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3 years ago

Solve system by elimination 6. 2x + 5y = 144x + 2 y = -4

2 answers:

7 0

Step by step:
Multiply the first one by -2 to be able to eliminate the x’s
-4x-10y=-28
Add them
-4x-10y=-28
4x+2y=-4
——————-
X’s cancel out your left with
-8y=-32
Divide by -8 to get y alone
Y= 4
Plug in for y to get x
4x+2(4)=-4
4x+8=-4
-8 -8
————-
4x=-12
x=-3
(-3,4)

forsale [732]3 years ago

3 0

Answer:

x=−3 and y=4

Step-by-step explanation:

Multiply the first equation by -2,and multiply the second equation by 1.

−2(2x+5y=14)

1(4x+2y=−4)

Becomes:

−4x−10y=−28

4x+2y=−4

Add these equations to eliminate x:

−8y=−32

Then solve−8y=−32for y:

−8y=−32

−8y

−8

−32

−8

(Divide both sides by -8)

y=4

Now that we've found y let's plug it back in to solve for x.

Write down an original equation:

2x+5y=14

Substitute4foryin2x+5y=14:

2x+(5)(4)=14

2x+20=14(Simplify both sides of the equation)

2x+20+−20=14+−20(Add -20 to both sides)

2x=−6

−6

(Divide both sides by 2)

x=−3

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Answer:

The Fundamental Theorem of Algebra assures that any polynomial f(x)=0 whose degree is n ≥1 has at least one Real or Imaginary root. So by the Theorem we have infinitely solutions, including imaginary roots ≠ 2i

Step-by-step explanation:

1) This claim is mistaken.

2) The Fundamental Theorem of Algebra assures that any polynomial f(x)=0 whose degree is n ≥1 has at least one Real or Imaginary root. So by the Theorem we have infinitely solutions, including imaginary roots ≠ 2i with real coefficients.

$a_{0}x^{n}+a_{1}x^{2}+....a_{1}x+a_{0}$

For example:

3) Every time a polynomial equation, like a quadratic equation which is an univariate polynomial one, has its discriminant following this rule:

$\Delta < 0\\b^{2}-4*a*c$

We'll have n different complex roots, not necessarily 2i.

For example:

Taking 3 polynomial equations with real coefficients, with

$\Delta < 0$

$-4x^2-x-2=0 \Rightarrow S=\left \{ x'=-\frac{1}{8}-i\frac{\sqrt{31}}{8},\:x''=-\frac{1}{8}+i\frac{\sqrt{31}}{8} \right \}\\-x^2-x-8=0 \Rightarrow S=\left\{\quad x'=-\frac{1}{2}-i\frac{\sqrt{31}}{2},\:x''=-\frac{1}{2}+i\frac{\sqrt{31}}{2} \right \}\\x^2-x+30=0\Rightarrow S=\left \{ x'=\frac{1}{2}+i\frac{\sqrt{119}}{2},\:x''=\frac{1}{2}-i\frac{\sqrt{119}}{2} \right \}\\(...)$

2.2) For other Polynomial equations with real coefficients we can see other complex roots ≠ 2i. In this one we have also -2i

$x^5\:-\:x^4\:+\:x^3\:-\:x^2\:-\:12x\:+\:12=0 \Rightarrow S=\left \{ x_{1}=1,\:x_{2}=-\sqrt{3},\:x_{3}=\sqrt{3},\:x_{4}=2i,\:x_{5}=-2i \right \}\\$

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3 years ago

Functionally important traits in animals tend to vary little from one individual to the next within populations, possibly becaus

Jet001 [13]

Answer:

The 95% confidence interval for the standard deviation is (0.14, 0.54).

Step-by-step explanation:

The complete data and question is:

Sloth CW Ratios ; {1.5 , 1.09 , 0.98 , 1.42 , 1.49 , 1.25}

The 95% confidence interval for the standard deviation of this data is < σ < (two decimals - include the leading zero) .

Solution:

Compute the sample standard deviation as follows:

$\bar x=\frac{1}{n}\sum x=\frac{1}{6}\times 7.73=1.2883\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{6-1}\times 0.2387}=0.2185$

The (1 - α)% confidence interval for the variance is:

$CI=\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2}}$

Confidence level = 95%

⇒ α = 0.05

The degrees of freedom is,

df = n - 1 = 6 - 1 = 5

Compute the critical values of Chi-square:

$\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.025,5}=12.833\\\\\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{0.975,5}=0.831$

*Use a Chi-square table.

Compute the 95% confidence interval for the variance as follows:

$CI=\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2}}$

$=\frac{5\times (0.2185)^{2}}{12.833}$

Thus, the 95% confidence interval for the standard deviation is (0.14, 0.54).

8 0

4 years ago

G(z) = 3z + 8 g(2w) =

Dima020 [189]

Answer:

$g(2w)=6w+8$

Step-by-step explanation:

We know that $g(z)=3z+8$

And we want to find $g(2w)$

So, we will simply substitute 2w for z. This yields:

$g(2w)=3(2w)+8$

Distribute. Therefore:

$g(2w)=6w+8$

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3 years ago

In a certain triangle x,y,z represents side lengths if x=7 and z=5 what must be true about y

irga5000 [103]

Answer:

$2 < y < 12$

Step-by-step explanation:

Given

$x = 7$

$z = 5$

Required

What must be true about y?

To answer this, we first calculate the range as follows;

$Minimum = |x - z|$

and

$Maximum = |x + z|$

For Minimum, we have:

$Minimum = |7 - 5|$

$Minimum = |2|$

$Minimum = 2$

For Maximum, we have:

$Maximum = |7 + 5|$

$Maximum = |12|$

$Maximum = 12$

The values of y are then bounded by the following:

$Minimum < y < Maximum$

This gives

$2 < y < 12$

4 0

3 years ago

Decide whether the sequence Is a arithmetic, geometric, or neither 5,1,-3,-7

IrinaK [193]

Answer:

Arithmetic

Step-by-step explanation:

5-4=1

1-4=-3

-3=4=-7

8 0

3 years ago

Read 2 more answers

Solve system by elimination 6. 2x + 5y = 144x + 2 y = -4​

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