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3 years ago

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the system ax+by=c has the solution (2,-3), where dx+ey=f a, b, c, d, e, and f are non-zero real numbers. select all the systems

of equations with the same solution

2 answers:

exis [7]3 years ago

8 0

Answer: The system of equations which has the same solution as the given system are,

(A-D)x+(B-E)y= C-F , Dx+Ey=F

And, (A-5D)x+(B-5E)y=C-5F, Dx+Ey=F

Step-by-step explanation:

Since here, Given System is, Ax+By=C has the solution (2,-3)

Where, Dx+Ey= F

⇒ If (2,-3) is the solution of Ax+By=C

Then By the property of family of the solution,

⇒ (2,-3) must be the solution of (A-D)x+(B-E)y=C-F, (A-5D)x+(B-5E)y=C-5F.

But it is not the solution of equation, (2A+D)x+(2B+E)y=C+2F, Ax+(B+E)y=C

Therefore second and fifth options are not correct.

Also we can not go to the third option.

Thus, Only Option first and fourth are correct.

Natasha_Volkova [10]3 years ago

7 0

It is definitely A and D since the equation is dependent, the equation should be multiples of each other

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A researcher wants to estimate the percentage of all adults that have used the Internet to seek pre-purchase information in the

Lubov Fominskaja [6]

Answer:

The required sample size for the new study is 801.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

25% of all adults had used the Internet for such a purpose

This means that $\pi = 0.25$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

What is the required sample size for the new study?

This is n for which M = 0.03. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.03 = 1.96\sqrt{\frac{0.25*0.75)}{n}}$

$0.03\sqrt{n} = 1.96\sqrt{0.25*0.75}$

$\sqrt{n} = \frac{1.96\sqrt{0.25*0.75}}{0.03}$

$(\sqrt{n})^2 = (\frac{1.96\sqrt{0.25*0.75}}{0.03})^2$

$n = 800.3$

Rounding up:

The required sample size for the new study is 801.

4 0

3 years ago

17x-3y=4 2x-4y=1 the solution to the system of equations is

Burka [1]

ANSWER

$x=\frac{13}{62}$

and

$y= \frac{-9}{62}$ e have

EXPLANATION

$17x-3y=4---(1)$

$2x-4y=1$

Let us make y the subject and call it equation (2)

$2x=1+4y$

$x=\frac{1}{2}+2y--(2)$

We put equation (2) in to equation (1)

$17(\frac{1}{2}+2y)-3y=4$

$\frac{17}{2}+34y-3y=4$

$34y-3y=4- \frac{17}{2}$

Simplify to get,

$31y= \frac{8-17}{2}$

$31y= \frac{-9}{2}$

Divide both sides by 31,

$y= \frac{-9}{2} \div 31$

$y= \frac{-9}{2} \times \frac{1}{31}$

$y= \frac{-9}{62}$

We put this value in to equation (2) to get,

$x=\frac{1}{2}+2\times -\frac{9}{62}$

$x=\frac{1}{2} -\frac{18}{62}$

We collect LCM to obtain,

$x=\frac{31-18}{62}$

$x=\frac{13}{62}$

7 0

3 years ago

What is the answer for the equation (2+3x)4

balandron [24]

Answer:

8+12x

Step-by-step explanation:

7 0

3 years ago

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A glass is 4/7 full . Then 70cm3 of orange juice is poured in . The glass is now 2/4 full. What is the total volume of the glss

Korolek [52]

Let
x--------------> total volume of a glass

we know that
(4/7)x-70=(2/4)x------------> (4/7)x-70=(1/2)x--------> 2*(4/7)x-2*70=x
(8/7)x-140=x

<span>multiplied by 7 the expresion
</span>7*(8/7)x-7*140=7*x-----------> 8x-980=7x--------> x=980 cm³

the answer is
<span>the total volume of the glass is 980 cm</span>³

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3 years ago

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klemol [59]

Answer:

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Step-by-step explanation:

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3 years ago