Use a comparison test (either normal or limit) to determine whether the following series converges or diverges. Be sure to clearly identify what you are comparing too and if that converges or diverges.

The term that must be added to the equation x2+4x=1 to make it into a perfect square is 4.

Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. Since there is no ax2 term, the equation is linear if a = 0, not quadratic.

This is true because the Latin word quadratum, which means "square," plus the fact that the area of a square with side length x is equal to x2, make up what is known as the quadratic (or "square-like") definition of a polynomial equation with exponent two.

x²+4x=1

as, the x has coefficient 4.

so,

half the coefficient of x and add and subtract the square of the remaining.

x²+4x + 2 ² - 2² =1

Now,

make the whole square term

x²+4x + 2 ² - 4 - 1=0

( x + 2)² -5= 0

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Answer:

  s = -24

Step-by-step explanation:

This is a 2-step linear equation, so can be solved the way all 2-step equations are solved.

Step 1

Identify the constant term on the side of the equation with the variable term, and add its opposite to both sides.

  [tex]7 = \dfrac{1}{6}s+11\qquad\text{given}\\\\7-11=\dfrac{1}{6}s+11-11\qquad\text{add $-11$ to both sides}\\\\-4=\dfrac{1}{6}s\qquad\text{simplify}[/tex]

Step 2

Multiply both sides by the inverse of the coefficient of the variable.

  [tex](6)(-4)=(6)\left(\dfrac{1}{6}s\right)\qquad\text{multiply both sides by 6}\\\\\boxed{-24=s}\qquad\text{simplify}[/tex]

Often, when equations contain fractions, you are advised to "eliminate fractions" as a first step. That generally means you multiply both sides of the equation by a suitable common denominator.

Here, the only denominator is 6, so the fraction can be eliminated by multiplying both sides of the equation by 6.

  [tex]7=\dfrac{1}{6}s+11\qquad\text{given}\\\\6(7)=6\left(\dfrac{1}{6}s+11\right)\qquad\text{multiply both sides by 6}\\\\42=s+66\qquad\text{simplify}\\\\42-66=s+66-66\qquad\text{add the opposite of 66 to both sides}\\\\\boxed{-24=s}\qquad\text{simplify}[/tex]

You will note this requires the same number of steps, but you don't have to mess with fractions after the first step.

The value we found for the variable can be checked in the original equation.

  [tex]7=\dfrac{1}{6}(-24)+11\\\\7=-4+11\qquad\text{true}[/tex]

Answer:

Option 2

Step-by-step explanation:

Using the quadrstic formula,

[tex]\tan \theta=\frac{-2 \pm \sqrt{2^2 - 4(\sqrt{3})(-\sqrt{3})}}{2\sqrt{3}} \\ \\ =\frac{-2 \pm 4}{2\sqrt{3}} \\ \\ =\frac{-1 \pm 2}{\sqrt{3}} \\ \\ = -\sqrt{3}, \frac{1}{\sqrt{3}}[/tex]

Case 1

[tex]\tan \theta=-\sqrt{3} \implies \theta=\frac{2\pi}{3}, \frac{5\pi}{3}[/tex]

Case 2

[tex]\tan \theta=\frac{1}{\sqrt{3}} \implies \theta=\frac{\pi}{6}, \frac{7\pi}{6}[/tex]

Just me:

? I will just explain what I understand

Answer:

(Think hard) If you cut a snake in half you get 1/2 but if you cut it into 4's 1/5

I tried.

Answer:x=5

Step-by-step explanation: 73+73+6x+4=180

150+6x=180

6x=30

x=5

The difference in mail handled between 195 and 1965 is -5.4 x 10

The data on the pieces of mail handled by the United States Postal Service is written in scientific notation. Scientific notation is used to compress larger numbers into smaller numbers.

In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, 1 x 10² is equivalent to 100

Difference in mail handled = mail handled in 1995 - mail handled in 1965

(1.8 x [tex]10^{11}[/tex]) - (7.2 x [tex]10^{10}[/tex])

(1.8 - 7.2)  x [tex]10^{11 - 10}[/tex]

-5.4 x 10

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The median value is 63 and Lower quartile range is 48 and Interquartile range is 80.

According to the given statement

we have given data set and we have to find the five number summary.

So, For this purpose,

the given data set is:

48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80

Firstly we have to find the upper quartile means median for it.

So, Median = n /2

median = 12/2

median = 6th term.

So, Upper quartile range for this data set is 63.

And

Lower quartile for data set is the lower value of the data set.

So, That's why

Lower quartile range for this data set is 48.

And now, we have to find the Interquartile range

so, Interquartile range means maximum value of data.

So, That's why

Interquartile range of this data is 80.

So, The median value is 63 and Lower quartile range is 48 and Interquartile range is 80.

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Answer:

its the 4th one i think

Step-by-step explanation:

The Option A is correct. The Numbers of Miles Driven for A Truck That Cost a Total Of $42.50 To Rent for One Day $25m + 0.35m = $42.50

According to the statement

we have given that the  Rental Truck Is Company Charges $25 Per Day Plus A Fee Of $0.35 For Every Mile (m) Driven. and a Truck That Cost A Total Of $42.50 To Rent For One Day.

