Since we have computer algebra systems that can solve polynomial division problems for us, why is it necessary to learn how to do these things by hand?

The geometric series out of the considered option having the common ratio as 2 is given by: Option C. 14, 28, 56, 112, ...

There are three parameters which differentiate between which geometric sequence we're talking about.

The first parameter is the initial value of the sequence.

The second parameter is the quantity by which we multiply previous term to get the next term.

The third parameter is the length of the sequence. It can be finite or infinite.

Suppose the initial term of a geometric sequence is 'a'

and the term by which we multiply the previous term to get the next term is 'r' (also called the common ratio)

Then the sequence would look like

[tex]a, \: ar, \: ar^2, \: ar^3, \: \cdots[/tex]

(till the terms to which it is defined)

If the initial term is 'a', then the geometric sequence with common ratio = 2 would look like:

[tex]a, \: a(2), \: a(2)^2, \: a(2)^3, \: \cdots\\\\a, \: a(2), \: a(4), \: a(8), \: \cdots[/tex]

Checking all the options to see which one has got common ratio 2:

Initial term a = 14,

The geometric sequence with a = 14, and r = 2 would be:

[tex]14, 14(2), 14(4), 56(8), \cdots\\\\14, 28, 56, 112, \cdots\\[/tex]

The sequence  14, 16, 18, 20, ... doesn't match with it, so its not correct option.

Initial term a = 64,

The geometric sequence with a = 14, and r = 2 would be:

[tex]64, 64(2), 64(4), 64(8), \cdots\\\\64, 128, 256, 512, \cdots\\[/tex]

The sequence 64, 32, 16, 8, ... doesn't match with it, so its not correct option.

Initial term a = 64,

The geometric sequence with a = 14, and r = 2 would be:

[tex]14, 14(2), 14(4), 56(8), \cdots\\\\14, 28, 56, 112, \cdots\\[/tex]

The sequence  14, 28, 56, 112, ... matches with it, so its correct option.

Initial term a = 87,

The geometric sequence with a = 87, and r = 2 would be:

[tex]87, 87(2), 87(4), 87(8), \cdots\\\\87, 174, 348, 696, \cdots\\[/tex]

The sequence 87, 85, 83, 81, ... doesn't match with it, so its not correct option.

Thus, the geometric series out of the considered option having the common ratio as 2 is given by: Option C. 14, 28, 56, 112, ...

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For this case we must find the value of the following expression:

[tex](+328.62) - (+ 98.6) =[/tex]

We apply distributive property to the term within the parenthesis taking into account tha:

[tex]- * + = -[/tex]

Rewriting we have:

[tex]+ 328.62-98.6 =[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]+328.62-98.6 = 230.02[/tex]

Answer:

230.02

Option B

Answer:

c. (6,1)

Step-by-step explanation:

Add both x and both y (11+1)=12 (5+-3)=2 then divide both by 2

(6,1)

Answer:

  11,184,808

Step-by-step explanation:

The n-th term of a geometric series is ...

  an = a1·r^(n-1)

To fill in the formula, we need a1·r^n, so need to multiply the last term shown by r.

The value of r is 32/8 = 4, and the other terms of interest are a1 = 8, a1·r^(n-1) = 8388608. So, the sum is ...

  [tex]S_n=\dfrac{ra_1r^{n-1}-a_1}{r-1}=\dfrac{4\cdot 8,388,608-8}{4-1}=11,184,808[/tex]

Answer:

See below in bold.

Step-by-step explanation:

If we add the 2 equations  we eliminate x  and we get 2y =2.

So y = 1.

Substituting y = 1 in the second equation 1 = x - 3.

So x = 4.

A. One solution: (4, 1).

If we drew a graph we would have 2 lines which intersect at the point (4, 1).

Answer:

Step-by-step explanation:

If we add the 2 equations  we eliminate x  and we get 2y =2.So y =1.

Substituting y = 1 in the second equation 1 = x - 3.So x = 4.

A.

One solution: (4, 1).If we drew a graph we would have 2 lines which intersect at the point (4, 1).

