Determine whether the sequence converges or diverges. How do you know if it converges or diverges? If it converges, give the limit. (7)

Answer:

-2

Step-by-step explanation:

You have to simplify numerator and denominator through factoring. The you should get an expression involving only a + b which is given as -2

Take numerator
[tex]a^2-b^2-12b-36[/tex]

Factor
[tex]-b^2-12b-36[/tex]

[tex]= - (b^2 + 12b + 36)\\\\= -(b+6)^2[/tex]

So numerator becomes
[tex]a^2-\left(b+6\right)^2[/tex]

Apply difference of squares formula: [tex]\displaystyle x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]

[tex]\mathrm{with\;} x^2 == > a^2, and y^2 == > (b + 6)^2[/tex]

[tex]\implies a^2-\left(b+6\right)^2 \\== \left(a+\left(b+6\right)\right)\left(a-b-6\right)[/tex]

Denominator
[tex]a^2-6a-b^2-6b[/tex]

can be factored as follows

[tex]a^2-b^2 = (a + b) (a -b)[/tex]
[tex]-6a-6b = -6\left(a+b\right)[/tex]

So denominator becomes
[tex]\left(a+b\right)\left(a-b\right)+-6\left(a+b\right)[/tex]

Factor out common term (a+b) to get
[tex]\left(a+b\right)\left(a-b-6\right)[/tex]

So the original expression with Numerator and denominator

[tex]\displaystyle =\frac{\left(a+b+6\right)\left(a-b-6\right)}{\left(a+b\right)\left(a-b-6\right)}[/tex]
Cancel the common factor (a-b-6) to get
[tex]\displaystyle \frac{a+b+6}{a+b}[/tex]

Since a + b = -2, plug in this value of (a+b) in both numerator and denominator to get
[tex]\displaystyle \dfrac{-2 + 6}{-2}[/tex]
[tex]\displaystyle = - 2[/tex]

Answer: -2

Answer:

y = -3x + 12

Step-by-step explanation:

If two lines are parallel, their slopes are equal, then m = -3

x intercept is 4 then y = 0

y = mx + b

0 = -3(4) + b

b = 12

y = -3x + 12

The number sold at the original price is 27 and they sold 64 at the reduced price.

Let x = number of pieces sold at 13.50

Let y = number of pieces sold at 9.50

The equation will be:

x + y = 91. ..... i

13.50x + 9.50y = 972.50 ..... ii

From equation i x = 91 - y

13.50x + 9.50y = 972.50

13.50(91 - y) + 9.50y = 972.50

1228.50 - 13.50y + 9.50y = 972.50

1228.50 - 4y = 972.50

4y = 1228.50 - 972.50

4y = 256

y = 256/4

y = 64

Since x + y = 91

x = 91 - 64 = 27

Therefore, the number sold at the original price is 27 and they sold 64 at the reduced price.

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The probability that if 3 donations are made, all 3 of them can be safely used on blood transfusion with someone that has type A will be D. (0.27 + 0.49)³ = 0.4390

It should be noted that probability simply means the chance that a particular event will occur.

In this case, the probability that if 3 donations are made, all 3 of them can be safely used on blood transfusion with someone that has type A will be:

= (27% + 49%)³

= (0.27 + 0.49)³

= 0.4390

The probability is 0.4390.

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Answer:

adjacent , linear pair ,

Step-by-step explanation:

and i don't think there is something else

The correct value of m = 6 and b = -9.

The function f(x) is differentiable at x = 3 and we know that if a function is differentiable at some point means that it is continuous at that point also.

Here function is continuous at x = 3 piecewise

m(3) + b = (3)²

3m + b = 9 .....(1)

and function is differentiable at ( x = 3 ) piecewise

d/dx ( m * x + b ) = d/dx (x)² at ( x= 3 )

( m + 0 ) = 2x  at ( x = 3 )

m = 2 * 3

m = 6

By placing the value of m in equation (1)

3m + b = 9

3 * 6 + b = 9

18 + b = 9

b = 9 - 18

b = -9

Therefore, the value of m = 6 and b = -9.

