Need help with geometric sequences
30 points

The area of pasture is 60000 square feet.

Step-by-step explanation:

Perimeter of rectangular pasture = 1000 feet

Width of pasture = w

Length of pasture = l = w+100

We know that,

Perimeter = 2(Length+width)

[tex]1000=2(w+100+w)\\1000=2(2w+100)\\1000=4w+200\\1000-200=4w\\800=4w\\4w=800[/tex]

Dividing both sides by 4

[tex]\frac{4w}{4}=\frac{800}{4}\\w=200[/tex]

Width is 200 feet.

Length = w+100 = 200+100 = 300 feet

Area of pasture = A = Length * Width

[tex]Area\ of\ pasture=300*200\\Area\ of\ pasture=60000 \ ft^2[/tex]

The area of pasture is 60000 square feet.

Keywords: rectangle, area

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The question is about calculating the area of a rectangular pasture given its perimeter and relation between its length and width. After setting up equations based on the given conditions and calculating, the area of the pasture is found to be 60,000 square feet.

The subject of this question is Mathematics, specifically dealing with the calculation of area from given perimeter and length-width relationship in a rectangle. Let's denote the width of the rectangular pasture as 'w', and its length would then be 'w+100'.

The formula for the perimeter of a rectangle is 2*(length + width). As given, the perimeter is 1000 feet, so we set up the equation: 1000 = 2*(w+100 + w).

Simplify this to get the width 'w' which is 200 feet and the length is 'w+100', so 300 feet.

The area of a rectangle is calculated by the formula length*width, therefore, calculating gives 200*300 = 60,000 square feet.

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Answer:

The line 2 and Line 3 are perpendicular to each others

But There is no relation between Line 1 and Line 2  , Line 1 and Line 3

Step-by-step explanation:

Given as :

The three line equation is

Line 1 : 2 y = 5 x + 6

Line 2 : y = [tex]\frac{2}{5}[/tex] x - 1

Line 3 : 10 x + 4 y = - 6

Now, The standard equation of line is

y = m x + c

where m is the slope of line

And c is the y intercept

So, From Line 1

2 y = 5 x + 6

or , y =  [tex]\frac{5}{2}[/tex] x + [tex]\frac{6}{2}[/tex]

I.e y =  [tex]\frac{5}{2}[/tex] x + 3

So,  slope of this line = [tex]m_1[/tex] =  [tex]\frac{5}{2}[/tex]

Again , From Line 2

y = [tex]\frac{2}{5}[/tex] x - 1

So, slope of this line =  [tex]m_2[/tex] =  [tex]\frac{2}{5}[/tex]

Similarly , From Line 3

10 x + 4 y = - 6

I.e 4 y = - 6 - 10 x

or, y = - [tex]\frac{6}{4}[/tex] -  [tex]\frac{10}{4}[/tex] x

I.e y =  - [tex]\frac{5}{2}[/tex] x  - [tex]\frac{6}{4}[/tex]

So, Slope of this line = [tex]m_3[/tex] = - [tex]\frac{5}{2}[/tex]

Now, If the lines are parallel , then the slope of the lines are equal

And  If the lines are perpendicular , then the product of the slopes of the lines = - 1

Now, From given lines

[tex]m_2[/tex] × [tex]m_3[/tex] = [tex]\frac{2}{5}[/tex] × ( - [tex]\frac{5}{2}[/tex] )

I.e [tex]m_2[/tex] × [tex]m_3[/tex] = - 1

So, The line 2 and Line 3 are perpendicular to each others

But There is no relation between Line 1 and Line 2  , Line 1 and Line 3

Hence The line 2 and Line 3 are perpendicular to each others

But There is no relation between Line 1 and Line 2  , Line 1 and Line 3 Answer

Answer:

Option(D)

Finger Painting can be hard for children to control, but helps free their tension

Explanation:

Finger painting is a form of art in which the paintings or drawings are created by using fingers instead of a pen, pencil or brush.In this the fingers are dipped in paint and then the drawings are made by using bare hands.

This is a hard technique to make a painting or illustration and hence can be hard for children to control, but since it involves sensing touch, it helps release the tension and soothe the mind of the person who does painting using this method.

Answer:

19??

Step-by-step explanation:

Answer:

yes it is 19 all you have to do is add 12 and 7

Answer: 19.5

Step-by-step explanation:

Answer:

$960.95

Step-by-step explanation:

The question is about finding the final amount after 4 years of a $700 investment with 8% interest, compounded quarterly. This can be solved using the compound interest formula.

