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Natasha2012 [34]
2 years ago
13

What polynomial has a graph that passes through the given points?

Mathematics
1 answer:
Evgen [1.6K]2 years ago
3 0
The answer is <span>B. y = x^3 + 4x^2 + 2x - 2 

A line that passes through all given point is the correct choice. Now, substitute x and y in all of the choices:

</span>B. y = x³ + 4x²<span> + 2x - 2 
Point 1: </span><span>(-2, 2) 
x = -2
y = 2
____
2 = (-2)</span>³ + 4 *(-2)² + 2 * (-2) - 2
2 = -8 + 4 * 4 + (-4) - 2
2 = -8 + 16 - 4 - 2
2 = 2
_____

Point 2: (-1, -1) 
x = -1
y = -1
____
-1 = (-1)³ + 4 *(-1)² + 2 * (-1) - 2
-1 = -1 + 4 * 1 + (-2) - 2
-1 = -1 + 4 - 2 - 2 
-1 = -1
____

Point 3: (1, 5) 
x = 1
y = 5
____
5 = (1)³ + 4 *(1)² + 2 * 1 - 2
5 = 1 + 4 * 1 + 2 - 2
5 = 1 + 4 + 2 - 2
5 = 5
____

Point 4: (3, 67) 
x = 3
y = 67
____
67 = (3)³ + 4 *(3)² + 2 * (3) - 2
67 = 27 + 4 * 9 + 6 - 2
67 = 27 + 36 + 6 - 2
67 = 67

So, line B passes through all choices.
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Can someone please help me figure out what’s 18 3/4 as a decimal
dmitriy555 [2]

Answer:

18.75

Step-by-step explanation:

If you covert this into a mixed fraction it would be 75/4 (4*18 is 72 then add the 3 in the numerator) then divide, 75/4 = 18.75 (sorry if explanation is bad)

7 0
2 years ago
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There are 250 wolves in a national park. the wolf population is increasing at a rate of 16% per year. write an exponential model
Helga [31]

\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ A=250(1 + 0.16)^{t}\implies A=250(1.16)^t \\\\[-0.35em] ~\dotfill

A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &1000\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ 1000=250(1.16)^t\implies \cfrac{1000}{250}=1.16^t\implies 4=1.16^t \\\\\\ \log(4)=\log(1.16^t)\implies \log(4)=t\log(1.16) \\\\\\ \cfrac{\log(4)}{\log(1.16)}=t\implies \stackrel{\textit{about 9 years and 4 months}}{9.34\approx t}

7 0
1 year ago
What is the arc length S what is shown below?
Solnce55 [7]

Answer:

  14 cm

Step-by-step explanation:

The applicable formula is ...

  s = rθ

  s = (7 cm)(2) = 14 cm

3 0
2 years ago
Please explain your answer
Ymorist [56]

Answer:

51

Step-by-step explanation:

11+(-7)^2-9 - original

11+49-9 - square the -7, since its in brackets the negative applies too and a negative x a negative = positive, so it ends up as 7x7+49

60-9 - add both positives 11+49=60

51 - subtract 9 from 60, 60-9=51

7 0
2 years ago
It is believed that 36% of the US population has never been married, 32% are divorced, 27% are married, and 5% are widowed. You
Katena32 [7]

Answer: the smallest number of people required for the sample to meet the conditions for performing inference is 100

Step-by-step explanation:

Given that;

36% of US population has never been married

32% are divorced

27% are married

5% are widowed

Taking a simple random sample of individuals to test this claim;

we need expected count in each cell to be at least 5, here the smallest proportion is 5% = 0.05

so we only need to satisfy condition for its expected count;

n × 0.05 ≥ 5

n = 5 / 0.05 = 100

Therefore the smallest number of people required for the sample to meet the conditions for performing inference is 100

6 0
2 years ago
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