What is the equation x^2+12x-3=16 written in the form (x-p)^2=q using the method of completing the square ?

Solution :

a).

Given :

R = 0.636, [tex]$S_x = 99$[/tex], [tex]$S_y=113, M_x=108, M_y=129$[/tex]

Here R = correlation between the two variables

        [tex]$S_x , S_y$[/tex] =  sample standard deviations of the distance and travel time between the two train stops, respectively.

      [tex]$M_x, M_y$[/tex] = means of the distance and travel between two train stops respectively.

The slope of the regression line is given by :

Regression line, [tex]b_1[/tex]  [tex]$=R \times \left(\frac{S_y}{S_x}\right)$[/tex]

                            [tex]$=0.636 \times \left(\frac{113}{99}\right)$[/tex]

                            = 0.726

Therefore, the slope of the regression line [tex]b_1[/tex] is 0.726

The equation of the regression line is given by :

[tex]$\overline {y} = b_0+b_1 \overline x$[/tex]

The regression line also has to pass through the two means. That is, it has to pass through points (108, 129). Substituting these values in the equation of the regression line, we can get the value of the line y-intercept.

The y-intercept of the regression line [tex]$b_0$[/tex] is given by :

[tex]$b_0=M_y-(b_1 \times M_x)$[/tex]

  = 129 - (0.726 x 108)

  = 50.592

Therefore, the equation of the line is :

Travel time = 20.592 + 0.726 x distance

b).[tex]\text{ The slope of the line predicts that it will require 0.726 minutes}[/tex] for each additional mile travelled.

The intercept of the line, [tex]$b_0$[/tex] = 0.529 can be seen as the time when the distance travelled is zero. It does not make much sense in this context because  it seems we have travelled zero  distance in 50.529 minutes, but we could interpret it as that the wait time after which we start travelling and calculating the distance travelled and the additional time required per mile. Or we could view the intercept value as the time it takes to walk to the train station before we board the train. So this is a fixed quantity that will be added to travel time. It all depends on the interpretation.

c). [tex]$R^2=0.404$[/tex]

This means that the model accounts for around 40.4% variation in the travel time.

Answer:

[tex]\textbf{Hello!}[/tex]

[tex]\Longrightarrow2^2+2z=0[/tex]

[tex]\Longrightarrow x_{1,\:2}=\frac{-2\pm \sqrt{2^2-4\cdot \:1\cdot \:0}}{2\cdot \:1}[/tex]

[tex]\Longrightarrow \sqrt{2^2-4\cdot \:1\cdot \:0}[/tex]

[tex]\Longrightarrow =\sqrt{2^2-0}[/tex]

[tex]\Longrightarrow =\sqrt{2^2}[/tex]

[tex]\Longrightarrow=2[/tex]

[tex]\Longrightarrow x_{1,\:2}=\frac{-2\pm \:2}{2\cdot \:1}[/tex]

[tex]\Longrightarrow x_1=\frac{-2+2}{2\cdot \:1},\:x_2=\frac{-2-2}{2\cdot \:1}[/tex]

[tex]\Longrightarrow\frac{-2+2}{2\cdot \:1}[/tex]

[tex]\Longrightarrow =\frac{0}{2\cdot \:1}[/tex]

[tex]\Longrightarrow =\frac{0}{2}[/tex]

[tex]=0[/tex]

[tex]\Longrightarrow\frac{-2-2}{2\cdot \:1}[/tex]

[tex]\Longrightarrow =\frac{-4}{2\cdot \:1}[/tex]

[tex]\Longrightarrow =\frac{-4}{2}[/tex]

[tex]\Longrightarrow =-\frac{4}{2}[/tex]

[tex]=-2[/tex]

[tex]x=0,\:x=-2\Longleftarrow[/tex]

[tex]\underline{HOPE ~IT~HELPS}[/tex]

Answer:

See below

Step-by-step explanation:

We want to prove that

[tex]\sin(x)\tan(x) = \dfrac{1}{\cos(x)} - \cos(x), \forall x \in\mathbb{R}[/tex]

Taking the RHS, note

[tex]\dfrac{1}{\cos(x)} - \cos(x) = \dfrac{1}{\cos(x)} - \dfrac{\cos(x) \cos(x)}{\cos(x)} = \dfrac{1-\cos^2(x)}{\cos(x)}[/tex]

Remember that

[tex]\sin^2(x) + \cos^2(x) =1 \implies 1- \cos^2(x) =\sin^2(x)[/tex]

