I have been asked this question and I substituted the value of x in f with g(x), and rearranged the equality but is incorrect. ​

Answer:

[tex]\sum\limits^{n=6}_{n=1} {(-4+8n)}[/tex] is the notation to represent the sum of first six terms of the sequence 4, 12, 20, ....

So, the option "the summation from n equals 1 to 6 of negative 4 plus 8 times n" is the correct option as:    [tex] \sum\limits^{n=N}_{n=1} {(-4+8n)}[/tex].

Step-by-step explanation:

Let us consider the sequence

4, 12, 20, ....

As d = 12-4 = 20 - 12 = 8

Hence, the sequence is an arithmetic as the common difference between consecutive terms is same (constant).

So,

For the arithmetic sequence,

a, a + d, a + 2d, a + 3d.........a + (n - 1)d

The nth term = a + (n - 1)d

a = first term, d = common difference

For the given sequence 4, 12, 20,...

a = 4, d = 8

Lets put these values in Summation Formula.

Sigma notation to represent the sum of the first six terms of the following sequence:  [tex] \sum\limits^{n=N}_{n=1} {a+(n-1)d}[/tex]

⇒   [tex] \sum\limits^{n=N}_{n=1} {4+(n-1)8}[/tex]

⇒   [tex] \sum\limits^{n=N}_{n=1} {(4+8n-8)}[/tex]

⇒   [tex] \sum\limits^{n=N}_{n=1} {(-4+8n)}[/tex]

Hence, [tex]\sum\limits^{n=6}_{n=1} {(-4+8n)}[/tex] is the notation to represent the sum of first six terms of the sequence 4, 12, 20, .....

So, the option "the summation from n equals 1 to 6 of negative 4 plus 8 times n" is the correct option as:  [tex] \sum\limits^{n=N}_{n=1} {-4+8n}[/tex].

Keywords: sigma notation, arithmetic sequence, series

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Answer:

the summation from n equals 1 to 6 of negative 4 plus 8 times n

Please see the attachment below.

All the information is in the problem you just have to format it into an equation.

Point slope form: [tex]y_{2}- y_{1}=m(x_{2}- x_{1})[/tex] where "m" is the slope.

The equation would look like...

y+9=-2(x-10)

Answer:

Stacy is 13 meters apart from Christopher.

Step-by-step explanation:

Given:

Austin is hiding 12 meters south of Stacy.

Christopher is hiding 5 meters east of Austin.

To find distance between Stacy and Christopher.

Solution:

From the given data, we will trace the positions of each as shown in the figure below.

We find that the distance between Stacy and Christopher is the hypotenuse side of a right triangle formed by their positions.

By Pythagorean theorem:

[tex]Hypotenuse^2=Leg1^2+Leg2^2[/tex]

From the triangle:

Leg 1 = 5 meters

Leg 2= 12 meters

Plugging in the values.

[tex]Hypotenuse^2=5^2+12^2[/tex]

Simplifying.

[tex]Hypotenuse^2=25+144[/tex]

[tex]Hypotenuse^2=169[/tex]

Taking square root both sides.

[tex]\sqrt{Hypotenuse^2}=\sqrt{169}[/tex]

[tex]Hypotenuse=13[/tex] meters

Thus, distance between Stacy and Christopher = 13 meters

Stacy and Christopher are 13 meters apart. This was calculated using the Pythagorean theorem to find the hypotenuse of a right triangle with sides 12 meters and 5 meters.

To determine the distance between Stacy and Christopher, we need to view Stacy's location and the hiding places of Austin and Christopher as points on a grid in which Stacy is at the origin. Since Austin is hiding 12 meters south of Stacy, we can consider him to be at point A(0, -12). Christopher is hiding 5 meters east of Austin, this makes him at point C(5, -12).

Now, to find the distance between Stacy and Christopher, we'll use the Pythagorean theorem which says that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be written as:

C² = A² + B²

Where C is the hypotenuse, A and B are the other two sides of the triangle. In this case, A is the distance south (12 meters) and B is the distance east (5 meters). Thus,

C² = 12² + 5²

C² = 144 + 25

C² = 169

C = √169

C = 13 meters

Therefore, Stacy and Christopher are 13 meters apart.

