MATHEMATICS MIDDLE SCHOOL

After a gas-filled balloon is released, it rises 90 feet by the end of the first minute. By the end of the second minute, the balloon rises 120 feet, and by the end of the third minute, it rises 150 feet. How many feet would the balloon rise in 8 minutes?

Answers

Answer 1
Answer:

Answer: 300 feet

Step-by-step explanation:

Note that:

120-90 = 30

150-120 = 30.

Then the balloon rises at a constant rate of 30 meters per minute.

We can represent this situation through an arithmetic sequence as shown below

a_n =a_1 + d(n-1)

Where a_1=90 is the first term of the sequence and a_n is the n-th term of the sequence and d=30 is the common difference between two consecutive terms.

In this case we look for the height of the balloon after 8 minutes.

Then we look for a_8

a_8 = 90 + 30(8-1)

a_8 = 90 + 30(7)

a_8 = 300
Answer 2
Answer:

Answer:

\boxed{\text{300 ft}}

Step-by-step explanation:

You have an arithmetic sequence in which

a₁ =  90

a₂ = 120

a₃ = 150

1. Calculate the explicit formula

This is an arithmetic sequence, because there is a constant difference of 30 between consecutive terms.

The explicit formula for the nth term of an arithmetic sequence is

aₙ = a₁ + d(n - 1 )

a₁ is the first term, and d is the difference in value between consecutive terms. Thus,  

aₙ = 90 + 30(n - 1) = 90 + 30n - 30

aₙ = 30n + 60

2. Calculate the eighth term

a₈ = 30 × 8 + 60 = 240 + 60 = 300

\text{In 8 min, the balloon rises }\boxed{\textbf{300 ft}}

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Answers

I'll do better than that !  I'll show you how to do it, because
the answer is no help if you don;t know how to work it out.

Do you see that little square in one corner of the triangle ?  That tells you
that the angle there is 90 degrees, and THAT tells you that the triangle is
a  RIGHT triangle.  This is a very helpful piece of information, because there's
a rule about the sides of  a right triangle that isn't true for any other kind of triangle. The rule is:

             (the longest side)² = (one of the other sides)² plus (the third side)²

Also, the longest side is always the one that doesn't touch the 90-degree angle.

In this triangle in the picture,

-- the longest side is 'A' ... it's 13 .
-- one of the other sides is ' b ' ... it's 12 .
-- the third side is ' C ' ... the one you have to find.

Using the formula up above, you know that      

             (13)² = (12)² + C²

Before you go to work on it, subtract (12)² from each side of this equation,
just to make it a little easier, and then you have      

         C² = (13)² minus (12)²

And right there is how to figure out the length of ' C '.

I'll give you even more information to help you, and then it's up to you
to finish it and get the answer.  Here it is:

       (13)² = 169

       (12)² = 144

Now you have everything you need.  Go to it !
To get the answer we can use Pythagorean theorem.
12^2+c^2=13^2 \n 144+c^2=169     /-144
c^2=25 \n c=5 - its the answer

Christine baked a pumpkin pie. She ate 1/6 of the pie. Her brother ate 1/3 of it , and gave the left overs to his friends . What fraction of the pie did he gave to his friends?

Answers

Ok, so first you need to get the fractions to have the same denominator:
1/3 = 2/6 and 1/6 = 1/6
Add the two eaten parts together : 2/6+1/6=3/6
Now, subtract the eaten part ( 3/6 ) from the whole pie ( 6/6 or 1 whole)
6/6 - 3/6 = 3/6
So, he gave half of the pie to his friends because 3/6 = 1/2
Hope this helps! If you have any questions let me know! 

The fraction of the pie given to his friend is (1)/(2)

  • Christine ate (1)/(6) of the pie
  • Her brother ate (1)/(3) of the pie

Further Explanation

The leftover given to his friends will be determined by adding the portion Christine and her brother ate which are (1)/(6) and (1)/(3) respectively, then subtracted from the whole portion.

= (1)/(6) + (1)/(3)  (The lowest common denominator of 6 and 3 = 6)

= (1 x 1) + (2 x 1) /6

= (1) + (2) / 6

= 1 + 2 / 6

= (3)/(6)

Thus, total portion of the pie eaten by Christine and her brother = (3)/(6). Also the fraction of the whole portion of the pie = (6)/(6)

Determining the portion given to the friend =

Subtracting (6)/(6) – (3)/(6)

= (6)/(6) – (3)/(6)  (The lowest common denominator of 6 and 6 = 6)

= (1 x 6) – (1 x 3) / 6

= (6) – (3) / 6

= 6 – 3 / 6

= (3)/(6)

= (1)/(2) (further broken down to this)

Therefore the fraction given to the friend is (1)/(2).  

The above mathematical problem is a typical fraction problem which was solved with the aid of some order of operations called BODMAS.

BODMAS simply means Brackets, Of, Division, Multiplication, Addition, Subtraction.

LEARN MORE:

KEYWORDS:

  • christine
  • pumpkin pie
  • bodmas
  • dividing
  • multiplying
  • denominator

1.Find the exact solution to the equation.(2 points)

log base four of x equals two.

Answers

Answer:

x = 16

Step-by-step explanation:

The equation is \log_(4) x = 2

Now, converting this logarithmic equation into exponential equation, we get

x = 4^(2) = 16(Answer)

Alternate solution:

Given,\log_(4) x = 2

⇒ \log_(4)x = 2\log_(4)4

{Since, we know that \log_(a)a = 1}

⇒ \log_(4)x = \log_(4)4^(2) = \log_(4)16

{Since, a\log b = \log b^(a) is a property of logarithm}

Cancelling log from both sides we get,

⇒ x = 16 (Answer)

Answer:

x = 8^4

Step-by-step explanation:

hey there,

< Here is what is given:

㏒_(8) x=4

There's actually a lot of different ways you can remember this but the way I remember this is x is equal to 2nd to the power of last.

So 8 is the 2nd (since log is first), 4 is last (very last thing in the equation).

x = 8^4

You can use any of your own ways to remember this, but this is just my personal way. :) >

Hope this helped! Feel free to ask anything else.

Tonya's car averages 240 miles for each 10 gallons. How many gallons of gasoline will the car need to travel 216 miles?

Answers

240/10=24+216=240 they are equal
240 miles / 10 gallons = 24 miles per 1 gallon
24 x = 216
x=216/24
simplify = 9 gallons

Angelo's pet rabbit weighs 1 pound less than twice the weight of Carmen's pet rabbit.Angelo's pet rabbit weighs 9 pounds. Write an equation that can be used to find (w) , the weight of Carmen's pet rabbit

Answers

w=(9+1)/2 i think? its worded strangely

A bird flies at 12.5 meters per second. The wind speed is 4.5 meters per second.What is the speed of the bird when it flies with the wind?
What is the speed of the bird when it flies against the wind?
Enter your answer in the space provided.

Answers

Answer: The speed of the bird when it flies against the wind would be 8 meters per second

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