Therefore,

[tex]\dfrac{1-\cos^2(x)}{\cos(x)} = \dfrac{\sin^2(x)}{\cos(x)} = \dfrac{\sin(x)\sin(x)}{\cos(x)}[/tex]

Once

[tex]\dfrac{\sin(x)}{\cos(x)} = \tan(x)[/tex]

Then,

[tex]\dfrac{\sin(x)\sin(x)}{\cos(x)} = \sin(x)\tan(x)[/tex]

Hence, it is proved

Answer: x+y = 9, 2x+3y = 24

Step-by-step explanation:

Answer:

(a) There is a significant relationship between y and [tex]x_1, x_2, x_3, x_4[/tex]

(b) [tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45[/tex]

(c) [tex]SSE_{(x_2,x_3)} = 100[/tex]

(d) [tex]x_1[/tex] and [tex]x_4[/tex] are significant

Step-by-step explanation:

Given

[tex]y = 17.6+3.8x_1 - 2.3x_2 +7.6x_3 +2.7x_4[/tex] --- estimated regression equation

[tex]n = 30[/tex]

[tex]p = 4[/tex] --- independent variables i.e. x1 to x4

[tex]SSR = 1760[/tex]

[tex]SST = 1805[/tex]

[tex]\alpha = 0.05[/tex]

Solving (a): Test of significance

We have:

[tex]H_o :[/tex] There is no significant relationship between y and [tex]x_1, x_2, x_3, x_4[/tex]

[tex]H_a :[/tex] There is a significant relationship between y and [tex]x_1, x_2, x_3, x_4[/tex]

First, we calculate the t-score using:

[tex]t = \frac{SSR}{p} \div \frac{SST - SSR}{n - p - 1}[/tex]

[tex]t = \frac{1760}{4} \div \frac{1805- 1760}{30 - 4 - 1}[/tex]

[tex]t = 440 \div \frac{45}{25}[/tex]

[tex]t = 440 \div 1.8[/tex]

[tex]t = 244.44[/tex]

Next, we calculate the p value from the t score

Where:

[tex]df = n - p - 1[/tex]

[tex]df = 30 -4 - 1=25[/tex]

The p value when [tex]t = 244.44[/tex] and [tex]df = 25[/tex] is:

[tex]p =0[/tex]

So:

[tex]p < \alpha[/tex] i.e. [tex]0 < 0.05[/tex]

Solving (b): [tex]SSE(x_1 ,x_2 ,x_3 ,x_4)[/tex]

To calculate SSE, we use:

[tex]SSE = SST - SSR[/tex]

Given that:

[tex]SSR = 1760[/tex] ----------- [tex](x_1 ,x_2 ,x_3 ,x_4)[/tex]

[tex]SST = 1805[/tex]

So:

[tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4)} = 1805 - 1760[/tex]

[tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45[/tex]

Solving (c): [tex]SSE(x_2 ,x_3)[/tex]

To calculate SSE, we use:

[tex]SSE = SST - SSR[/tex]

Given that:

[tex]SSR = 1705[/tex] ----------- [tex](x_2 ,x_3)[/tex]

[tex]SST = 1805[/tex]

So:

[tex]SSE_{(x_2,x_3)} = 1805 - 1705[/tex]

[tex]SSE_{(x_2,x_3)} = 100[/tex]

Solving (d): F test of significance

The null and alternate hypothesis are:

We have:

[tex]H_o :[/tex] [tex]x_1[/tex] and [tex]x_4[/tex] are not significant

[tex]H_a :[/tex] [tex]x_1[/tex] and [tex]x_4[/tex] are significant

For this model:

[tex]y =11.1 -3.6x_2+8.1x_3[/tex]

[tex]SSE_{(x_2,x_3)} = 100[/tex]

[tex]SST = 1805[/tex]

[tex]SSR_{(x_2 ,x_3)} = 1705[/tex]

[tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45[/tex]

[tex]p_{(x_2,x_3)} = 2[/tex]

[tex]\alpha = 0.05[/tex]

Calculate the t-score

[tex]t = \frac{SSE_{(x_2,x_3)}-SSE_{(x_1,x_2,x_3,x_4)}}{p_{(x_2,x_3)}} \div \frac{SSE_{(x_1,x_2,x_3,x_4)}}{n - p - 1}[/tex]

[tex]t = \frac{100-45}{2} \div \frac{45}{30 - 4 - 1}[/tex]

[tex]t = \frac{55}{2} \div \frac{45}{25}[/tex]

[tex]t = 27.5 \div 1.8[/tex]

[tex]t = 15.28[/tex]