Answer:

The answer is 8, so 8^1

Step-by-step explanation:

You add and subtract exponents when multiplying and dividing.

Answer:

C. [tex]52\sqrt{3}\ ft^2[/tex]

Step-by-step explanation:

Use formula for the area of trapezoid

[tex]A=\dfrac{a+b}{2}\cdot h,[/tex]

where a is the smaller base, b is the larger base and h is the height.

From the diagram,

[tex]a=11\ ft\\ \\b=15\ ft\\ \\h=4\sqrt{3}\ ft[/tex]

So, the area of trapezoid is

[tex]A=\dfrac{11+15}{2}\cdot 4\sqrt{3}=13\cdot 4\sqrt{3}=52\sqrt{3}\ ft^2[/tex]

Answer:

x=1 if I understood correctly.

Step-by-step explanation:

[tex] \sqrt{x} + 5 + x - 3 = 4[/tex]

[tex] \sqrt{x} + 2 + x = 4[/tex]

[tex] \sqrt{x} + x = 2[/tex]

At this point if you try all the integers, you will find that only 1 is the solution to this equation, because:

[tex] \sqrt{1} + 1 = 2[/tex]

[tex]1 + 1 = 2[/tex]

[tex]2 = 2[/tex]

Hope I helped!

For this case we must solve the following equation:

[tex]\sqrt {x + 5} -3 = 4[/tex]

We add 3 to both sides of the equation:

[tex]\sqrt {x + 5} = 4 + 3\\\sqrt {x + 5} = 7[/tex]

We raise the square to eliminate the root:

[tex]x + 5 = 7 ^ 2\\x + 5 = 49[/tex]

We subtract 5 on both sides of the equation:

[tex]x = 49-5\\x = 44[/tex]

Answer:

[tex]x = 44[/tex]

Answer:

The correct answer is option A.  23 in

Step-by-step explanation:

It us given that, the length of a rectangle is 5 more than 3 times its width. The perimeter of the rectangle is 58 in.

To find the length of rectangle

Let 'x' be the width of rectangle.

Length = 3x + 5

Perimeter of rectangle = 2(length + width)

58 = 2(3x + 5 + x)

58 = 2(4x + 5)

29 = 4x + 5

4x = 29 - 5

4x = 24

x = 24/4 = 6

Therefore length of rectangle = 3x + 5

 = 3*6 + 5 = 23 in

The correct answer is option A.  23 in

Answer:

sin(x°) = 11/s

Step-by-step explanation:

The tangent is the ratio of sine to cosine, so ...

tan(x°) = sin(x°)/cos(x°)

Multiplying by cos(x°) gives ...

sin(x°) = cos(x°)·tan(x°) = (r/s)·(11/r)

sin(x°) = 11/s

Answer:

sin x° = 11 divided by s

Step-by-step explanation:

Given,

tan x° = 11 divided by r

[tex]\implies tan x^{\circ}=\frac{11}{r}[/tex]

Also, cos x° = r divided by s

[tex]\implies cos x^{\circ}=\frac{r}{s}[/tex]

We know that,

[tex]\frac{sinx^{\circ}}{cos x^{\circ}}=tan x^{\circ}[/tex]

[tex]\implies sinx^{\circ}= tan x^{\circ}\times cos x^{\circ}[/tex]  ( by cross multiplication )

By substituting the values,

[tex]sin x^{\circ}=\frac{11}{r}\times \frac{r}{s}=\frac{11r}{rs}=\frac{11}{s}[/tex]

⇒ sin x° = 11 divided by s

Answer:

The maximum height of the marshmallow is 49 feet.

Step-by-step explanation:

The vertex form of a parabola is

[tex]y=a(x-h)^2+k[/tex]           .... (1)

Where, (h,k) is vertex of the parabola is a is constant.

The given function is

[tex]h=-16(t-14)^2+49[/tex]              ..... (2)

Where, h is height of the marshmallow (in feet) and t is the time (in seconds) after he throws the marshmallow.

From equation (1) and (2), we get

[tex]a=-16,h=14,k=49[/tex]

The value of a is -16, which is less than 0. So, the given function is a downward parabola.