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The formula in terms of H is H = V ÷ πr². Value of height is 5.

We are given the formula -

V = πr²H, where V represents volume and H represents height. To rewrite the formula in terms of H, we will shift it to Left Hand Side -

H = V ÷ πr²

Keep the value of Volume and radius in formula to find the height.

H = 45π ÷ π(3)²

Taking square of 3 and cancelling π

H = 45 ÷ 9

Performing division to find the value of height

H = 5

Therefore, the formula is V ÷ πr² and value of height is 5.  

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The complete question is attached in figure.

The answers of the following part are:

a) 22

b) -76

c) -13

For solving this particular sum we need to know the about functions Function is generaaly defined as a set of inputs having one output each. every function as a domain and a co-domain or range. A function is generally denoted by f(x) where x is the variable and it is also the input.The general representation of function is y = f(x).

In the given sum we will just put the values in place of x and will find the answer

The given equation is f(x)=-13+7x

a) Here it is given f(5)  so we will put 5 in all places of x

Substituting the value x as 5 we will get :

f(5) = -13+7*5

= -13+35

=22

the value f(5) will be 22

b) In this part of the vaule of x is given as -9

Substituting the value of x as -9 we get

f(-9)=-13+7*(-9)

= -13-63

= -76

the valur of f(-9) is -76

c) here the value of x is given as 0

Substituting the value of x as 0

f(0)= -13+7*0

= -13+0

=-13

the value of f(0) is -13

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Answer: 96

Step-by-step explanation:

Length = Area/Width

7584/79 = 96 feet

96 x 79 = 7584 ft²

Answer: 164 degrees

Step-by-step explanation:

IHG=JHG+IHJ

19x-7=84+7x+17

19x-7=101+7x

12x-7=101

12x=108

x=9

IHG=19x-7

IHG=19(9)-7

IHG=171-7

IHG=164 degrees

Answer:

89.50 = 7.75 + 27.25p

subtract 7.75 from both sides

89.50 - 7.75 = 27.25p

81.75 = 27.25p

divide both sides by 27.25

p = 81.75 / 27.25

p = 3

Step-by-step explanation:

The number of people who can go to the amusement park is 3 people

Answer: p=3

Hence, the Linear Equation in two variables is used to determine the total number of people who go to the park is - y=7.75+27.25p

Step-by-step explanation:

89.50=7.75+27.25p

89.50-7.75+27.25p

81.75=27.25

81.75/27.25

p=3

Answer:  It's not linear.

Step-by-step explanation: A linear function must have a degree of 0 or 1. This function equals to y= -1/x. -1/x has a degree of negative 1 since x^-1 =1/x. So this is not linear.

Answer: 21

Step-by-step explanation:

Use a calculator

THIS ANSWER WAS DELETED DUE TO NOT BEING TRUE.

Answer:          410 possible points

To solve for the possible points in the course, use a proportion and cross multiply.

A proportion is two fractions that are equal to each other. For the fractions to be equal, they are proportionate. In our math problem, percentage is proportionate the the number of points.

The fractions represent information you have, and one variable will represent what you are solving for.

Your points = 361

Points to get an 'A' = your points + 8

'A' = 90% of possible points

Points to get an 'A' = your points + 8

= 361 + 8

= 369

let x be the amount of possible points

We know the number of points for 90% is 369 points. Remember that 90% is the same as 90/100.

Keep the information with the same units inside the same fraction. Here, percentage is represented by the first fraction. Points is represented by the second fraction.

[tex]\displaystyle{\frac{90}{100}=\frac{369}{x}}[/tex]

We can solve using cross multiplication. This is when we multiply each numerator by the denominator from the other fraction.

[tex]90x = 369*100[/tex]        Simplify by multiplying.

[tex]90x = 36,900[/tex]            Isolate the variable x.

[tex]\displaystyle{\frac{90x}{90} = \frac{36,900}{90}}[/tex]           Divide both sides by 90 to cancel out 90 on the left.

