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3 years ago

Solve these simultaneous linear equation3x - 4y = 16x + 7y = 13

Mathematics

1 answer:

DiKsa [7]3 years ago

6 0

9514 1404 393

Answer:

(x, y) = (59/45, 11/15) ≈ (1.311, 0.733)

Step-by-step explanation:

A graphing calculator shows us the solution is not integer values, so we may find it easiest to solve these equations using the "cross-multiplication method."

Writing the equations in general form, we have ...

3x -4y -1 = 0

6x +7y -13 = 0

Then we can form an array of the coefficients, repeating the first column:

$\begin{array}{cccc}3&-4&-1&3\\6&7&-13&6\end{array}$

Forming differences of cross products involving adjacent pairs of columns gives ...

d1 = (3)(7) -(6)(-4) = 45

d2 = (-4)(-13) -(7)(-1) = 59

d3 = (-1)(6) -(-13)(3) = 33

Then the solutions are found from ...

1/d1 = x/d2 = y/d3

x = d2/d1 = 59/45

y = d3/d1 = 33/45 = 11/15

The solution is (x, y) = (59/45, 11/15) ≈ (1.311, 0.733).

_____

<em>Additional comment</em>

This takes longer to explain than to do. One reason we like it is that the number of math operations is slightly smaller than the number of math operations required for substitution or elimination. It is especially nice when the solution is not a pair of integers.

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F(x) = 4x – 10<br> g(x) = -8x2 + 6x – 10<br> Find: f(x) · g(x)

Lilit [14]

Answer: f(x) · g(x)=-32x³+104x²-100x+100

Step-by-step explanation:

Since we are given f(x) and g(x), all we have to do is multiply them together.

f(x) · g(x)=(4x-10)(-8x²+6x-10) [distribute by FOIL]

f(x) · g(x)=-32x³+24x²-40x+80x²-60x+100 [combine like terms]

f(x) · g(x)=-32x³+104x²-100x+100

Now, we have multiplied them together, we have f(x) · g(x)=-32x³+104x²-100x+100.

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3 years ago

Maria is play a game where you score -5 points each time you guess the correct answer.The goal is to get the lowest score.To win

oee [108]

Answer:

Step-by-step explanation:

Just notice that correct answers are whole numbers.

And, to win the game,Maria must have a score less than -80, it means she needs to score al least -85 ( it can not be -81, -82.. because 1 correct answer score -5, only multiples of -5 are accepted)

So, we take: $\frac{-85}{-5}$ = 7 correct answers to win the game.

Hope it will find you well.

5 0

3 years ago

Factorise x^2 - 8/X pls help

DochEvi [55]

Answer:

(x-2)(x^2 +2x +4)/x

Step-by-step explanation:

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4 0

3 years ago

Thirty-seven percent of all Americans drink bottled water more than once a week (Natural resources Defense Council, December 4,

lesantik [10]

Answer:

a) The sampling distribution for n=540 has a mean sample proportion of p=0.37 and a standard deviation of σs=0.0208.

b) probability = 0.99998

d) probability = 0.99874

e) You gain 0.12% in probability for an increase of 80% in sample size.

The increase in sample size is not justified by the increase in probability, for this margin of error (Δp=0.09).

Step-by-step explanation:

a) We have a known population proportion π=0.37 and we have to describe the sampling distribution when the sample size is n=540.

The mean sample proportion is expected to be the same as the population proportion:

$\bar p = \pi = 0.37$

The standard deviation of the sampling will be the population standard deviation divided by the square root of the sample size:

$\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.37*0.63}{540}}=\sqrt{0.000431667}=0.0208$

Then, we can say that the sampling distribution will have a p=0.37 and a standard deviation σs=0.0208.

b) We have to calculate the probability that the sample proportion will be within 0.09 of the population proportion.

We can calculate the z-value as:

$z_1=\dfrac{p_1-\bar p}{\sigma_s}=\dfrac{0.09}{0.0208}=4.3269\\\\\\z_2=\dfrac{p_2-\bar p}{\sigma_s}=\dfrac{-0.09}{0.0208}=-4.3269$

As the distribution is symmetrical, we can calculate the probabilty that he sample proportion will be within 0.09 of the population proportion as:

$P(|p-\bar p|$

probability = 0.99998

d. Now the sample is smaller (n=300), so the standard deviation of the samping distribution:

$\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.37*0.63}{300}}=\sqrt{0.000777}=0.0279$

We have to recalculate the z-scores:

$z_1=\dfrac{p_1-\bar p}{\sigma_s}=\dfrac{0.09}{0.0279}=3.2258\\\\\\z_2=\dfrac{p_2-\bar p}{\sigma_s}=\dfrac{-0.09}{0.0279}=-3.2258$

And the probability is:

$P(|p-\bar p|$

probability = 0.99874

e. The increase in sample size is 80%

$\Delta n\%=\dfrac{n_1}{n_2}-1=\dfrac{540}{300}-1=1.8-1=0.8=80\%$

and the increase in probability is 0.12%

$\Delta P\%=\dfrac{P_1}{P_2}-1=\dfrac{0.99998}{0.99874}-1=1.0012-1=0.0012=0.12\%$

You gain 0.12% in probability for an increase of 80% in sample size.

The increase in sample size is not justified by the increase in probability, for this margin of error (Δp=0.09).

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3 years ago

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horsena [70]

The answer is (x+1)x(3x-2)

5 0

3 years ago

Solve these simultaneous linear equation3x - 4y = 16x + 7y = 13​

Solve these simultaneous linear equation3x - 4y = 16x + 7y = 13