The vertex of a downward parabola is the point of maxima.

The value of h is 14 and the value of k is 49. So, the vertex of the parabola is (14,49). It means the maximum height of the marshmallow is 49 feet in 14 seconds.

Therefore the maximum height of the marshmallow is 49 feet.

Answer:

1/4,9

Step-by-step explanation:

might be wrong tbh

Answer:

14 cups

Step-by-step explanation:

3 pizzas needed

1 pizza means 2 cups of flour

So for 3 pizzas he will need 6 cups of flour

If he has 20 cups of flour and he uses 6, how much is left?

20-6=14

Answer:

14 cups of flour

Step-by-step explanation:

The three pizzas will require 6 cups of flour.

3 x 2 = 6 cups of flour needed to make 3 pizzas.

20 - 6 = 14 cups left

Answer:

  (g◦f)(-6) = -9

Step-by-step explanation:

(g◦f)(-6) means g(f(-6))

Put the number where the variable is and evaluate.

  f(-6) = 3/2(-6) +5 = -9 +5 = -4

  g(f(-6)) = g(-4) = 7 -(-4)² = 7 -16 = -9

Then ...

  (g◦f)(-6) = -9

Volume = (edge)^3

Volume = (3/4)^3

Volume = (27/64) inches^3

Done.

Latest time he can leave to be home by a quarter before 5 is 4:13

Step-by-step explanation:

Given Max's trip home takes 32 minutes. we have to find the time at which he can leave to be home by a quarter before 5.

quarter before 5 means 4:45

Max's takes 32 min to come to home so he has to leave 32 minutes before the given time.

Hence, latest time he can leave to be home by a quarter before 5 is 4:45-32 = 4:13

Answer:

Max must leave home at 4:58 to get their before half past 5.

Step-by-step explanation:

The range for this situation represents all possible values of the cost of filling the gas tank in dollars.

The range for this situation represents the set of all possible outputs of the function, which in this case is the cost of filling the gas tank.

Since the equation given is p(g) = 3.5g, the range would be all possible values of p, the cost of filling the gas tank.

The range would depend on the values of g, the amount of gas in gallons, that you input into the equation.

For example, if you fill the tank with 1 gallon of gas, the cost would be p(1) = 3.5 * 1 = $3.50.

If you fill the tank with 3 gallons of gas, the cost would be p(3) = 3.5 * 3 = $10.50.

Therefore, the range for this situation would be all values of p, the cost, that can be obtained by inputting different values of g, the amount of gas in gallons, into the equation p(g) = 3.5g.

The range for this situation is from $0 (empty tank) to $42 (full tank). The cost can be any value in this range depending on the number of gallons pumped into the tank.

In this context, the function [tex]\( p(g) = 3.5g \)[/tex] represents the cost  p  of filling the gas tank with  g  gallons of gas. The range of the function is the set of all possible values for the cost.

Since the cost is directly proportional to the number of gallons, we can evaluate the function for the minimum and maximum values of  g . The minimum value of  g  is 0 gallons (empty tank), and the maximum value is 12 gallons (full tank).

1. For g = 0 , [tex]\( p(0) = 3.5 \times 0 = 0 \)[/tex]. So, the minimum cost is $0.

2. For  g = 12 , [tex]\( p(12) = 3.5 \times 12 = 42 \)[/tex]. So, the maximum cost is $42.

Therefore, the range for this situation is from $0 (empty tank) to $42 (full tank). The cost can be any value in this range depending on the number of gallons pumped into the tank.

ANSWER

[tex]{(2x - 3)}^{3} = {8x}^{3} - 36 {x}^{2} + 54x - 27[/tex]

EXPLANATION

Using the binomial theorem of Pascal's triangle, the coefficient of the third exponent binomial is :

1,3,3,1

The expansion for

[tex] {(a - b)}^{3} = {a}^{3} - 3 {a}^{2} b + 3a {b}^{2} - {b}^{3} [/tex]

To find the expansion for:

[tex] {(2x - 3)}^{3} [/tex]

We put a=2x and b=3

This implies that,

[tex]{(2x - 3)}^{3} = {(2x)}^{3} - 3 {(2x)}^{2} ( 3) + 3(2x) {(3)}^{2} - {3}^{3} [/tex]

This simplifies to:

[tex]{(2x - 3)}^{3} = {8x}^{3} - 36 {x}^{2} + 54x - 27[/tex]

Answer:

  C.  f^-1(x) = 1/5x

Step-by-step explanation:

You know that f^-1(f(x)) = x, so you can try the answers.