Answer:

60 I think

Step-by-step explanation:

1100-400=700 12×60=720

59 hours

She has to save $700

If r and p are perpendicular:

1 + 2 = 90°

3 = 90°

4 + 5 = 90°

6 = 90°

If any one of these are true, r and p must be perpendicular

Answer:

Yes

Step-by-step explanation:

First you will have to find out the scale

Then you will find out the numbers that are

Perpendicular

Answer:

0ne week= 8 miles

W=5n

The money can you accumulate over the course of a year if you opt to save the money instead will be $82.68.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

It is also known as the product. If the object n is given to m times then we just simply multiply them.

Assume you drink eight sodas per week & they cost $1.59 each.

We know that there are 52 weeks in a year.

The money can you accumulate over the course of a year if you opt to save the money instead will be

⇒ $1.59 × 52

⇒ $82.68

The money can you accumulate over the course of a year if you opt to save the money instead will be $82.68.

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One roll of plain costs $20 and one roll of shiny costs $20 also.

Step-by-step explanation:

Let,

Cost of one roll of plain = x

Cost of one roll of shiny = y

According to given statement;

2x+2y=80     Eqn 1

8x+10y=360    Eqn 2

Multiplying Eqn 1 by 4

[tex]4(2x+2y=80)\\8x+8y=320\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](8x+10y)-(8x+8y)=360-320\\8x+10y-8x-8y=40\\2y=40[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{40}{2}\\y=20[/tex]

Putting y=20 in Eqn 1

[tex]2x+2(20)=80\\2x+40=80\\2x=80-40\\2x=40[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{40}{2}\\x=20[/tex]

One roll of plain costs $20 and one roll of shiny costs $20 also.

Keywords: linear equation, elimination method

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Answer:

The dimensions of the desk are

Length: 54 inches

Width: 30 inches

Step-by-step explanation:

we know that

The area of rectangle is equal to

[tex]A=LW[/tex]

where

L is the length

W is the width

we have

[tex]A=1,620\ in^2[/tex]

so

[tex]1,620=LW[/tex] ----> equation A

[tex]L=W+24[/tex] ----> equation B

substitute equation B in equation A

[tex]1,620=(W+24)W[/tex]

solve for W

[tex]1,620=W^2+24W[/tex]

[tex]W^2+24W-1,620=0[/tex]

Solve the quadratic equation by graphing

The solution is W=30 in

see the attached figure

Find the value of L

[tex]L=30+24=54\ in[/tex]

therefore

The dimensions of the desk are

Length: 54 inches

Width: 30 inches

Answer:

A

Step-by-step explanation:

We know that negative numbers are smaller than positive numbers, so let's compare the 2 negative numbers. Unlike positive numbers, the more negative it has, the smaller it is. So we know the smallest is -20. Without looking at the other numbers (even though I did just in case) we know that this is correct. They say least to greatest, so -20 should be first. A is the only one that starts with -20.

Answer:

the answer is D.) 4/3

Step-by-step explanation:

when you look for a slope that is perpendicular to the slope you are given you take the reciprocal and change the sign

Answer:

4/3

Step-by-step explanation:

Because perpendicular means negative reciprocal.

Answer:

256

Step-by-step explanation:

Answer:

Step-by-step explanation:he rate of return on Karen investment is 10%. Explanation: Given that. Bought price = P = $78500. Sale price = S =$850,000.

Answer:

The left side continues up, and the right side continues down.

Step-by-step explanation:

[tex]f(x) = -9x^3 + 8x^2 - 16x + 3[/tex]

To find the end behavior, determine the highest degree and leading coefficient

Highest degree is 3  and leading coefficient is -9

highest degree 3 is odd and leading coefficient is negative

As x->-infinity , y -> infinity

As x->infinity , y ->-infinity

The left side continues up, and the right side continues down.

Answer:

Correct answer is C.

Step-by-step explanation:

Answer:

62.28

Step-by-step explanation:

Answer:

  (a) d = 0.012v^2

  (b) 4.8 m

  (c) 25 m/s

Step-by-step explanation:

(a) Writing an equation to fit a bunch of data is often a matter of trial and error. You can often get an idea of the sort of function that is involved by graphing the data points.*

When we do that, we see the relationship is non-linear with an upward curvature. It might be described by a polynomial or exponential function.

