How can I solve the following systems using Gaussian elimination method, w+2x-y=4, x-y=3 , w+2x-2y=7 2u+4v+w+7x=7?​

9514 1404 393

Answer:

  x = {-0.5-√1.25, -0.5+√1.25, 2, -0.5+i√0.75, -0.5-i√0.75}

Step-by-step explanation:

I like to use a graphing calculator to find clues as to the roots of higher-degree polynomials. Here, we see that x=2 is the only real rational root. Dividing that out by synthetic division, we see the remaining quartic factor is ...

  2x^5 -6x^3 -4x^2 -2x +4 = 0

  2(x -2)(x^4 +2x^3 +x^2 -1) = 0

We can recognize that the quartic factor is actually the difference of two squares:

  x^4 +2x^3 +x^2 -1 = (x^2 +x)^2 -1 = 0

So it resolves to two quadratic factors.

  (x^2 +x +1)(x^2 +x -1) = 0

One will have real roots, as shown by the graph. The other will have complex roots.

  x^2 +x + 1/4 = 1 +1/4 . . . . complete the square for the factor with real roots

  (x +1/2)^2 = 5/4

  x = -1/2 ± √(5/4) . . . . . . irrational real roots

__

  x^2 +x = -1 . . . . . . . . . . the quadratic factor with complex roots

  (x +1/2)^2 = -1 +1/4 . . . complete the square

  x = -1/2 ± i√(3/4) . . . . irrational complex roots

__

In summary, the values of x that satisfy the equation are ...

 x = 2

  x = -1/2 ± √(5/4)

  x = -1/2 ± i√(3/4)

Answer:

Step-by-step explanation:

[tex]\text{To maximize -4x + 5y + 70 subject to } \\ \\ 2x + y \le 8 --- (1) \\ \\ x + 3y \ge 5 --- (2) \\ \\ x + y \le 6----(3) \\ \\ x \ge 0, y \ge 0[/tex]

[tex]\text{From above equationn (1)} : 2x + y = 8 \\ \\ \text{Divide boths sides by 8} \\ \\ \dfrac{2x}{8} + \dfrac{y}{8} = \dfrac{8}{8}[/tex]

[tex]\dfrac{x}{4} + \dfrac{y}{8} = 1 \\ \\ x = 4; y = 8[/tex]

[tex]\text{From above equationn (2)} : x + 3y = 5 \\ \\ \text{Divide boths sides by 5} \\ \\ \dfrac{x}{5} + \dfrac{3y}{5} = \dfrac{5}{5} \\ \\ x = 5; \ y = 1.66[/tex]

[tex]\text{From above equation (3)} : x + y = 6 \\ \\ \text{Divide boths sides by 5} \\ \\ \dfrac{x}{6} + \dfrac{y}{6} = \dfrac{6}{6} \\ \\ x = 6; \ y = 6[/tex]

[tex]\text{From the image attached below, we can see the representation in the graph}[/tex]

-   [tex]\text{Now from equation (1) ad (III)} \\ \\ 2x + y = 8 \\ \\ x+y = 6[/tex]

    [tex]x[/tex]      [tex]= 2[/tex]

[tex]From : x + y = 6 \\ \\ 2 + y = 6 \\ \\ y = 6-2 \\ \\ y =4[/tex]

[tex]\text{From equation (1) and (II) } \\ \\ \ \ 2x + y = 8 \\ - \\ \ \ x + 3y = 5 \\ \\[/tex]

[tex]-5y = -2 \\ \\ y = \dfrac{2}{5} \ o r\ 0.4 \\ \\ From : 2x+ y = 8 \\ \\ 2x = 8 - \dfrac{2}{5} \\ \\ x = \dfrac{ 8 - \dfrac{2}{5} }{2} \\ \\ x = 3.8[/tex]

Answer:

to standard form

3x-y = -10

Answer:

-60

Explanation:

6x(2x-5) always do what's in the parentheses first

6x(-10)

= -60

Answer: where is the trapezoid

Step-by-step explanation:

Answer:

Gamba obtained 75 more votes than Ahmed.

Step-by-step explanation:

Given that in the finals of a singing contest at Greenvale Middle School, 300 students voted on which contestant they liked best, and Gamba got 35% of the votes while Ahmed got 10%, to determine how many more votes did Gamba get than Ahmed the following calculation should be performed:

(300 x 0.35) - (300 x 0.10) = X

105 - 30 = X

75 = X

Thus, Gamba obtained 75 more votes than Ahmed.

Answer:

yes

Step-by-step explanation:

Sugar and water amounts used change proportionately.

Answer:

D

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

6 square feet

Step-by-step explanation:

Area = L * w

26    =  L * 4 1/3

26  =   L * 13/3

L  = 26 divided by 13/3

L = 26 * 3/13  =  6

answer = 6

Answer:

is your answer

0.00483091

Step-by-step explanation:

Answer:

c=$60/3.  $20 dollars per class.

Step-by-step explanation:

I will try i had this unit last year, basically the diameter is 5 in this problem, which you multiply by pi (in this case I will use 3.14 as the shortened version since its on-going) which gives you 15.7, then you multiply that by 3 in this problem to get 47.1!

Answer:

Step-by-step explanation:

Volume of a cylinder formula = πr^2h

r (radius) = 5/2 = 2.5

h (height) = 3

Answer: 3π(2.5)^2 = 3π(6.25) = 18.75π cubic units

Answer:

a) y=4

b) x=8

Step-by-step explanation:

we know the a line is on point 4 on the y axis. So it would be y=4

The second one is the same. line b is on the point 8 on the x axis, so x=8

Answer:

Step-by-step explanation:

7/10 are black therefore 14/20 are black

Answer:

b. the average calorie count of a large number of fruit smoothie brands has a sampling distribution that is close to Normal.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Applying to this question:

The distribution of the number of calories in fruit smoothies is strongly skewed to the right. However, in a sample with a large number of fruit smoothies, the sampling distribution will be approximately normal, so the correct answer is given by option B.

