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3 years ago

What is Y-3x=-2 and Y+x=-6

2 answers:

5 0

Rearranging the first equation gives:

$y=3x-2$

Substituting this into the other equation gives:

$y+x=-6
\\(3x-2)+x=-6
\\4x-2=-6
\\4x=-4 \\x=-1$

If x=-1:

$y+(-1)=-6
\\y=-5$

So x=-1, y=-5

Andrej [43]3 years ago

3 0

Y - 3x = -2 ⇒ 2y - 6x = -4
y + x = -6 ⇒ 2y + 2x = -12
 -8x = 8
 -8 -8
 x = -1
 y - 3(-1) = -2
 y + 3 = -2
 -3 -3
 y = -5
 (x, y) = (-1, -5)

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Graph the following piecewise function. 2 f(x)= x+3 if 4 < x <8 2x if x 28 2

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Answer:Find y: 5 + y = -15

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3 years ago

The Students' Conjectures Emily and Zach have two different polynomials to multiply: Polynomial product A: (4x2 – 4x)(x2 – 4) Po

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Complete Question:

Emily and Zach have two different polynomials to multiply: Polynomial product A: (4x2 – 4x)(x2 – 4) Polynomial product B: (x2 + x – 2)(4x2 – 8x) They are trying to determine if the products of the two polynomials are the same. But they disagree about how to solve this problem.

Answer:

$A = B$

Step-by-step explanation:

See comment for complete question

Given

$A: (4x^2 - 4x)(x^2 - 4)$

$B: (x^2 + x - 2)(4x^2 - 8x)$

Required

Determine how they can show if the products are the same or not

To do this, we simply factorize each polynomial

For, Polynomial A: We have:

$A: (4x^2 - 4x)(x^2 - 4)$

Factor out 4x

$A: 4x(x - 1)(x^2 - 4)$

Apply difference of two squares on x^2 - 4

$A: 4x(x - 1)(x - 2)(x+2)$

For, Polynomial B: We have:

$B: (x^2 + x - 2)(4x^2 - 8x)$

Expand x^2 + x - 2

$B:(x^2 + 2x - x - 2)(4x^2- 8x)$

Factorize:

$B:(x(x + 2) -1(x + 2))(4x^2- 8x)$

Factor out x + 2

$B:(x -1) (x + 2)(4x^2- 8x)$

Factor out 4x

$B:(x -1) (x + 2)4x(x- 2)$

Rearrange

$B: 4x(x - 1)(x - 2)(x+2)$

The simplified expressions are:

$A: 4x(x - 1)(x - 2)(x+2)$ and

$B: 4x(x - 1)(x - 2)(x+2)$

Hence, both polynomials are equal

$A = B$

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3 years ago

Haroldo, Xerxes, Regina, Shaindel, Murray, Norah, Stav, Zeke, and Georgia are

anastassius [24]

And this problem, we're trying to figure out the probability that Xerxes arrives first and Regina arrives last. Now, the first thing to note is that there are nine people. So if we list off nine different spaces, there's nine spaces and now the order in which they arrive could be any order. So for the first spot there are nine different ways that someone can show up, Anyone can show up first and then once someone has shown up first, the person who arrives second, there are eight different ways to choose that person. Similarly, the person who arrives third, there are seven people remaining, so there's seven ways to choose that and so on. And so there are actually nine factorial ways that the people can arrive to the party. Now if xerxes needs to be in the first spot and Regina needs to be in the last spot than in these remaining seven spaces, we can put any people, so there can be any ordering between xerxes and Regina. So there is seven factorial ways to order the people between xerxes and Regina. So the probability that we end up with is seven factorial divided by nine factorial. So that is seven factorial. And remember that nine factorial can be written as nine times eight times seven factorial. The seven factorial are going to cancel. We get 1/7 times eight which is equal 1/72 which is equal to approximately zero point 014 and that's it

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2 years ago

A manufacturing company produces valves in various sizes and shapes. One particular valve plate is supposed to have a tensile st

ss7ja [257]

Answer:

Step-by-step explanation:

Hello!

The researcher wants to test if the valve plates manufactured have the expected tensile strength of 5 lbs/mm. So he took a sample of 42 valve plates and measured their tensile strength, obtaining a sample mean of X[bar]= 5.0611 lbs/mm and a sample standard deviation of S=0.2803 lbs/mm.

The study variable is:

X: tensile strength of a valve plate (lbs/mm)

The parameter of interest is the mean tensile strength of the valve plates, μ.

If the claim is that the valve plates of the sample have on average tensile strength of 5 lbs/mm, symbolically: μ = 5

a) The statistic hypotheses are:

H₀: μ = 5

H₁: μ ≠ 5

b) To determine the critical values and rejection region of a hypothesis test you need three to determine three factors of the hypothesis test:

1) The statistical hypothesis.

2) The significance level.

3) The statistic to use for the analysis.

The statistic hypothesis determines the number of critical values and the direction of the rejection region, in this case, the test is two-tailed you will have two critical values and the rejection region will be divided into two.

With the statistic, you will determine the distribution under which you will work and the significance level determines the probability of rejecting the null hypothesis.

To study the population mean you need that the variable of interest has at least a normal distribution, there is no information about the distribution of the study variable but the sample size is large enough n≥30, so you can apply the central limit theorem to approximate the distribution of the sample mean to normal: X[bar]≈N(μ;σ²/n)

Thanks to this approximation it is valid to use an approximation of the standard normal distribution for the test:

$Z= \frac{X[bar]-Mu}{\frac{Sigma}{\sqrt{n} } }$ ≈N(0;1)

The critical values are:

$Z_{\alpha /2}= Z_{0.05}= -1.648$

$Z_{1-\alpha /2}= Z_{0.95}= 1.648$

You will reject the null hypothesis if $Z_{H_0}$ ≤-1.648 or if $Z_{H_0}$ ≥1.648

You will not reject the null hypothesis if -1.648< $Z_{H_0}$ <1.648

$Z_{H_0}= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } }= \frac{5.0611-5}{\frac{0.2803}{\sqrt{42} } }= 1.41$

d) The value of the statistic is between the two critical values so the decision is to not reject the null hypothesis. Then using a significance level of 10% there is no significant evidence to reject the null hypothesis so the valve plates have on average tensile strength of 5 lbs/mm.

e) The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis). If the test is two-tailed, so is the p-value, you can calculate it as:

P(Z≤-1.41) + P(Z≥1.41)= P(Z≤-1.41) + (1 - P(Z≤1.41))= 0.079 + ( 1 - 0.921)= 0.158

p-value: 0.158

I hope it helps!

5 0

3 years ago