The subject of your question pertains to compound interest in mathematics. Given the parameters, we want to find the amount after 4 years when $700 is invested at an interest rate of 8%, compounded quarterly. To solve this, we can use the compound interest formula, A = P(1 + r/n)^(nt), where 'A' is the amount of money accumulated after n years, including interest, 'P' is the principal amount (the initial amount of money), 'r' is the annual interest rate (in decimal form), 't' is the time the money is invested for in years, and 'n' is the number of times that interest is compounded per year. Plugging the values in, we get A = $700(1 + 0.08/4)^(4*4) which gives us the total amount after 4 years.

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The value of x is determined as 64 by solving the first equation. This value is then used to find the percentage n, which turns out to be 16%.

First, let's solve the equation 125% of x is 80. 1.25 times x equals 80. Therefore, x equals 64. Now, we can use that value to solve the second equation, x is n % of 400. This means 64 is what percent of 400. Expressing this as a proportion: 64/400 = n/100. Evaluating this gives n = 16%.

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Answer:

(9 x+6)   =  3( 3x + 2)

(3x+2) represent the cost of each ticket.

Step-by-step explanation:

Here, the given expression representing  the cost for three friends to go to the movies  is  : (9 x+6 )

Now,simplifying the given expression, we get:

(9 x+6)   =  3( 3x + 2)

So, the given expression represents 3 times ( 3x + 2 ).

So, here (3x+2) represent the cost of each ticket.

And the expression 3 ( 3x+2)  represent the cost 3 tickets combined.

Answer:

Step 4: 44 32/24 - 37 15/24= 8 17/24

Here we can finally find out the mistake done by Noa. The result is 7 17/24 and not 8 17/24.

Step-by-step explanation:

1. Let's review carefully all the steps taken by Noa to calculate the difference of the circumferences of the two trees.

Circumference Tree 1 = 37 5/8 inches around

Circumference Tree 2 =  45 1/3 inches around

Step 1: 45 1/3- 37 5/8

The measures are correct, no issues copying them.

Step 2: 45 8/24 - 37 15/24

Noa looked for common denominators

1/3 * 8/8 = 8 /24 is correct; 5/8 * 3/3 = 15/24 is also correct.

Step 3: 44 32/24 - 37 15/24

Noa looked for making the fraction part higher on the left side:

45 8/24 = 44 32/24 is correct because 24/24 = 1

Step 4: 44 32/24 - 37 15/24= 8 17/24

Here we can finally find out the mistake done by Noa. The result is 7 17/24 and not 8 17/24.

Answer:

step 4 is correct so D

Step-by-step explanation:

i just took the test

Answer:

See step-by-step explanation

Step-by-step explanation:

Whole numbers are [tex]0,\ 1,\ 2,\ 3,\ 4,\ ...[/tex]

Integer but not whole numbers are [tex]...,\ -4,\ -3,\ -2,\ -1[/tex]

Rational numbers are fractions

Irrational numbers are numbers that are not rational

[tex]\pi[/tex] is irrational number

[tex]-100[/tex] is integer but not whole number

[tex]-34[/tex] is integer but not whole number

[tex]-4[/tex] is integer but not whole number

[tex]-\dfrac{8}{4} =-2[/tex] is integer but not whole number

[tex]0.333...=\dfrac{1}{3}[/tex] is rational number

[tex]0.456783...[/tex]  is irrational number

[tex]3[/tex] is whole number

[tex]9.23456=\dfrac{923,456}{100,000}[/tex] is rational number

[tex]\sqrt{4}=2[/tex] is whole number

[tex]\sqrt{8}=2\sqrt{2}[/tex] is irrational number

[tex]\dfrac{1}{2}[/tex] is rational number

[tex]\dfrac{49}{7}=7[/tex] is whole number

[tex]\dfrac{89}{10}[/tex] is rational number

[tex]zero[/tex] is whole number

Answer:

3:2

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Let ∠4 be x then ∠6 is [tex]\frac{1}{8}[/tex] x

∠4 and ∠6 are same side interior angles and are supplementary, thus

x + [tex]\frac{1}{8}[/tex]x = 180

Multiply through by 8 to clear the fraction

8x + x = 1440, that is

9x = 1440 ( divide both sides by 9 )

x = 160

Hence ∠4 = 160° and ∠6 = 160° ÷ 8 = 20°

Answer:

[tex]m \angle 4 = 160 \°\\m \angle 6 = 20 \°[/tex]

Step-by-step explanation:

From the graph, we can say that

[tex]m \angle 6 + m \angle 4 = 180 \°[/tex]

Because they are consecutive interior angles, and they sum 180° by definition. So, the reason of third statement is "by definition of consecutive interior angles".