When we try a quadratic equation, we find the fit is really quite good. The graphing calculator that does this quadratic regression analysis tells us the equation is essentially ...

  d = 0.012·v^2

__

(b) The equation predicts a depth of 4.8 m.

  d = 0.012·20^2 = 4.8

__

(c) Solving for speed, we get a speed of 25 m/s.

  7.5 = 0.012v^2

  625 = v^2 . . . . . . divide by .012

  25 = v . . . . . . . . . take the square root

_____

* The energy of a falling object is proportional to the square of its speed. If we assume that the depth of penetration into the clay is proportional to the energy absorbed, then it is not surprising to see a quadratic relationship between speed and distance. What is surprising is that this relationship would show up in middle school math problem, not a high-school physics problem.

Essentially, you have to assume the form of the equation, then find the coefficients that make it so. Working with the evenly spaced table values of 5, 10, 15 m/s can simplify the effort.

A graphing calculator or spreadsheet can do the bulk of the work once the data is entered.

Answer:

45% of 31 days is 13.95 days, theres your answer.

Question:

At noon a tank contains 6 cm of water after several hours it contains 3 cm of water what is the percent decrease of water in the tank

Answer:

The percent Decrease of water in the tank  is 50%

Step-by-step explanation:

Given:

Initial amount of water in the tank at the noon = 6 cm

amount of water remained in water after several hours = 3 cm

To Find:

The percent decrease =?

Solution:

The percent decrease in the tank

=>[tex]\frac{\text {water present after some hours }}{\text {initial water contained in the tank }} \times 100[/tex]

Substituting the values

=>[tex]\frac{3}{6} \times 100[/tex]

=>[tex]\frac{1}{2} \times 100[/tex]

=>[tex]\frac{100}{2}[/tex]

=> 50

Answer:

2020

Step-by-step explanation:

This is an example of what is called an "infinite continued fraction".

For the repeated fraction:

y = 2019 / (2 + 2019 / (2 + 2019 / (2 + 2019 / ...

We can rewrite using substitution:

y = 2019 / (2 + y)

Solving for y:

y (2 + y) = 2019

2y + y² = 2019

y² + 2y + 1 = 2020

(y + 1)² = 2020

y + 1 = ±√2020

y = -1 ± √2020

Since the repeated fraction must be positive, y = -1 + √2020.

Therefore:

x = (1 + y)²

x = (1 + -1 + √2020)²

x = 2020

Answer:

Part A) 170.66$ would be the original price.

Part B) 256$ would be the price that the store paid for the music player.

Part B) What you need to balance is your markup, meaning how much to raise your price, and your markdown or discount, meaning, how to much to decrease prices.

Step-by-step explanation:

Part A) Determining the Original Price

Note: when a shopkeeper devalues of a certain product or commodity as he/she is being unable to sold the product or commodity at the original selling price that was planned, it normally means the product or commodity is being markdown due to certain issues.

So, a music player was marked down by 1/4 of the original price, and we have to calculate the original price if the sales price is $128.

Let 'p' be the original price

As a music player was marked down by 1/4 of the original price

So, Markdown = 1/4p

As the sales price is $128

As the Sale price = [tex]p - \frac{p}{4}[/tex] ⇒ [tex]\frac{3p}{4}[/tex]

[tex]128 = \frac{3p}{4}[/tex]

[tex]552 =3p[/tex]

[tex]p =170.66[/tex]          

Hence, 170.66$ would the original price.

Part B) Determining the Price that the store paid for the music player

When an amount is added to the cost price of a product or commodity in order to determine the selling price, it means the the product or commodity is being marked up.

So, as the music player was marked up by 1/2 before it was placed on the sales floor and we have to determine the price that store paid for the player.

So, dividing the original price by 2 and adding the result to the original price would give us the price that store had to pay for the music player.

As the original price is 170.66.

So, the price that the store paid for the music player can be calculated as:

price = 170.66 + 170.66/2

price = 170.66 + 85.33

price = 255.99$  ≈ 256$

Therefore, 256$ was the price that the store paid for the music player.

