a}=\\\\=\frac{2\pm  \sqrt{4+16}}{2}=\frac{2\pm  \sqrt{20}}{2}=\frac{2\pm  2\sqrt{5}}{2}=1\pm\sqrt{5}\\\\
x_1 =1+\sqrt{5}\\
x_2 =1-\sqrt{5}\\
\Longrightarrow P(x)= 3x^3-5x^2-14x-4 =\boxed{(3x+1)(x-1-\sqrt{5})(x-1+\sqrt{5})}



7 0
3 years ago
Write to explain how you can break apart 16*34 into four simpler multiplication problems
____ [38]
16 is 10 +6, and 34 is 30+4
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4*6=24
add them up: 300+40+180+24=544

Using an array to break
<span>https://www.lake.k12.fl.us/cms/lib05/FL01000799/Centricity/Domain/7908/Topic%204%20Centers%204th%20g...</span>


8 0
4 years ago
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