in a G.P the 7th term is 16 times the 3rd term and the sum of the 2nd term and the 6th term is 102.if the common ratio(r) is positive .find the
1 common ratio
2 first term
3 sum of the 8th term

length×width = 108

length + 2×width = 30

length = 30 - 2×width

using that in the first equation

(30 - 2×width)×width = 108

-2×width² + 30×width - 108 = 0

the general solution to such a quadratic equation like

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

so,

width = (-30 ± sqrt(30² - 4×-2×-108))/(2×-2) =

= (-30 ± sqrt(900 - 864))/-4 =

= (-30 ± sqrt(36))/-4 = (-30 ± 6)/-4

width1 = (-30 + 6)/-4 = -24/-4 = 6 ft

width2 = (-30 - 6)/-4 = -36/-4 = 9 ft

for width = 6 ft

length = 30 - 2×width = 30 - 12 = 18 ft.

for width = 9 ft

length = 30 - 2×width = 30 - 18 = 12 ft

given the request that the length sound be as long as possible,

width = 6 ft

length = 18 ft

is our solution.

Answer:

figure it out best of luck tho.

The probability of raffle ticket is a winner is 0.0002.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an occurrence may be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

Given:

probability that your raffle ticket is not a winner = 0.9998.

Now, we know if we have to find the complement probability we can use

P(E) = 1 - P(not E)

where E is any event.

Here, E = not winner

So, P( raffle ticket is a winner)

= 1- 0. 9998                                                  

= 0.0002

Hence, the probability of raffle ticket is a winner is 0.0002.

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The ratio of the number of history majors to the number of mathematics majors is 3 to 2.

When two objects are related using numbers or amounts, the relationship is known as a ratio.

Let E be the number of English majors, H be the number of history majors, and M is the number of math majors.

Now,

There are twice as many English majors as history majors.

E = 2 × H

There are three times as many English majors as mathematics majors.

E = 3 × M

Now, let's assume E = 6.

Then,

6 = 2 × H

H = 3 and,

6 = 3 × M

M = 2

Therefore, the ratio of the number of history majors to the number of mathematics majors will be:

H: M = 3 : 2

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The graph of an exponential function has a y-intercept of 9 and contains the point (2,144). the function that describes the graph.

y=9(4)^x

This is further explained below.

Generally, the Standard form of an exponential function

y=a b^x

Where

y= is the y component of the graph

x=  is the x component of the graph

a and b are equation vaiables

Given the y-intercept (0,9) and the point (2,144) Applying both.

a=9,

144=9 b^2

Solve further by making b the subject of formular

b^2=144/9

b^2=16

b[tex]= \sqrt{ 16}[/tex]

Therefore  b=4

So, y=9(4)^x

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Answer: about $100,000.

Step-by-step explanation: i gave an estimate because your answer calls for an estimate, not an exact answer. $100,000 is correct because 24,897*4 = 99,588.

Answer:

4.62 segments should be brought to complete the job.

Step-by-step explanation:

I guess you only need the answer so, is it okay with no explanation?

If she thinks that after 8 months, she will have spent around $75.00 total.  Dominique's estimate is not reasonable?

We have to make use of the given data to find whether amount of $75 which she estimated that she will spent after 8 months is reasonable

Total cost:

Total cost =$15.50  + 10 × $0.99 × 8

Total cost = $15.50 + 9.9 × 8

Total cost = $15.50 +$79.2

Total cost = $94.7

Hence,

$94.70 ≥ $75.00

Based on the above calculation the amount she estimated is not a reasonable amount because the total cost is greater that the estimated amount.

Therefore we can conclude that the estimate is unreasonable.

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The estimate of the Dominique's is not reasonable.

Given that,
Dominique paid $15.50 to join an online music service. She purchases 10 songs each month at a cost of $0.99 per song. Dominique thinks that after 8 months, she will have spent around $75.00 total. Is Dominique's estimate reasonably is to be justified.

Here,
According to the question,
The total cost of the song for 8 months = 8 (0.99 x 10)
                                                            = $ 79.2
Total cost  = 15.50 + 79.2 = $94.7
Since the total cost exceeds Dominique's estimate so her estimate is not reasonable.