____

You can also solve for f^-1(x). It will be "y" when ...

  f(y) = x

  5y = x

  y = 1/5x . . . . . divide by 5

To find the cost of one bag of windflower bulbs and one package of crocus bulbs, we can use the substitution method. By setting up a system of equations and solving for the variables, we find that the cost of one bag of windflower bulbs is $45 and the cost of one package of crocus bulbs is $7.50.

To find the cost of one bag of windflower bulbs and one package of crocus bulbs, we can set up a system of equations. Let's use the substitution method.

Let x represent the cost of one bag of windflower bulbs and let y represent the cost of one package of crocus bulbs.

We can set up two equations:

2x + 5y = 105

9x + 5y = 164.50

From the first equation, we can rewrite it as: 2x = 105 - 5y. We can substitute this expression for 2x in the second equation:

9(105 - 5y) + 5y = 164.50

Solving for y, we get y = 7.50. Substituting this value back into the first equation, we can solve for x: 2x + 5(7.50) = 105. Solving for x, we get x = 45.

Therefore, the cost of one bag of windflower bulbs is $45 and the cost of one package of crocus bulbs is $7.50.

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Follow below steps:

Mark and Julio are selling flower bulbs for a school fundraiser. To find the cost of one bag of windflower bulbs and one package of crocus bulbs, we set up two equations based on the information given, and then solve them using the substitution method.

Let x be the cost of one bag of windflower bulbs and y be the cost of one package of crocus bulbs. According to Mark's sales, the equation is:

2x + 5y = 105 ...(1)

According to Julio's sales, the equation is:

9x + 5y = 164.50 ...(2)

To use the substitution method, we first isolate y in equation (1):

y = (105 - 2x) / 5 ...(3)

Next, we substitute equation (3) into equation (2):

9x + 5((105 - 2x) / 5) = 164.50

9x + 105 - 2x = 164.50

7x = 59.50

x = 8.50

Now that we have the value for x, we can use it to find y by substituting x back into equation (3):

y = (105 - 2(8.50)) / 5

y = (105 - 17) / 5

y = 88 / 5

y = 17.60

Therefore, the cost of one bag of windflower bulbs is $8.50 and the cost of one package of crocus bulbs is $17.60.

Answer:

  irrational

Step-by-step explanation:

Pi is irrational.

-1 is rational.

Their sum is irrational.

_____

In general, the sum of a rational number and an irrational number is irrational.

The number 'pi' is an irrational number. When we subtract 1 from 'pi', we still obtain an irrational number, therefore 'pi-1' is irrational.

The number pi is a well-known irrational number. An irrational number cannot be expressed as a ratio of two integers, and its decimal expansion never ends or repeats. When we subtract 1 from pi, we get another number. Since we are creating a new number by subtracting an integer from an irrational number, that number remains irrational. Therefore, pi-1 is also an irrational number.

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The equation used to solve for x in the given diagram is 7x + 11x = 90, representing the total sum as 90 degrees.

In the diagram, you have an angle formed by two given lines. To find the value of x, you can use the fact that the total sum is 90 degrees.

1. The first angle of the diagram is labeled as 7x.

2. The second angle of the diagram is labeled as 11x.

So, the equation for the sum of these angles should equal 90 degrees:

7x + 11x = 90

Now, you can simplify the equation:

18x = 90

To isolate x, divide both sides by 18:

18x / 18 = 90/ 18

x = 5

So, the equation used to solve for x is indeed 7x + 11x = 90, which simplifies to 18x = 90 when considering the angles around the point.

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The given question pertains to different aspects of probability in Mathematics, such as combinations, proportions and matched pairs. Each concept is used to determine the likelihood of an event occurring and they all play integral roles in statistical analysis.