Next, we calculate the p value from the t score

Where:

[tex]df = n - p - 1[/tex]

[tex]df = 30 -4 - 1=25[/tex]

The p value when [tex]t = 15.28[/tex] and [tex]df = 25[/tex] is:

[tex]p =0[/tex]

So:

[tex]p < \alpha[/tex] i.e. [tex]0 < 0.05[/tex]

Hence, we reject the null hypothesis

Answer:

576

Step-by-step explanation:

5 square root 2 is 25

25 minus 1 is 24

24 square root 2 is 576

Answer:

25

Step-by-step explanation:

[tex](5\sqrt{(2-1)} ^{2}[/tex]

[tex](5\sqrt{1}) ^{2}[/tex]

Answer:

The equation of the line is [tex]y + 3 = m(x + 4)[/tex], in which m is found as such [tex]am = -1[/tex], considering a the slope of the given line.

Step-by-step explanation:

Equation of a line:

The equation of a line, in point-slope form, is given by:

[tex]y - y_0 = m(x - x_0)[/tex]

In which m is the slope and the point is [tex](x_0,y_0)[/tex]

Perpendicular lines:

If two lines are perpendicular, the multiplication of their slopes is -1.

Passes through the point (-4,-3)

This means that [tex]x_0 = -4, y_0 = -3[/tex]

So

[tex]y - y_0 = m(x - x_0)[/tex]

[tex]y - (-3) = m(x - (-4))[/tex]

[tex]y + 3 = m(x + 4)[/tex]

The equation of the line is [tex]y + 3 = m(x + 4)[/tex], in which m is found as such [tex]am = -1[/tex], considering a the slope of the given line.

Answer:

m = 6

n = 2√3

Step-by-step explanation:

Reference angle = 30°

Hypotenuse = 4√3

Opposite = n

Adjacent = m

✔️To find m, apply CAH:

Cos θ = Adj/Hypo

Substitute

Cos 30° = m/4√3

4√3 × Cos 30° = m

4√3 × √3/2 = m (cos 30 = √3/2)

(4*3)/2 = m

6 = m

m = 6

✔️To find n, apply SOH:

Sin θ = Opp/Hypo

Substitute

Sin 30° = n/4√3

4√3 × Sin 30° = n

4√3 × ½ = n (Sin 30 = ½)

2√3 = n

n = 2√3

9514 1404 393

Answer:

  True

Step-by-step explanation:

In a geometric sequence, the terms a[n+1] and a[n] are related by the common ratio. If the sequence is otherwise unspecified, two sequential terms may have any a relation you like.* Either could be larger or smaller than the other.

__

* If one is zero, the other must be as well. Multiplying 0 by any finite common ratio will give zero as the next term.

Answer:

n = 975

Step-by-step explanation:

[tex]a_1 = 5 = 5 \times 1\\a_2 = 10 = 5 \times 2\\\\Therefore, \ a_n = 5 \times n\\[/tex]

[tex]Given \ a_n = 4875\\\\So, a_n = 5 \times n \\\\=> 4875 = 5 \times n\\\\=>\frac{4875}{5} = n\\\\=> 975 = n[/tex]

Answer:

A. Whole numbers less than or equal to 100

Step-by-step explanation:

The domain is the set of x numbers that can be plugged in to a certain equation.

Since the capacity of this movie theater is 100, x can be between 0 and 100, inclusive.

Answer choice A makes sense because whole numbers are definitionally positive integers and this choice caps out at 100.

Answer:

The expected value for the person buying the insurance is of -$48.

Step-by-step explanation:

Expected value:

0.169% = 0.00169 probability of earning the death benefit of $100,000, subtracting 217, 100000 - 217 = $99,783.

100 - 0.169 = 99.831% = 0.99831 probability of losing $217.

What is the expected value for the person buying the insurance?

[tex]E = 0.00169*99783 - 0.99831*217 = -48[/tex]

The expected value for the person buying the insurance is of -$48.

Answer:

a) P(X > 10) = 0.6473

b) P(X > 20) = 0.4190

c) P(X < 30) = 0.7288

d) x = 68.87

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Mean equal to 23.