Answer:

B

Step-by-step explanation:

The answer is (2x+6)(3x-1)

Answer:

area = 138 m²

Step-by-step explanation:

radius of large circle = 12 m

radius of small circle = 10 m

large circle area = πr² = (3.14)(12²) = 452.16 m²

small circle area = πr² = (3.14)(10²) =314 m²

452.16 - 314 = 138.16 m²

Answer:

We accept the null hypothesis, that is, that the mean weight of the cans is still of 12 ounces of fruit.

Step-by-step explanation:

Pineapple Corporation (PC) maintains that their cans have always contained an average of 12 ounces of fruit.

This means that the null hypothesis is: [tex]H_0: \mu = 12[/tex]

The production group believes that the mean weight has changed.

This means that the alternate hypothesis is:

[tex]H_a: \mu \neq 12[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

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

12 is tested at the null hypothesis:

This means that [tex]\mu = 12[/tex]

They take a sample of 15 cans and find a sample mean of 12.05 ounces and a sample standard deviation of .08 ounces.

This means, respectibely, that [tex]n = 15, X = 12.05, \sigma = 0.08[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{12.05 - 12}{\frac{0.08}{\sqrt{15}}}[/tex]

[tex]z = 2.42[/tex]

Pvalue of the test:

We are testing if the mean is different from a value, which means that the pvalue is 2 multiplied by 1 subtracted by the pvalue of z = 2.42.

Looking at the z-table, z = 2.42 has a pvalue of 0.9922

1 - 0.9922 = 0.0078

2*0.0078 = 0.0156

What conclusion can we make from the appropriate hypothesis test at the .01 level of significance?

0.0156 > 0.01. This means that at the 0.01 level, we accept the null hypothesis, that is, that the mean weight of the cans is still of 12 ounces of fruit.

Answer:

16

Step-by-step explanation:

Arrange date in order

3,5,8,12,15,16,20

find median  in this case its 12 also khown as 2nd quartile know  find the themedian of data that is on the right right of median or 2nd Quartiles  That will be the 3rd quartile...

Answer:

x=66

Step-by-step explanation:

Hello There!

∠BAC ≅ ∠CDB because in a parallelogram opposite angles are congruent

So all we have to do is solver for ∠BAC

Remember the sum of the triangles angles is 180 so to find ∠BAC

we subtract the given angles (83 and 31) from  180

180-83-31=66

so ∠BAC = 66

like stated before

∠BAC≅∠BDC so if ∠BAC = 66 then x also equals 66

Answer:

x = 66

Step-by-step explanation:

x = 66 degree

Answer:

i think x= 13.5

Step-by-step explanation:

Answer:4

Step-by-step explanation: Since she did it by completing the square, then you must do the same thing to get the same form so you can see what that number is.

So first subtract the constant which is -12 so we need to add twelve to get the constant on the other side. So we now have 2x^2+16x=12

The constant of the x^2 must be 1 so we need to divide by 2 on every term to get x^2+8x=12

So to make it so to get a perfect factor we need to divide the x factor by 2 so we get 4.

So the answer is 4 cause it is a perfect factor so were going to get 4 on both factors.

Answer:

4

Step-by-step explanation:

x²+2(x)(?)+?²=22

multiply by 2 because the coefficient of the higher degree in the first equation is 2

2x²+2(2(x)(?))+2(?²)-2(22)=0

2x²+4x(?)+2?²-44=0

Comparison

4x(?)=16x

?=4

2?²-44=-12

So, 2?²=-12+44

2?²=32

?²=16

?=4

Answer:

I hope this helps you

Step-by-step explanation:

1/8 ÷ 3 = 1/8 × 1/3

= 1/24

= 0.0416666667

Answer:

B) (1/2, -8)

Step-by-step explanation:

(1, -6) and (0, -10)

Midpoint formula:

((x1+x2)/2, (y1+y2)/2)

Solving for x:

(x1+x2)/2

(1 + 0)/2

1/2

Solving for y:

(y1+y2)/2

(-6-10)/2

(-16)/2

-8

Answer:

x = 2√3

Step-by-step explanation:

x² = √6² + √6²

x² = 6 + 6 = 12

x = √12 = 2√3

Answer:

9 . right triangle

Step-by-step explanation:

9. has right angle

Answer:

x = 35 degrees

Step-by-step explanation:

supplementary angles = 180 degrees

m<A + m<B = 180

(2x - 5) + 3x = 180

5x - 5 = 180

5x = 175

x = 35

Answer:

horizontal asymptote at y = 0

Step-by-step explanation:

According to the definition of asymptotes, it is a line that the function gets closer and closer to as x goes to plus or minus infinity. The definition clearly does not mention anything about the finite value of x.

However, crossing of asymptotes does not happen in the case of vertical asymptotes because for a given x, the function has only one value but the same y can be obtained for different values of x.

It is a common misconception that graphs of functions can’t cross the asymptotes. This is true only for vertical asymptotes. In fact, there are several examples of functions whose graphs cross the horizontal asymptote. For example:

f(x) = (xe)^((-x)^2)

The horizontal asymptote of the above function is y=0 but it still crosses the x axis at x=0.

hope that helps, I really don't know thought. Quite tricky