Thus, the estimate of the Dominique's is not reasonable.

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Answer:

x = 4

Step-by-step explanation:

80 is equal to 20x because they are alt ext angles

so

80 = 20x

divide to both sides

4 = x

that is your answer

Answer:

0.55

Step-by-step explanation:

( x1, y1 ) = ( 2, 11.9 )

Here,

x1 = 2

y1 = 11.9

( x2. y2 ) = ( 4, 13 )

Here,

x2 = 4

y2 = 13

Formula : -

Rise over run = ( y2 - y1 )/( x2 - x1 )

Rise over run = ( 13 - 11.9 )/( 4 - 2 )

                      = 1.1/2

Rise over run = 0.55

Answer:

-3

Step-by-step explanation:

f(x) = (x^2 - 4)/(x + 2)

Substituting x = -1,

f(-1) = (1 - 4)/(-1 + 2)

f(-1) = -3

The solution is ; 5/6 = 0.833... (recurring decimal)

Let J be Jasmine age and S the sister's age. Then, we have

this equality means Jasmine is 5 years younger than twice her sister's age. Now, we also know that J=39 years then by substituying this value into the last equality, we have

and now, we can solve this equation for S. First, we must move -5 to the right hand side as 5. It reads

and finally, we obtain

therefore, Jasmine's sister has 22 years old.

[tex]Answer:\ \boxed {-n+3}[/tex]

Step-by-step explanation:

                            y=mx+b

1.

To find m, choose any two coordinates from the table: (1,2) and (0,3)

and use the formula for the slope of the line:

                            [tex]\displaystyle\\\boxed {The\ slope\ m=\frac{y_2-y_1}{x_2-x_1} }[/tex]

[tex]\displaystyle\\m=\frac{3-2}{0-1} \\\\m=\frac{1}{-1} \\\\m=-1\\\\Hence,\ y=-x+b\ \ \ \ (1)[/tex]

2.

To find b, choose any coordinate from the table: (2,1) and substitute its values into the formula (10):

[tex]2=-(1)+b\\\\2=-1+b\\\\2+1=-1+b+1\\\\3=b\\\\Thus,\ b=3\\\\Hence, \ y=-x+3[/tex]

1) 20 percent of 60 is 12

2) 25 percent of 24 is 6

3) 4 percent of 600 is 24

4) 88 is 110 percent of 80

5) 18 is 20 percent of 90

To calculate the proportion of value to the original value, the percentage concept is employed. For calculating a company's profit or loss percentage , percentages are frequently employed in business. Additionally, it's a common way for universities and schools to display the grades that pupils have earned. An estimation of the pupils' grades can be made using a percentage calculation. A ratio of any value to the total value multiplied by 100 is how percentages are typically defined. The percentage is shown as % in symbols.

1) [tex]\frac{20}{100}[/tex]×x=12

x=[tex]\frac{1200}{20}[/tex]

x = 60

2) x ×[tex]\frac{24}{100}[/tex] = 6

x=25%

3)[tex]\frac{4}{100}[/tex]×600 = 24

4) [tex]\frac{110}{100}[/tex]×x = 88

x =[tex]\frac{8800}{110}[/tex]

x= 80

5) [tex]\frac{x}{100}[/tex]×90 = 18

x = 20

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Answer:

i believe it is 20

Step-by-step explanation:

to find the diameter you just deveide the circumference by pi thats it and i got 20.0101433

so i believe its 20

hope this helped :)

Answer:

c=125 dollars

Step-by-step explanation:

c=25p

p(people)=5

c=25*5

c=125

Answer:

100/21

Step-by-step explanation:

The value of x is 17/12.

Given equation:-

3/4 = x - 4/6

We have to find the value of x from the given equation.