We already know that

[tex]m \angle 6 = \frac{1}{8} \times m \angle 4[/tex]

But,

[tex]m \angle 6 + m \angle 4 = 180 \°\\m \angle 6 = 180\° - m \angle 4[/tex]

Replacing this, we have

[tex]180\° - m \angle 4=\frac{1}{8}(m \angle 4)\\(\frac{1}{8}+1) (m\angle 4)=180\°\\\frac{9}{8}(m\angle 4) = 180 \°\\ m \angle 4 = \frac{180(8)}{9}= 160\°[/tex]

Then,

[tex]m \angle 6 + m \angle 4 = 180 \°\\m \angle 6 + 160\° =180\°\\m \angle 6 = 180-160=20[/tex]

Therefore, the measures of these two angles are

[tex]m \angle 4 = 160 \°\\m \angle 6 = 20 \°[/tex]

There were 980 student desks originally.

Step-by-step explanation:

Number of desks purchased = 295

Desks bought for teacher = 50

Desks for students = No. of desks purchased - desks bought for teachers

Desks for students = 295 - 50 = 245

This is 1/4 of number of original student desks.

Let x be the number of original student desks.

According to statement;

[tex]\frac{1}{4}\ of\ x=245\\\frac{1}{4}x=245[/tex]

Multiplying both sides by 4;

[tex]4*\frac{1}{4}x=245*4\\x=980[/tex]

There were 980 student desks originally.

Keywords: subtraction, multiplication

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Answer:

The height is 1343.13 meters.

Step-by-step explanation:

Air pressure may be represented as a function of height h in meters above the surface of Earth as shown below :

[tex]P(h) = P. e^{-0.000121h}[/tex] ......... (1)

In this function, P is air pressure at sea level and h is measured in meters.

Let at a height of h meters the pressure is 85% of the sea level pressure.  

Hence, from equation (1), we get

[tex]0.85 = e^{- 0.000121 h}[/tex]

Taking ln both sides, we can write

ln 0.85 = -0.000121 h (ln e) {Since [tex]\ln a^{b} = b \ln a[/tex]}

⇒ h = 1343.13 meters (Answer)

When trying to find the point-slope equation of a line you need to pick a point and plug it into the plain equation with your slope.

-3 = 1/3(-1) +b

Multiply your slope with your x

-3 = -1/3 +b

Move the -1/3 to the other side by doing the opposite operation, in this case being addition.

-3 +1/3 = b

-2 2/3 = b

y = 1/3x - 2 2/3

I can't really give an explanation, since it's just multiplication, so here are the answers:

1. 32

2. 12

3. 24

4. 40

5. 20

6. 12

7. 12

Answer:The formula for variable h can be calculated by the following steps;

Step-by-step explanation:

f=8gh

f/8g=h

Or

h=f/8g

To solve for the variable h in the formula f = 8gh, divide both sides of the equation by 8g. The formula for the variable h is h = f / (8g).

To solve the formula for the variable h, we need to isolate h on one side of the equation. In this case, the equation is f = 8gh. To isolate h, we divide both sides of the equation by 8g. This gives us:

h = f / (8g)

So the formula for the variable h is h = f / (8g).

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Cancelling out both the -6 we get 12=0 which is not true, hence the equation is incorrect.

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}\\\\\text{Calculate what fraction of 30 is 18 and convert it to percent:}\\\\\dfrac{18}{30}=\dfrac{18:6}{30:6}=\dfrac{3}{5}\\\\\dfrac{3}{5}\cdot100\%=\dfrac{300}{5}\%=60\%[/tex]

[tex]\bold{METHOD\ 2:}\\\\\begin{array}{ccc}30&-&100\%\\\\18&-&p\%\end{array}\qquad\text{cross multiply}\\\\\\(30)(p)=(18)(100)\\\\30p=1800\qquad\text{divide both sides by 30}\\\\\dfrac{30p}{30}=\dfrac{1800}{30}\\\\p=60[/tex]

Final answer:

18 is 60% of 30, calculated by dividing 18 by 30 and then multiplying the result by 100.

Explanation:

Calculating the Percentage

To determine what percentage 18 is of 30, you can use the formula for calculating percentages:

Divide the number you want to find the percentage of (18 in this case) by the total number or 'whole' value (which is 30).