The details indicate that this question pertains to probability in Mathematics especially applied to situations like combinatorics, proportions and matched pairs. So let's explore each of those concepts with the details given:

In probability, the concept of combinations is important because it helps to determine the likelihood of a particular event occurring. For instance, P(choosing all five numbers correctly) relates to the probability of choosing numbers correctly in a given set. It's determined by P(choosing 1st number correctly) * P(choosing 2nd number correctly) * P(choosing 5th number correctly).

The term 'two proportions' perhaps refers to odds ratio or probability comparison between two events.

This is a statistical technique often used in studies where each individual or item has a unique match - for example, a study comparing the math scores of twins. Here, it seems like an insight into statistical analysis where outcomes are compared within matched pairs. Therefore, these different concepts are all part of probability and statistics.

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Answer:

Option B) The variable Y will cancel out first.

Step-by-step explanation:

we have

5x-y=-21 ----> equation A

x+y=-3 ----> equation B

Solve by elimination

Adds equation A and equation B

5x-y=-21

x+y=-3

--------------

5x+x=-21-3 ----->variable y will be eliminated first

6x=-24

x=-4

We know that, Final Amount in Compound Interest is given by :

[tex]\bigstar\;\;\boxed{\mathsf{Amount = Principal\left(1 + \dfrac{Rate\;of\;interest}{100}\right)^{Number\;of\;Years}}}[/tex]

Given :

●  Principal = $5000

●  Rate of interest = 1.25

●  Number of Years = 10

Substituting the values in the Formula, We get :

[tex]\implies \mathsf{Amount = 5000\left(1 + \dfrac{1.25}{100}\right)^{10}}[/tex]

[tex]\implies \mathsf{Amount = 5000\left(1 + \dfrac{0.25}{20}\right)^{10}}[/tex]

[tex]\implies \mathsf{Amount = 5000\left(1 + \dfrac{0.05}{4}\right)^{10}}[/tex]

[tex]\implies \mathsf{Amount = 5000\left(\dfrac{4.05}{4}\right)^{10}}[/tex]

[tex]\implies \mathsf{Amount = 5000\times (1.0125)^{10}}[/tex]

[tex]\implies \mathsf{Amount = 5661.354}[/tex]

Answer : $5661.354 money will be in the account 10 years later

Answer: $5,661.35

Step-by-step explanation:

I used the exponential growth formula to get my answer.

Answer:

  $2248.75

Step-by-step explanation:

Susan's monthly payment is ...

  total payment = loan payment + insurance payment

  = $2128.00 + (483,000×0.30/100)/12

  = $2128.00 + 1449/12

  = $2128.00 + 120.75

  = $2248.75

Answer:

Step-by-step explanation:

485'228.3

Answer:

Sherina should have added 56 to both sides of the equation.

Step-by-step explanation:

To solve this equation: x-56=230 you need to add 56 to both sides of the equation:

x-56 + 56=230 + 56 → x = 286.

Therefore, Sherina should have added 56 to both sides of the equation.

Answer:

Last option: Sherina should have added 56 to both sides of the equation.

Step-by-step explanation:

To solve the equation [tex]x-56=230[/tex] Sherina needed to solve for the variable "x".

To calculate the value of the variable "x" it is important to remember the Addition property of equality. This states that:

[tex]If\ a=b\ then\ a+c=b+c[/tex]

Therefore, Sherina should have added 56 to both sides of the equation.

The correct procedure is:

[tex]x-56+(56)=230+(56)\\x=286[/tex]

Answer:

  x = 3, x = -1/6 are the zeros

Step-by-step explanation:

I find graphing the equation using a graphing calculator to be about the fastest way to find the zeros.

__

For this equation, you can look for factors of 6·(-3) = -18 that have a sum of -17. Those are -18 and +1, so the factorization of the equation is ...

  y = (1/6)(6x -18)(6x +1) = (x -3)(6x +1)

The roots are the values of x that make the factors be zero, so x=3 and x=-1/6.