Part C) Determining the difference between the discount price and the price that the store paid for the music

For example, let suppose you are a shopkeeper and have a jeans fabric business. You want to make money from it. But, in order to earn money from selling jeans fabric, you have to make sure that your price must be at the right value price both in terms of generating money and also giving your customer a great value for the money to given them a decent deal.

What you need to balance is your markup, meaning how much to raise your price, and your markdown, meaning, how to much to decrease prices.

In business, the conditions may never always remain favorable due to certain circumstance, hence bad days. Sometimes, the conditions get ideal for business, hence good days.

As I earlier sated that when a shopkeeper devalues of a certain product or commodity as he/she is being unable to sold the product or commodity at the original selling price that was planned, it normally means the product or commodity is being markdown due to certain issues.

For example, the cost price of 1 Jeans fabric is 10$, and you want to earn profit. So, you mark up your fabric to 30$.  As $30 is $20 more than $10. So, markup value will be 2. In terms of percentage, it means you have a markup of 200%.

But, due to certain issues, your sales are being effected due to certain condition. In order to not affect the sales, you want to markdown the price - a kind of discount. Your starting price was $30 and want to decrease the price to $20. It means the difference is $10. So, you have made a markup or given a discount of $30/$10 = 0.33. In terms of percentage, it is around 33%. So, you have given the discount of 33% to hope for the great sales.

So, in the question, when the music player was marked down by 1/4 of the original price, it means the discount of 1/4 of the original price was provided. As the sale price was $128, and original price was $170.66. So, discount of 1/4 or 25% was offered.

As the original price was $170, and it was marked up by 1/2 by the owner or creator of music player before it was placed on the sales floor. So, 256$ was the price that the store paid for the music player.

Keywords: markdown, markup, discount, price

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Final answer:

Jada's speed (⅔ mile per minute) is three times faster than her cousin's speed (⅔ mile per minute); thus, Jada is moving faster.

Explanation:

To determine who is moving faster between Jada and her cousin, we need to calculate their swimming speeds and compare them. Speed can be calculated by dividing the distance by the time it takes to cover that distance.

Jada's Speed:

Jada swims 2 miles in 12 minutes. To find her speed, we use the formula:

Speed = Distance ÷ Time

Speed = 2 miles ÷ 12 minutes = ⅔ mile per minute

Jada's Cousin's Speed:

Jada's cousin swims 1 mile in 24 minutes. Using the same formula:

Speed = 1 mile ÷ 24 minutes = ⅔ mile per minute

Comparison and Result:

Jada's speed is ⅔ mile per minute, whereas her cousin's speed is ⅔ mile per minute. Jada is swimming at a higher speed because she covers more distance in less time compared to her cousin. Specifically, she swims three times faster, evidenced by comparing their speeds:

Jada's speed ÷ Cousin's speed = ⅔ mile per minute ÷ ⅔ mile per minute = 3

Therefore, Jada is moving three times faster than her cousin.

[tex]\text{The constant of variation is a fancy word for rate of change}\\\\\text{You're trying to find the rate of change in this scenario, which would}\\\text{be your constant of varaition}\\\\\text{To find this, we need to know how much he makes each hour}\\\\\text{Find this by dividing 175 by 15:}\\\\175\div15= 11.666\\\\\text{Round to the nearest hundredths}\\\\11.67\\\\\boxed{\text{Constant of variation: 11.67}}[/tex]

Based on the information given the constant of variation is 11.67.

Using this formula

Constant of variation=Amount earned/Time

Where:

Amount earned=$175

Time=15 hours

Let plug in the formula

Constant of variation=$175/15

Constant of variation=11.66

Constant of variation=11.67 (Approximately)

Inconclusion  the constant of variation is 11.67.