And we have to find the equation for this.

So, for given purpose,

we know that the A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

And from the given values the equation formed that the

In the equation the charges per mile is added to the original charges is equal to the total charges per day.

So, The equation become

$25m + 0.35m = $42.50

And by this equation we represent the all given conditions related charges.

So, The Option A is correct. The Numbers of Miles Driven for A Truck That Cost a Total Of $42.50 To Rent for One Day $25m + 0.35m = $42.50

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Answer:

$50

Step-by-step explanation:

x is distance and y is cost because the cost is dependent on the distance which makes the distance the independent variable. you can always use y=mx+b for these problems!!

Intercepts with the axes are where your line touches the x or y axis. An example is a straight line, say, y=4x+2. In this case, the y-intercept is 2 because the line touches the y-axis at (0, 2). With y=mx+b format, the y-intercept is b. To find the x-intercept of an equation in y=mx+b format, set y to zero and solve for x. In a parabola, the x-intercepts would be the roots. An example of this is x^2 - 5x + 4 = 0. The roots here are (4,0) and (1,0). Hopefully this helped.

The value of the mean absolute percentage error of the forecast for march found by the exponential smoothing method with a smoothing constant of 0. 3 is  16.94%

The equation is given as

∝At + (1-∝) Ft

The value for Alpha = 0.7

1 - ∝ = 1 - 0.7

= 0.3

Forecast in match = 62

Ft = 51. 5

the difference = 62 - 51.5

= 10.5

The error = 10.5/62 * 100

= 16.94%

Hence the value of the  mean absolute percentage error of the forecast for march found by the exponential smoothing method with a smoothing constant of 0. 3 is  16.94%

The past demand data shown below can be regarded as stationary.

Month Demand

January

50

February

55

March

62

April

45

What is the mean absolute percentage error of the forecast for March found by the exponential smoothing method with a smoothing constant of 0.3?

O a. 14.68%

Ob. 16.94%

O c. 12.57%

Od. 11.33%

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Answer:

c. 3  

yes you are right, good job!!

Step-by-step explanation:

18 divided by what equals 2?

18 / 2 = 9 so 18 / 9 = 2

so 27 / 9 = y which y = 3

check: 9 x 3 = 27

Answer:

Yes, C

Step-by-step explanation:

18/2 = 9 so you need to divide 27 by 9 to get 3

Step-by-step explanation:

x = 7

y = 5

[tex] = {x}^{2} + {y}^{2} [/tex]

[tex] = (7 {)}^{2} + (5 {)}^{2} [/tex]

= 7 × 7 + 5 × 5

[tex] = 49 + 25 [/tex]

[tex] = 74[/tex]

Hey there!

x^2 + y^2

= 7^2 + 5^2

= 7 * 7 + 5 * 5

= 49 + 25

= 74

Therefore, your answer should be: 74

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The missing length of given right triangle is equal to 1500.

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean  Theorem.

The Pythagorean Theorem says: [tex]hypotenuse^2=(leg_1)^2+(leg_2)^2[/tex] . And the main trigonometric ratios are: sin (x),  cos (x) and tan (x) , where:

[tex]sin(x)=\frac{opposite\ side}{hypotenuse} \\ \\ cos(x)=\frac{adjacent\ side}{hypotenuse} \\ \\ tan (x)= \frac{opposite\ side}{adjacent\ side}[/tex]

There is another important property, where h²=m*n. See the attached image.

From the previous informations presented, you can solve the given question.

Thus, if h²=m*n. You can write:

h²=900*1600

[tex]h=\sqrt{1440000}\\ \\ h=1200[/tex]

If h=1200, you can find x from Pythagorean  Theorem.

x²=1200²+900²

x²=1440000+810000

x²=2250000

x=[tex]\sqrt{2250000}[/tex]

x=1500

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These are some of the ways you can make 15 by adding three numbers together.

The first way is doing  6+6+3.There are some more ways to do it too.

2nd way is 6+4+5.

3.   1+6+6

4.   5+5+5

The solution to the system of equations is x = 1, y = 10 and z = 4

The system of equations is given as:

3x +2y +4z = 11

2x -y +3z = 4

5x -3y +5z = -1

Multiply the second equation by 2

So, we have

4x - 2y + 6z = 8

Add this equation to the first equation

3x + 4x + 2y - 2y + 4z + 6z = 11 + 8

Evaluate the like terms

7x + 10z = 19

Multiply the second equation by 3

So, we have

6x - 3y + 9z = 12

Subtract this equation from the third equation

6x - 5x - 3y + 3y + 9z - 5z = 12 + 1

Evaluate the like terms

x + 4z = 13

Make x the subject

x = 13 - 4z

Substitute x = 13 - 4z in 7x + 10z = 19

7(13 - 4z) + 10z = 19

Expand

91 - 28z + 10z = 19

Evaluate the like terms

-18z = -72

Divide

z = 4

Substitute z = 4 in x = 13 - 4z

x = 13 - 4 * 4

Evaluate

x = 1

We have:

2x -y +3z = 4

This gives

2(1) - y + 3 * 4 = 4

Evaluate

2 - y + 12 = 4

This gives

y = 10

Hence, the solution to the system of equations is x = 1, y = 10 and z = 4

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Using it's concept, the domain of the function is given as follows:

{x| –2 ≤ x <= 5}

The domain of a function is the set that contains all possible input values for the function.