__

You can also use the quadratic formula to find the zeros. That tells you the solution to ...

  ax² +bx +c = 0

is

  x = (-b ±√(b²-4ac))/(2a)

Comparing your equation to the standard form, you can identify the coefficients as ...

  a = 6, b = -17, c = -3

so the zeros are ...

  x = (-(-17) ±√((-17)² -4(6)(-3)))/(2(6))

  x = (17 ±√369)/12 = (17 ±19)/12 = {-2, 36}/12 = {-1/6, 3}

The zeros are x = -1/6 and x = 3.

To find zeros of a quadratic equation, you use the quadratic formula. Applying this formula to the equation y = 6x^2 - 17x - 3 yields two solutions, representing the two points where the function intersects the x-axis.

The subject of this question concerns finding the zeros of a given quadratic equation, y = 6x^2 - 17x - 3. Zeros are the x-values that make the equation equal to zero or to point where the function intersects the x-axis.

To find the zeros, we'll use the quadratic formula, which is derived from an equation of the form ax² + bx + c = 0: x = [ -b ± sqrt(b^2 - 4ac) ] / (2a).

Applying the quadratic formula to your equation, with a = 6, b = -17, and c = -3, we get the two solutions, which are the zeros of the equation: x = [ 17 ± sqrt((-17)^2 - 4*6*-3) ] / (2*6). Computing this, we get two solutions, or two zeros, which are the points where your function y = 6x^2 - 17x -3 crosses the x-axis.

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Answer:

D = {0 , 1 , 2 , 3 , 4 , 5} and R = {1 , 2 , 4 , 8 , 16 , 32} ⇒ answer D

Step-by-step explanation:

* Lets talk about the domain and the range of a function

- The domain is the input values

- The range is the output values

- f(x) = y,  x is the input then x is the domain of the function and y is the

  output then y is the range of the function

- Example:

# If x = {2 , 3 , 5) and f(x) = 2x

- The input is x to find f(x) substitute the values of x in f(x)

- f(2) = 2(2) = 4 , f(3) = 2(3) = 6 , f(5) = 2(5) = 10

- The output is f(x) = {4 , 6 , 10}

- From all steps above the domain of f(x) is {2 , 3 , 5) and the range

 is {4 , 6 , 10}

* Lets solve the problem

- There are 32 teams participating  in a single-elimination soccer

 tournament

- x is the number of rounds

- f(x) is the number of teams

- only the winning teams from each round progress to the next

 round of the tournament

* Lets look to the graph and find the domain and the range

- The domain the the values of x and the range is the values of f(x)

∵ At x = 0 then f(0) = 32 ⇒ 32 teams inter the 1st round

∵ At x = 1 then f(1) = 16 ⇒ 16 teams inter the 2nd round

∵ At x = 2 then f(2) = 8 ⇒ 8 teams inter the 3rd round

∵ At x = 3 then f(3) = 4 ⇒ 4 teams inter the 4th round

∵ At x = 4 then f(4) = 2 ⇒ 2 teams inter the 5th round

∵ At x = 5 then f(5) = 1 ⇒ 1 team in win

- From all above:

∴ The domain is {0 , 1 , 2 , 3 , 4 , 5} and the range is {1 , 2 , 4 , 8 , 16 , 32}

* D = {0 , 1 , 2 , 3 , 4 , 5} and R = {1 , 2 , 4 , 8 , 16 , 32}

Answer:

x=ysq2-2

Step-by-step explanation:

because you get the x alone and subtract the variable

Answer:

Graph A

Step-by-step explanation:

because the function given is y= (x+3)(x+3) the vertex is (-3,0)

Answer:

(d-5)x2

Step-by-step explanation:

you said a number d is subtracted by 5 then doubled so lets make an example. d=6

(6-5)x2

(6-5)=6-5=1

(1)x2=1x2=2

If a number d is decreased by 5 and then doubled, then we can represent that event with an algebraic expression as:

[tex]2\times (d-5)[/tex]

The number d decreased by 5 is written as: [tex]d - 5[/tex]

When we double a thing, we multiply by 2.

Thus we have the algebraic form of given condition as:

[tex]2\times(d-5)[/tex]

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