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The one should pay [tex]2\frac{3}{16}[/tex] dollars

Step-by-step explanation:

Let us revise how to multiply a mixed number by a proper fraction

∵ One yard of a ribbon costs [tex]3\frac{1}{2}[/tex] dollars

∵ We need to find the cost of [tex]\frac{5}{8}[/tex] yards

- Multiply the cost of 1 yard by [tex]\frac{5}{8}[/tex]

∵ [tex]3\frac{1}{2}[/tex] = [tex]\frac{3(2)+1}{2}[/tex] = [tex]\frac{6+1}{2}[/tex]

∴ [tex]3\frac{1}{2}[/tex] = [tex]\frac{7}{2}[/tex]

∵ The cost = [tex]\frac{7}{2}[/tex] × [tex]\frac{5}{8}[/tex]

∴ The cost = [tex]\frac{7(5)}{2(8)}[/tex]

∴ The cost = [tex]\frac{35}{16}[/tex]

Change the improper fraction to a mixed number

∵ 35 ÷ 16 = 2 and remainder 3 ⇒ (16 × 2 = 32)

∴ [tex]\frac{35}{16}[/tex] = [tex]2\frac{3}{16}[/tex]

∴ The cost = [tex]2\frac{3}{16}[/tex] dollars

The one should pay [tex]2\frac{3}{16}[/tex] dollars

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Answer:

2.1875

Step-by-step explanation:

Answer:

(3, - 25 )

Step-by-step explanation:

Given a quadratic in standard form : y = ax² + bx + c : a ≠ 0

The the x- coordinate of the turning point is

x = - [tex]\frac{b}{2a}[/tex]

Given

y = (x + 2)(x - 8) ← expand factors using FOIL

  = x² - 6x - 16 ← in standard form

with a = 1 and b = - 6, thus

x = - [tex]\frac{-6}{2}[/tex] = 3

Substitute x = 3 into the equation for corresponding value of y

y = (3 + 2)(3 - 8) = 5(- 5) = - 25

turning point at (3, - 25 )

Answer:

Table #4

Step-by-step explanation:

because for every one x added, 2 y are added( if that makes any sense)

Answer:

Second from the top

The answer you have selected:

40:8 , 50:10, 60:14, 90:18

Proportions can be viewed as fractions:

40/8, 50/10, 60/14, 90/18

Now we have to simplify these fractions

5 , 5 , 4.3, 5

Unfortunately, they do not all come out to the same number, so this answer is incorrect

The second answer from the top:

4/2 , 7/3.5, 8/4, 10/5

These all equal 2 when simplified

2, 2, 2, 2

This shows a proportional relationship between x and y. If you would like to continue to make sure the bottom two are incorrect, you can use the steps that I have used for the first two. Hope this helps :)

Answer:

g>=-12

Step-by-step explanation:

g+11>=-1

g>=-1-11

g>=-12

Answer:

40 mg

Step-by-step explanation:

Given,

The prescribed dosage the medicine for an adult = 180 milligrams,

Since, the minimum age of an adult = 18 years,

So, the prescribed dosage of the medicine for 18 years old person = 180 milligrams,

Thus, the ratio of prescribed dosage of medicine ( in mg ) and age of person ( in years ) = [tex]\frac{180}{18}[/tex]

Suppose prescribed dosage of a certain medicine for a child 4 years old is x mg,

So, ratio of prescribed dosage of medicine and age = [tex]\frac{x}{4}[/tex]

[tex]\frac{x}{4}=\frac{180}{18}[/tex]

[tex]\frac{x}{4}=10[/tex]

[tex]\implies x = 4\times 10 = 40[/tex]

Hence, the prescribed dosage of a certain medicine for a child 4 years old would be 40 mg.

Answer:

k=3

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In this problem we have

[tex]y=3x[/tex]

therefore

The constant of proportionality  is k=3

Answer:

k=3

Step-by-step explanation:

i went on knan and it worked

Answer:

4 terms

Step-by-step explanation:

Terms are separated by adding or subtracting.

The terms are:

14m

-8.8n

5p

-1

The variables are not separate terms because they are multiplying with the coefficient, not adding or subtracting.

Answer:

411

1000 is divisible by 4, 600 is divisible by four, and 44 is divisible by for: add up you get 250+150+11

Step-by-step explanation:

411

Using place value, the quotient of 1,644 and 4 is: 411.

Given the dividend, 1,644, to divide it by the divisor, 4, break down 1,644 using place value, and divide by 4 separately.

1,644/4 = (1,000 ÷ 4) + (600 ÷ 4) + (44 ÷ 4)

1,644/4 = (250) + (150) + (11)

1,644/4 = 411

Therefore, using place value, the quotient of 1,644 and 4 is: 411.

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