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3 years ago

Acellus Find the next term in this arithmetic sequence. 7/2,9/4,1,-1/4,-2/3 ,___

Mathematics

1 answer:

KiRa [710]3 years ago

8 0

Answer:

-11/4

(I think you meant -3/2 not -2/3 at the end there.)

Step-by-step explanation:

If it is arithmetic, it's going up or down by same number.

So we started with 7/2 and went down to 9/4.

If we can find how much it went down, then we can find the next term after -3/2.

Find difference

7/2-9/4

Find common denominator

14/4-9/4

5/4

So we are going down by 5/4 each time.

That means the following equations should ve true:

7/2-5/4=9/4

9/4-5/4=1

1-5/4=-1/4

-1/4-5/4=-3/2

And all of these are in fact true.

The next term in the sequence will be

-3/2-5/4.

Find common denominator

-6/4-5/4

-11/4

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3 years ago

In a recent flu epidemic, the number of flu cases increased by 40% each week. There were 3,000 flu cases during the first week o

Alborosie

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Step-by-step explanation:

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2 years ago

Can someone please help!!!

RideAnS [48]

Answers:

System 1: x = 3 and y = -5
System 2: x = 1 and y = 2

==========================================================

Explanation:

For now, let's focus on system 1.

We have identical copies of "2y" in each equation, which means that if we were to subtract the equations straight down, then the y terms cancel out. That allows us to solve for x.

The x terms subtract to 7x-x = 6x
The y terms subtract to 0 and go away
The right hand sides subtract to 11 minus (-7) = 11-(-7) = 11+7 = 18

After doing those subtractions, we have the new equation 6x = 18 which solves to x = 3. Divide both sides by 6 to isolate x.

Once we know x, we can find out y.

7x+2y = 11

7(3)+2y = 11

21+2y = 11

2y = 11-21

2y = -10

y = -10/2

y = -5

or we can say

x+2y = -7

3+2y = -7

2y = -7-3

2y = -10

y = -10/2

y = -5

We should lead to the same y value either way. This helps confirm we have the correct x value.

Overall, the solution to system 1 is (x,y) = (3, -5)

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

Now onto system 2.

Unfortunately, we don't have identical y terms this time. But what we can do is double everything in the second equation to go from -x+y = 1 to -2x+2y = 2.

The new equivalent system is

$\begin{cases}7x+2y = 11\\-2x+2y = 2\end{cases}$

Now we have the same situation as before: Subtract straight down, solve for x.

The x terms subtract to 7x-(-2x) = 7x+2x = 9x
The y terms go away when subtracting
The right hand sides subtract to 11-2 = 9

So we have 9x = 9 and that solves to x = 1.

We'll use this x to find the y value.

7x+2y = 11

7(1)+2y = 11

7+2y = 11

2y = 11-7

2y = 4

y = 4/2

y = 2

Or you could pick on the second equation

-x+y = 1

-1+y = 1

y = 1+1

y = 2

6 0

2 years ago

Question 2 of 4

Alexxandr [17]

Answer:

The time it took for the bottle rocket to reach a height of 200 feet is 60 seconds.

Step-by-step explanation:

The function for the height of the bottle rocket (in feet), <em>t</em> seconds after it is launched is:

$h(t)=1157-16\ t$

Compute the value of <em>t</em> as follows:

$h(t)=1157-16\ t$

$200=1157-16t$

$16t=1157-200\\16t=957\\$

$t=59.8125\\t\approx60$

Thus, the time it took for the bottle rocket to reach a height of 200 feet is 60 seconds.

8 0

3 years ago

Acellus Find the next term in this arithmetic sequence. 7/2,9/4,1,-1/4,-2/3 ,___​

Acellus Find the next term in this arithmetic sequence. 7/2,9/4,1,-1/4,-2/3 ,___