[tex]\displaystyle{x = \frac{36,900}{90}}[/tex]              Divide.

[tex]x = 410[/tex]                    Solved for x, representing the possible points.

∴ The possible points in the art course is 410.

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Answer:

410 possible points

Step-by-step explanation:

Answer:

To write this is true scientific notation the decimal point needs to be moved 1 place to the right so the exponent for the 10s term will be negative:

0.514=5.14×10

−1

Answer:5.14

Step-by-step explanation:

Using proportional relationships, we have that:

A. The function does not show a direct linear relationship.

B. The function shows a direct linear relationship.

C. The function does not show a direct linear relationship.

A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, in the case of a direct relationship, as follows:

y = kx

In the case of an inverse relationship, we have that:

y = k/x.

From the format of these equations, we have that:

A function is classified as linear if the exponent of x is of 1, hence item c does not show a linear function.

The functions A, B, C are missing, and are given as follows.

A. 9/x.

B. x/11.

C. x²/8.

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Answer:

so xtime sy ,fe fwvnvf nfdv bregbrrsikrwnknrhvnk vnf vknvns;;abjwrjkgwnkgwjknnnxnfnfsvmsr

4K = 120 can be used to find the number of emergency kits K Elise packs. The total number of emergency kits packed by Elsie and her mom are 30.

Here, we are given that Elise puts 4 water bottles into each emergency kit.

Let the number of kits packed = K

Then the total number of bottles packed = 4 × K

= 4K

Also, we are given that Elsie packs a total of 120 bottles.

Thus, we get the following linear equation-

4K = 120

We can use this equation to find the number of emergency kits K Elise packs.

dividing by 4 on both sides, we get

4K/4 = 120/4

K = 30

Hence, the total number of emergency kits packed by Elsie and her mom are 30.

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Answer:

Step-by-step explanation:

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[tex]\implies[/tex]The answer is Adjacent and Complementary.

The mass, in grams, of 1 cubic centimeter of the sand in scientific notation is 7 x 10^(-1).

Scientific notation is a way of writing very large or very small numbers.

Now it is given that,

Average mass of grain = 7 x 10-4 gram

Number of grains in 1 cubic centimeter = 1,000 grains =  10^3 grains

Thus,

Mass of 1 cubic centimeter of the sand = Average mass of grain * Number of grains in 1 cubic centimeter

⇒ Mass of 1 cubic centimeter of the sand =  7 x 10-4 * 10^3 grams

⇒ Mass of 1 cubic centimeter of the sand =  7 x 10^(-4+ 3) grams

⇒ Mass of 1 cubic centimeter of the sand =  7 x 10^(-1) grams

Thus, the mass, in grams, of 1 cubic centimeter of the sand in scientific notation is 7 x 10^(-1).

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Answer:

What is the sum equal to?

Step-by-step explanation:

The distance between City C and City D is represented by 13.67 inches on a certain wall​ map.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Let x inches would be far apart are they on the same​ map

We can write this as a ratio as

As per the given information,

9 inches : 2700 miles = x inches : 4100 miles

⇒ 9/2700 = x/4100

⇒ x = (4100×9)/2700

⇒ x = 13.67 inches

Therefore, on a certain wall​ map, the distance between City C and City D is represented by 13.67 inches.

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The value of 'x' for the given expression is calculated as (x = 48).

A linear equation in one variable is an equation that has only one solution.

Now, for the given expression;

(3x-5) + (x+1) = 180

Open the brackets.

3x-5 + x+1 = 180

Add the similar parts;

4x - 4 = 180

Further simplifying;

4x = 180 + 4

4x = 184

x = 184/4

x = 48

Therefore, the value of 'x' is estimated as 48.

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Answer:

A: [tex]b < \frac{3}{2}[/tex] and the second equation is: [tex]b > \frac{1}{3}[/tex]

B: [tex]x > \frac{1}{6}[/tex] and the second equation is: [tex]x < 2[/tex]

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Hope this helps!

Have a great day and God bless! :)