Multiply the result from step 1 by 100 to find the percentage.

So, the calculation is (18 ÷ 30) × 100, which equals 60%. Therefore, 18 is 60% of 30.

Answer:

x=60.4

Step-by-step explanation:

Add 7.6 on both sides

1/4x=15.1

Multiply both sides by 4

x= 60.4

Answer:

The total miles driven equation is [tex]y=27x[/tex]

Step-by-step explanation:

Given:

Number of gallons of gas is x.

Total miles driven is y.

Carl's new car gets 27 miles per gallon.

Hence to calculate total miles driven we need to multiply 27 with number of gallons of gas.

Hence the equation becomes.

[tex]y=27x[/tex]

[tex](fog)(x) = -x[/tex]

Step-by-step explanation:

The composition is calculated by putting the other function in place of variable

Given

[tex]f(x) = x - 1\\g(x) = -x+1[/tex]

The composition will be:

[tex](fog)(x) = g(x) -1\\=(-x+1) -1\\=-x+1-1\\=-x[/tex]

Hence,

[tex](fog)(x) = -x[/tex]

Keywords: Composition, Functions

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A 6-pack of t-shirts for $3.12 because 3.12 ÷ 6 is 0.52

Answer:

the last one is the least expensive it's only $0.52

Step-by-step explanation:

$2.24 ÷ 8 = $0.56

$3.00 ÷ 3 = $1.00

$4.24 ÷ 8 = $0.53

$3.12 ÷ 6 = $0.52

Answer:

h=11.3 and c=8(or 8.1 depending on what you do first)

Step-by-step explanation:

so we do the same thing like last time and 8√2 rounded is 11.3, and 7/√3, or 7√3/3 is 4( 4.04 gets rounded down). now we multiply by two because of the theorems and get 8(if this is wrong then try 8.1 because the answer differs depending on what you do first.)

This is an incomplete question, here is a complete question.

Debnil has 6 teaspoons of salt. The ratio of teaspoons to tablespoons is 3:1 How many tablespoons does Debnil have?

A. 1/18

B. 1/2

C. 2

D.18​

Answer : The correct option is, (C) 2

Step-by-step explanation :

As we are give that Debnil has 6 teaspoons of salt.

The ratio of teaspoons to tablespoons is 3 : 1.

It means,

if he has 3 teaspoons then he has 1 tablespoons

if he has 1 teaspoons then he has [tex]\frac{1}{3}[/tex] tablespoons

So,

if he has 6 teaspoons then he has [tex]6\times \frac{1}{3}=2[/tex] tablespoons

Therefore, Debnil have 2 tablespoons of salt.

The number of tablespoons that debnil has is;

C: 2

We are told that;

Thus, if the total spoons is x. Then;

¾x = 6

Thus;

x = (4 × 6)/3

x = 8 spoons

Thus, number of tablespoons she has = 8 - 6 = 2

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Answer:

The amount which real estate agency gets is $  21,010  .

Step-by-step explanation:

Given as :

The selling price for a house = $ 382,000

The commission rate for real estate agency = 5.5 %

The commission rate for the agent = 30 %

So, the commission which real estate agency get = 5.5 % of $ 382,000

I.e the commission which real estate agency get = 0.055 × $ 382,000

Or, the commission which real estate agency get = $ 21,010

Again ,

The commission which agent get = 30 % of $ 382,000

I.e the commission which agent get = 0.3 × $ 382,000

Or, the commission which agent get = $ 114,600

Hence The amount which real estate agency gets is $  21,010  . answer

The agent earns a commission of $6,303 from the $382,000 house sale. This is calculated by first determining the real estate agency's commission of 5.5% on the sale price, which is $21,010. Then calculating 30% of this figure, which is the agent's earnings.

To calculate the total commission the agent will receive, you first have to calculate how much the real estate agency gets, and then calculate the agent's earnings based on that number.

The real estate agency's commission is 5.5% of the total sold price of the house. This can be calculated as:

(5.5 / 100) * $382,000 = $21,010

The agent then receives 30% of this amount, which you calculate as:

(30 / 100) * $21,010 = $6,303

Therefore, the agent earns a commission of $6,303 from the sale of the house.

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Answer:

Ivan isn't the son

Step-by-step explanation:

To complete the pairs and have a difference of 3, add 4 to both sides of the equation.

To complete the pairs and have a difference of 3, the first number of the pair should be the larger number.

So, the equation ? - 4 = 3 can be solved by adding 4 to both sides of the equation.

? - 4 + 4 = 3 + 4

? = 7