The function described is defined for x between -2 and 5, hence the domain is given by the following interval:

{x| –2 ≤ x <= 5}

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Answer:

{x| –2 ≤ x < 5}

Step-by-step explanation:

The directrix of the parabola with equation (y + 3)² = 8 · (x - 3) is equal to y = - 5. (Correct choice: B)

According to the given statement, we have a parabola of the form (y - k)² = 4 · p · (x - h), whose axis of symmetry is parallel to the x-axis. The directrix is always perpendicular to the axis of symmetry and therefore the equation of the directrix is equivalent to x = h - p, where p is the distance from the vertex to the focus.  

If we know that the equation of the parabola (y + 3)² = 8 · (x - 3), the equation of the directrix is:

y = - 3 - 2

y = - 5

The directrix of the parabola with equation (y + 3)² = 8 · (x - 3) is equal to y = - 5. (Correct choice: B)

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Answer:

y = 8x+7

Step-by-step explanation:

firstly reduce the equation to an arithmetic series starting from the 0th term so:
7, 15, 23, 31, 39....

Secondly, identify the common difference: 8
we now know that the answer must contain 8x

Thirdly, form the equation 8x + c = y where y is a constant. Afterwards insert the values of any given x and y so:
8*0 + c = 7
c = 7
Thusly we now know that the series and thus equation is 8x+7 = y

Answer:

y = 8x + 7

Step-by-step explanation:

the equation of a linear function in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2-y_{1} } }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1,15) and (x₂, y₂ ) = (2, 23) ← 2 ordered pairs from the table

m = [tex]\frac{23-15}{2-1}[/tex] = [tex]\frac{8}{1}[/tex] = 8

the ordered pair (0, 7 ) indicates c = 7

y = 8x + 7 ← equation of linear function

The image of the point P(-3, 2) under the translation T<2,1> is (-1, 3)

The coordinate point is given as:

P = (-3, 2)

The translation is given as

T<2,1>

The translation can be represented as:

(x, y) = (x + 2, y + 1)

So, we have the following equation

P' = (-3 + 2, 2 + 1)

Evaluate the sum

P' = (-1, 3)

Hence, the image of the point P(-3, 2) under the translation T<2,1> is (-1, 3)

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Answer:

Step-by-step explanation:

part A:   when you graph both y=7x-9 and y=3x-1 the two lines will intersect this is how you solve the graphing part of the system of equations.

Both of these lines are in slope form (y=mx+b) where m is the slope which is 7 and 3 and b is the y-intercept which is -1 and -9.

part B

7x-9=3x-1

subtract 3x from both sides

4x-9=-1  

add 9 to both sides

4x=8  

divide both sides by 4

x=2,

making y=3x-1 become:

y=3(2)-1=6-1=5,  

the answer is (2,5)

Answer:

The graph of g(x) has a y-intercept at (0,0) and a slope of -2.

The correct statements about the solids are:

To find which statements are correct:

Congruent base: This is used to indicate that the triangles' bases are the same and that they have the same shape.

The volume of the first triangle is: [tex]2x^{2} h[/tex]

The volume of the second triangle is: [tex]x^{2} h[/tex]

Therefore, the correct statements about the solids are:

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The complete question is given below:
One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. Which statements about the two rectangular solids are true? Check all that apply.

A) The bases are congruent.

B) The solids are similar.

C) The ratio of the volumes of the first solid to the second solid is 8:1.

D)The volume of the first solid is twice as much as the volume of the second solid.

E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more

surface area than the second solid.

Answer:

Step-by-step explanation:

Convert 2y=-3x+2 into y=mx+b form

[tex]\frac{2y}{2} =\frac{-3x+2}{2}[/tex]

[tex]y=\frac{-3x}{2} +1[/tex]

Y intercept is 1, slope is -3/2

Graph looks like this:

**Disclaimer** Hi there! I am not fully sure what [ T ] represents. From the answer that I got [ 38π / 3 ], it does not match any one of them, so I choose none of the above. If there's a specific meaning of [ T ] and I am incorrect, please let me know and I will modify my answer.

Answer: None of above

Step-by-step explanation:

Given formula

S = r θ

Given information

radius = 19 ft

Angle = 2π / 3

Substitute values into the formula

S = r θ

S = (19) (2π / 3)

Simplify by multiplication

[tex]\Large\boxed{S=\frac{38\pi}{3} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Resistance

Step-by-step explanation:

Answer:

option c

Step-by-step explanation:

option c is a correct answer

Answer: 4/10, 6/15, 8/20

Hope this helps!

Answer:

-6

Step-by-step explanation:

Additive inverse is the number that when added to A gives a result of zero

A + inverse = 0

6 + inverse = 0

inverse = -6