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VLD [36.1K]
2 years ago
5

49x^2 + 42xy + 9y^2 Factor completely.

Mathematics
2 answers:
Oduvanchick [21]2 years ago
8 0
49x^2+42xy+9y^2

To factor a quadratic of the form ax^2+bx+c, you must find two values, j and k, which satisfy two conditions:

jk=ac=441 and j+k=42, so j and k must be 21 and 21.

Now replace bx with jx and kx in the original equation.

49x^2+21xy+21xy+9y^2  now factor 1st and 2nd pair of terms...

7x(7x+3y)+3y(7x+3y)  which is equal to

(7x+3y)(7x+3y)  which is equal to

(7x+3y)^2
mario62 [17]2 years ago
6 0
(7x-3y)^2 hope this helps
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In the past, the average age of employees of a large corporation has been 40 years. Recently, the company has been hiring older
Viktor [21]

Answer:

p_v =P(t_{(63)}>2.5)=0.0075  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the mean age is significantly higher than 45 years at 5% of significance.  

Step-by-step explanation:

1) Data given and notation  

\bar X=45 represent the mean height for the sample  

s=16 represent the sample standard deviation for the sample  

n=64 sample size  

\mu_o =40 represent the value that we want to test

\alpha=0.05 represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean age is higher than 40 years, the system of hypothesis would be:  

Null hypothesis:\mu \leq 40  

Alternative hypothesis:\mu > 40  

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

t=\frac{45-40}{\frac{16}{\sqrt{64}}}=2.5    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=64-1=63  

Since is a one right tailed test the p value would be:  

p_v =P(t_{(63)}>2.5)=0.0075  

Conclusion  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the mean age is significantly higher than 45 years at 5% of significance.  

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lilavasa [31]

Answer:

z = 2

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Step-by-step explanation:

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7) A photo booth charges a $500 fee for two hours at a party, plus $50 per additional hour. Cindy doesn't want to spend more tha
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Since the photo booth charges a $500 fee for two hours at the party and an additional 50 dollars per hour, we have:

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X is proportional to square root y where y&gt; 0
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Step-by-step explanation:

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