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3 years ago

Which statement describes the system of equations?

Mathematics

2 answers:

Kruka [31]3 years ago

6 0

Answer: The system has infinitely solutions.

Step-by-step explanation:

The given system of equations : -

$-5x-4y=-4\\\Rightarrow\ -5x-4y+4=0-----(1)\\\\25x+ 20y = 20\\\Rightarrow\ 25x+20y-20=0----(2)$

Compare these equation with $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ respectively , we get

$a_1=-5\ ;b_1=-4\ ;\ c_1=4$

$a_2=25\ ;b_2=20\ ;\ c_2=-20$

Now, $\dfrac{a_1}{a_2}=\dfrac{-5}{25}=\dfrac{-1}{5}$

$\dfrac{b_1}{b_2}=\dfrac{-4}{20}=\dfrac{-1}{5}$

$\dfrac{c_1}{c_2}=\dfrac{4}{-20}=\dfrac{-1}{5}$

Thus , $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}=\dfrac{-1}{5}$

It means these lines are coincident, thus they have infinite number of solutions.

qwelly [4]3 years ago

3 0

Answer:

Step-by-step explanation:

-5x-4y=-4 ...(1)

25x+ 20y = 20 ....(2)

multiply (1) by -5 you have : 25x+ 20y = 20 ....(2) same equation , same line

so : The system has infinitely solutions.

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lys-0071 [83]

Answer:

the answer is c. no relationship

4 0

3 years ago

Read 2 more answers

A normally distributed random variable with mean 4.5 and standard deviation 7.6 is sampled to get two independent values, X1 and

mr Goodwill [35]

Answer:

Bias for the estimator = -0.56

Mean Square Error for the estimator = 6.6311

Step-by-step explanation:

Given - A normally distributed random variable with mean 4.5 and standard deviation 7.6 is sampled to get two independent values, X1 and X2. The mean is estimated using the formula (3X1 + 4X2)/8.

To find - Determine the bias and the mean squared error for this estimator of the mean.

Proof -

Let us denote

X be a random variable such that X ~ N(mean = 4.5, SD = 7.6)

Now,

An estimate of mean, μ is suggested as

$\mu = \frac{3X_{1} + 4X_{2} }{8}$

Now

Bias for the estimator = E(μ bar) - μ

= $E( \frac{3X_{1} + 4X_{2} }{8}) - 4.5$

= $\frac{3E(X_{1}) + 4E(X_{2})}{8} - 4.5$

= $\frac{3(4.5) + 4(4.5)}{8} - 4.5$

= $\frac{13.5 + 18}{8} - 4.5$

= $\frac{31.5}{8} - 4.5$

= 3.9375 - 4.5

= - 0.5625 ≈ -0.56

∴ we get

Bias for the estimator = -0.56

Now,

Mean Square Error for the estimator = E[(μ bar - μ)²]

= Var(μ bar) + [Bias(μ bar, μ)]²

= $Var( \frac{3X_{1} + 4X_{2} }{8}) + 0.3136$

= $\frac{1}{64} Var( {3X_{1} + 4X_{2} }) + 0.3136$

= $\frac{1}{64} ( [{3Var(X_{1}) + 4Var(X_{2})] }) + 0.3136$

= $\frac{1}{64} [{3(57.76) + 4(57.76)}] } + 0.3136$

= $\frac{1}{64} [7(57.76)}] } + 0.3136$

= $\frac{1}{64} [404.32] } + 0.3136$

= $6.3175 + 0.3136$

= 6.6311

∴ we get

Mean Square Error for the estimator = 6.6311

6 0

3 years ago

Y=3/2x+2 <br> 5x-y=5<br> At what point do they meet?

RSB [31]

(2,5) ...........................................................................................

7 0

3 years ago

A certain number, formed of two digits is seven times the sum of its digits it is also 27 less than the number if formed by reve

notsponge [240]

Answer:

Step-by-step explanation:

7 0

3 years ago

A(1)=20

Paladinen [302]

Answer:

-14

Step-by-step explanation:

You've got a(1)=20

a(1) means a(n) when n=1

the sequence is telling you to take the previous value of a(n), which is a(n-1) and subtract 17

then:

a(2) = a(1)-17 = 20 - 17 = 3

a(3) = a(2) - 17 = 3-17 = -14

3 0

3 years ago