The line y = 2x +k is a tangent to the curve x² + 2xy + 20 = 0.

-3x+4y=12 and 2x+y=-8. How do you solve this using substitution ?

elena-s [515]

Answer:

in point from: (-4,0) in equation from: x=-4,y=0

Step-by-step explanation:

8 0

2 years ago

Rewrite the equation by completing the squares x^2-x-20

yuradex [85]

Answer: x = ¹/₂ ± √⁸¹

------------

2

Step-by-step explanation:

First write out the equation

x² - x - 20

Now we now write the equation by equating to 0

x² - x - 20 = 0

We now move 20 to the other side of the equation. So

x² - x = 20,

We now add to both side of the equation square of the half the coefficient of the (x) and not (x²) which is (1) . So, the equation now becomes

x² - x + ( ¹/₂ )² = 20 + ( ¹/₂ )²

x² - ( ¹/₂ )² = 20 + ¹/₄

( x - ¹/₂ )² = 20 + ¹/₄, we now resolve the right hand side expression into fraction

( x - ¹/₂ )² = ⁸¹/₄ when the LCM is made 4

Taking the square root of both side to remove the square,we now have

x - ¹/₂ = √⁸¹/₄

x - ¹/₂ = √⁸¹/₂

Therefore,

x = ¹/₂ ± √⁸¹

-----------

2

3 0

3 years ago

PLEASE LOOK AT PHOTO! WHOEVER ANSWERS CORRECTLY I WILL MARK BRAINIEST!!

Andrei [34K]

Answer:

(a) HFE ,,, EFH

b) GF ,, FE

c)F

3 0

3 years ago

A dairy scientist is testing a new feed additive. She chooses 13 cows at random from a large population of cows. She randomly as

mina [271]

Answer:

Step-by-step explanation:

Given that a dairy scientist is testing a new feed additive. She chooses 13 cows at random from a large population of cows. She randomly assigns nold = 8 to get the old diet, and nnew = 5 to get the new diet including the additive.

From the data given we get the following

N Mean StDev SE Mean

Sample 1 8 43 5.1824 1.832

Sample 2 5 73 21.0832 9.429

df = 11

Std dev for difference = 13.3689

a) Yes the two are independent. The two sets of cows randomly chosen are definitely independent. Paired means equal number should be there and homogeneous conditions should be maintained.

b) Enclosed

c) Comparison of two means is the test recommended here. Because independent samples are used.\

d) Test statistic= -3.1233

(because of unequal variances we use that method)

95% confidence interval = ( -56.6676 , -3.3324 )

p value <0.05 our alpha

So reject null hypothesis.

The two means are statistically significantly different.

3 0

3 years ago

In a recent year, Washington State public school students taking a mathematics assessment test had a mean score of 276.1 and a s

Oksi-84 [34.3K]

Answer:

a) $\mu_{\bar x} =\mu = 276.1$

$\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3$

b) From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)$

c) $P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)$

$P(Z\geq2.070)=1-P(Z$

Step-by-step explanation:

Let X the random variable the represent the scores for the test analyzed. We know that:

$\mu=E(X) = 276.1 , \sigma=Sd(X) = 34.4$

And we select a sample size of 64.

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Part a

For this case the mean and standard error for the sample mean would be given by:

$\mu_{\bar x} =\mu = 276.1$

$\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3$

Part b

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)$

Part c

For this case we want this probability:

$P(\bar X \geq 285)$

And we can use the z score defined as:

$z=\frac{\bar x -\mu}{\sigma_{\bar x}}$

And using this we got:

$P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)$

And using a calculator, excel or the normal standard table we have that:

$P(Z\geq2.070)=1-P(Z$

8 0

3 years ago