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2 years ago

What is the solution to the system of equationsY=4x+11 and y =-2x-1

Mathematics

1 answer:

pav-90 [236]2 years ago

5 0

For this case we must solve a system of two equations with two unknowns, given by "x" and "y".

We have:

$y = 4x + 11\ (1)\\y = -2x-1\ (2)$

We multiply (2) by -1:

$-y = 2x + 1\ (3)$

We add (1) and (3):

$y-y = 4x + 2x + 11 + 1\\0 = 6x + 12$

Clearing x:

$-12 = 6x\\x = \frac {-12} {6}\\x = -2$

We substitute $x = -2$ in (2)

$y = -2 (-2) -1\\y = 4-1\\y = 3$

Thus, the solution of the system is $(x, y) = (- 2,3)$

Answer:

The solution of the system is $(x, y) = (- 2,3)$

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Jamie lost 27 pounds in one year. on average how many pounds did jamie lose per month?

aleksandr82 [10.1K]

Since there are 12 months in a year, all we need to do is divide 27 pounds by 12, and we get that he lost, on average, 2.35lbs per month.

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3 years ago

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El precio de un ordenador portátil ha aumentado un 25% y posteriormente fue rebajado un cierto porcentaje.Calcule que porcentaje

ZanzabumX [31]

Answer:

Se requiere un 20 por ciento de descuento.

Step-by-step explanation:

(This exercise has been presented in Spanish and for that reason explanation will be held in the same language)

Sea $p_{o}$ el precio original del computador portatil, el nuevo precio es:

$p_{1} =\left(\frac{100\,\% + 25\,\%}{100\,\%} \right)\cdot p_{o}$

$p_{1} = 1.25\cdot p_{o}$

Si $p_{2} = p_{o}$ , entonces el porcentaje requerido para recuperar el precio original es:

$r = \left(1-\frac{p_{2}}{p_{1}} \right)\times 100\,\%$

$r = \left(1-\frac{p_{o}}{1.25\cdot p_{o}} \right)\times 100\,\%$

$r = \left(1-\frac{1}{1.25} \right)\times 100\,\%$

$r = 20\,\%$

Se requiere un 20 por ciento de descuento.

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2 years ago

in right triangle ABC, C is the right angle. Given measure of angle A = 40 degrees and a =6, which of the following are the leng

qaws [65]

Tan 40° = 6 / AC
AC = 6 / tan 40°
AC = 6 / .8391
AC = 7.15

AB² = 6² + 7.15²
AB² = 36 + 51.123
AB² = 87.12
AB = 9.33

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3 years ago

A machine, when working properly, produces 5% or less defective items. Whenever the machine produces significantly greater than

vovikov84 [41]

Answer:

The pvalue of the test is 0.0007 < 0.01, which means that we reject the null hypothesis and accept the alternate hypothesis that the percentage of defective items produced by this machine is greater than 5%.

Step-by-step explanation:

A machine, when working properly, produces 5% or less defective items.

This means that the null hypothesis is:

$H_0: p \leq 0.05$

Test if the percentage of defective items produced by this machine is greater than 5%.

This means that the alternate hypothesis is:

$H_a: p > 0.05$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.05 is tested at the null hypothesis:

This means that $\mu = 0.05, \sigma = \sqrt{0.05*0.95}$

A random sample of 300 items taken from the production line contained 27 defective items.

This means that $n = 300, X = \frac{27}{300} = 0.09$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.09 - 0.05}{\frac{\sqrt{0.05*0.95}}{\sqrt{300}}}$

$z = 3.18$

Pvalue of the test:

Testing if the mean is greater than a value, which means that the pvalue of the test is 1 subtracted by the pvalue of Z = 3.18, which is the probability of a finding a sample proportion of 0.09 or higher.

Looking at the Z-table, Z = 3.18 has a pvalue of 0.9993

1 - 0.9993 = 0.0007

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2 years ago

joel has 24 sports trophies. of the trophies, 1/8 are soccer trophies. how many soccer trophies does joel have?

hichkok12 [17]

Answer:

3 soccer trophies does Joel have

Step-by-step explanation:

As per the statement:

Joel has 24 sports trophies.

⇒Total sport trophies Joel have= 24

It is also given: of the trophies, 1/8 are soccer trophies

We have to find how many soccer trophies does Joel have.

$\text{Joel have soccer trophies} =\frac{1}{8} \cdot 24$

Simplify:

$\text{Joel have soccer trophies} =3$

Therefore, 3 soccer trophies does Joel have

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3 years ago

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