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3 years ago

Determine if the equation x^2 + 3y^2= 3 defines y as a function of x

Mathematics

1 answer:

belka [17]3 years ago

4 0

Answer:

y is NOT a function.

Step-by-step explanation:

The equation given to us is:

x² + 3y² = 3

Rearrange the equation:

3y² = 3 - x²

y² = (3 - x²)/3

y² = 1 - (x²)/3

y = ±√(1 - x²/3)

For any equation to be a function, there should be only one output for one input. Which means that for any value of x, there should be only one value of y. However, in this equation, as the underroot gives two values of any terms under it, it shows that if we put any value of x, we'll get 2 values of y. Therefore, y is not a function.

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Question 2 i have no idea with functions

sergey [27]

Answer:

the range of all the function is [-1, + infinity[

but when it limits the domain it gonna be

(-1,0,3,8)

3 0

3 years ago

In a study of the effect of college student employment on academic performance, the following summary statistics for GPA were re

11Alexandr11 [23.1K]

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. The population standard deviations are not known. Let μemployed(μ1) be the sample mean of students who are employed and μnot employed(μ2) be the sample mean of students who are not employed

The random variable is μ1 - μ2 = difference in the mean of the employed and unemployed students.

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 < μ2 H1 : μ1 - μ2 < 0

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(μ1 - μ2)/√(s1²/n1 + s2²/n2)

From the information given,

μ1 = 3.22

μ2 = 3.33

s1 = 0.475

s2 = 0.524

n1 = 172

n2 = 116

t = (3.22 - 3.33)/√(0.475²/172 + 0.524²/116)

t = - 1.81

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [0.475²/172 + 0.524²/116]²/[(1/172 - 1)(0.475²/172)² + (1/116 - 1)(0.524²/116)²] = 0.00001353363/0.00000005878

df = 230

We would determine the probability value from the t test calculator. It becomes

p value = 0.036

Since alpha, 0.05 > than the p value, 0.036, then we would reject the null hypothesis.

Therefore, at a 5% significant level, this information support the hypothesis that for students at this university, those who are not employed have a higher mean GPA than those who are employed

3 0

3 years ago

Which ordered pair is a solution of the system of equations?<br><br> y = 3x + 1<br> y = 5x - 1

kodGreya [7K]

Answer:

y=3x+1=4

y=5x-1=4

Step-by-step explanation:

DO THE MATH

5 0

3 years ago

What is the perimeter of the trapezoid with vertices Q(8, 8), R(14, 16), S(20, 16), and T(22, 8)? Round to the nearest hundredth

EleoNora [17]

Check the picture below.

so... you can pretty much see how long RS and QT are, you can just count the units off the grid.

now, let's find QR's length

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&Q&(~ 8 &,& 8~) 
% (c,d)
&R&(~ 14 &,& 16~)
\end{array}~~ 
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
QR=\sqrt{(14-8)^2+(16-8)^2}\implies QR=\sqrt{6^2+8^2}
\\\\\\
QR=\sqrt{36+64}\implies QR=\sqrt{100}\implies QR=10$

and let's also find the length for ST

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&S&(~ 20 &,& 16~) 
% (c,d)
&T&(~ 22 &,& 8~)
\end{array}~ 
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
ST=\sqrt{(22-20)^2+(8-16)^2}\implies ST=\sqrt{2^2+(-8)^2}
\\\\\\
ST=\sqrt{4+64}\implies ST=\sqrt{68}\implies ST=\sqrt{4\cdot 17}
\\\\\\
ST=\sqrt{2^2\cdot 17}\implies ST=2\sqrt{17}$

so, add the lengths of all sides, and that's the perimeter of the trapezoid.

8 0

4 years ago

Read 2 more answers

I need help on #19 and 20<br> please help !!!

tekilochka [14]

-3x - 3y > 5
-3x + 3y - 3y > 3x + 5
-3y > 3x + 5
-3 -3
y < -x - 1²/₃

The answer is C.

y < |x + 4| + 2

The answer is B.

3 0

3 years ago