Rearranging the terms to find the solution, we can write,

x = 3/4 + 4/6

Least Common Multiple (LCM) of 4 and 6 = 12

Hence, we can write,

x = (3*3) + (2*4)/12

x = (9 + 8)/12

x = 17/12

Least Common Multiple (LCM)

In arithmetic, Least Common Multiple (LCM) of two or more numbers is the least positive number that can be divided by both the numbers, without leaving the remainder. It is also known as Lowest Common Multiple (LCM), Least Common Denominator, and Smallest Common Multiple.

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Answer:

Step-by-step explanation:

36÷3=1236+12=48100-48=52EN İYİ SEÇERSEN SEVİNİRİM BAŞARILAR DİLERİM

Answer:

Supplementary: 2,3

Complementary: 1,4,5

Vertical Angles (VA): 1 is equivalent to 4

Step-by-step explanation:

Supplementary angles are angles that equal up to 180 degrees.

Complementary angles are angles that are 90 degrees.

VA (Vertical Angles) are angles that are basically across from other (take a look at 1 and 4) AND NO, 2,3 or 5 would be considered as Vertical angles as they do not Aline.

The most appropriate choice for rationalization will be given by

What is rationalization?

When a surd is present in the denominator of a fraction, the surd has to be removed form the denominator. The process by which surds in the denominator of a fraction can be eliminated is called rationalization.

Here,

let [tex]\sqrt{x}[/tex] = a

[tex]x = a^2[/tex]

[tex]\frac{2a-9}{a^2 -5a + 6} - \frac{a + 3}{a-2} - \frac{2a+1}{3-a}[/tex]

[tex]\frac{2a-9}{a^2 -2a-3a + 6} - \frac{a + 3}{a-2} - \frac{2a+1}{3-a}[/tex]

[tex]\frac{2a-9}{a(a -2)-3(a -2)} - \frac{a + 3}{a-2} + \frac{2a+1}{a - 3}[/tex]

[tex]\frac{2a-9}{(a-2)(a-3)} - \frac{a + 3}{a-2} + \frac{2a+1}{a-3}[/tex]

[tex]\frac{2a-9 - ((a + 3)(a-3)) + (2a+1)(a-2)}{(a-2)(a-3)}[/tex]

[tex]\frac{2a-9-a^2+9+2a^2-4a+a-2}{(a-2)(a-3)}[/tex]

[tex]\frac{2a-a^2+2a^2-3a-2}{(a-2)(a-3)}[/tex]

[tex]\frac{a^2-a-2}{(a-2)(a-3)}[/tex]

[tex]\frac{a^2-2a+a-2}{(a-2)(a-3)}[/tex]

[tex]\frac{a(a-2)+1(a-2)}{(a-2)(a-3)}[/tex]

[tex]\frac{(a-2)(a+1)}{(a-2)(a-3)}[/tex]

[tex]\frac{\sqrt{x} +1}{\sqrt{x} -3}[/tex]

[tex]\frac{(\sqrt{x} +1)(\sqrt{x}+3) }{(\sqrt{x} -3)(\sqrt{x} +3)}[/tex]

[tex]\frac{x + 3\sqrt{x} + \sqrt{x} +3 }{x -9}[/tex]

[tex]\frac{x + 4\sqrt{x} +3 }{x -9}[/tex]

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The first offer is better from the perspective of a customer but the second one is better from the perspective of a seller.

Here we have different 2 cases, and to find the answer we have to follow a few steps.

First of all, we should simplify these two cases and will try to give them a proper equation format.

Let's assume the price of each yogurt is $x.

Therefore the total price of 2 pots is (2× x) = $2x.

But the condition is if we buy 2 pots, get the 3rd one for free. So, we can purchase a total of 3 pots at the same cost.

∵ If 3 pots cost $2x, then the average cost for each pot is 2x/3 =$0.67x

( average value of each unit = Total value / total unit )

In the second case, if we buy 1 pot we can get the second one at half price.

Therefore, the total price of two pots is, ( x + 0.5x ) = $1.50x

∵ If 2 pots cost $1.50x, then the average cost for each pot is 1.50x/2 = $0.75x

( average value of each unit = Total value / total unit ).

The price of yogurt per pot in the first case <  The price of yogurt per pot in the second case.

As $0.67 <  $0.75.

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