This means that [tex]m = 23, \mu = \frac{1}{23} = 0.0435[/tex]

(a) P(X >10)

[tex]P(X > 10) = e^{-0.0435*10} = 0.6473[/tex]

So

P(X > 10) = 0.6473

(b) P(X >20)

[tex]P(X > 20) = e^{-0.0435*20} = 0.4190[/tex]

So

P(X > 20) = 0.4190

(c) P(X <30)

[tex]P(X \leq 30) = 1 - e^{-0.0435*30} = 0.7288[/tex]

So

P(X < 30) = 0.7288

(d) Find the value of x such that P(X > x) = 0.05

So

[tex]P(X > x) = e^{-\mu x}[/tex]

[tex]0.05 = e^{-0.0435x}[/tex]

[tex]\ln{e^{-0.0435x}} = \ln{0.05}[/tex]

[tex]-0.0435x = \ln{0.05}[/tex]

[tex]x = -\frac{\ln{0.05}}{0.0435}[/tex]

[tex]x = 68.87[/tex]

Answer:

4.2025 [tex]\pi m^{2}[/tex]

Step-by-step explanation:

Answer:

1060

Step-by-step explanation:

Answer:

B. y + z = x

Step-by-step explanation:

x is an exterior angle of the triangle.

y and z are the opposite angles opposite the exterior angle.

The exterior angle theorem of a triangle states that the measure of an exterior angle equals the measure of the sum of the two angles opposite the exterior angle.

Thus:

y + z = x

Step-by-step explanation:

{x:x is an integer where x>-3 and x<3}

x=17/2

don't forget to follow me

Given:

The given statements are:

[tex]p:2x=16[/tex]

[tex]q:3x-4=20[/tex]

To find:

The converse of [tex]p\to q[/tex].

Solution:

The statement [tex]p\to q[/tex] means if p, then q and the converse of this statement is [tex]q\to p[/tex].

[tex]q\to p[/tex] means if q , then p.

We have, [tex]p:2x=16[/tex] and [tex]q:3x-4=20[/tex].

So, the converse of given statement is:

[tex]q\to p:[/tex] If [tex]3x-4=20[/tex], then [tex]2x=16[/tex].

Therefore, the correct option is D.

Answer: Therefore, the correct option is D.

Step-by-step explanation:

Given:

p: 2x = 16

q: 3x – 4 = 20

RE

Which is the converse of p - q?

ООО

If 2x + 16, then 3x - 47 20.

If 3x - 420, then 2x + 16.

If 2x = 16, then 3x – 4 = 20.

If 3x - 4 = 20, then 2x = 16

To find:

The converse of .

Solution:

The statement  means if p, then q and the converse of this statement is .

means if q , then p.

We have,  and .

So, the converse of given statement is:

If , then .

Therefore, the correct option is D.

Answer:

[tex]40 - 8 = 32 \\ \frac{32}{40} \times 100 \\ = 80\%[/tex]

maybe 28 is the answer...

Answer:

no not correct it should be horizontally left 2 units and vertically down 5 units

Given:

Lines DE and AB intersect at point C.

To find:

The value of x.

Solution:

In the given figure it is clear that the angles  and  are lie on a straight line AB.

              [Linear pair]

Subtract 5 from both sides.

Divide both sides by 7.

Therefore, the correct option is B.

Answer:

Tan A = 8/15

Sin A = 8/17

Cos A = 15/17

I start feeling tired now

9514 1404 393

Answer:

  4² = 16

Step-by-step explanation:

The applicable rule of exponents is ...

  1/a^-b = a^b

So, ...

 [tex]\dfrac{1}{4^{-2}}=\boxed{4^2 = 16}[/tex]

_____

Additional comment

If you were to evaluate this using the Order of Operations, you would evaluate the exponent first:

  1/4^-2 = 1/(1/16)

Then, you would do the division.

 1/(1/16) = 16

__

We sometimes find it convenient to manipulate exponential terms to the form with the smallest positive exponents before we begin the evaluation.

D. 63

2a+5b+3c

2(12)+5(6)+3(3)

24+30+9=63

Hope this helps! :)

Answer:

Add them:

Squares to squares, a to and number to number:

8a^2+3a+13

The simplified sum of the given expressions 7a² - 9a + 5 and 11a + a² + 8​ is 8a² + 2a + 13.

To find the sum of the expressions 7a² - 9a + 5 and 11a + a² + 8, we simply combine like terms.

The given expressions contain terms with different powers of "a."

Combining the terms with the same powers, we have:

7a² + a² = 8a² (the coefficient for the "a²" term is 7 + 1 = 8)

-9a + 11a = 2a (the coefficient for the "a" term is -9 + 11 = 2)

Finally, we combine the constant terms:

5 + 8 = 13

Putting it all together, the sum of the expressions 7a² - 9a + 5 and 11a + a² + 8 is:

8a² + 2a + 13

To learn more about polynomials click on,

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