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Rasek [7]
3 years ago
5

You bike 1 mile the first day of your​ training, 1.3 miles the second​ day, 1.9 miles the third​ day, and 3.1 miles the fourth d

ay. If you continue this​ pattern, how many miles do you bike the seventh​ day?
On the seventh day you bike ____miles.
Mathematics
1 answer:
JulsSmile [24]3 years ago
7 0

Answer:

19.9 miles

Step-by-step explanation:

In this problem we have:

d_1=1 mi is the distance travelled during the 1st day

d_2=1.3 mi is the distance travelled during the 2nd day

d_3=1.9 mi is the distance travelled during the 3rd day

d_4=3.1 mi is the distance travelled during the 4th day

We notice that the difference between the distance travelled on the (n+1)-th day and the distance travelled on the n-th day doubles every day. In fact:

d_2-d_1=0.3\\d_3-d_2=2\cdot 0.3 = 0.6\\d_4-d_3=2\cdot 0.6 = 1.2

Which can be rewritten using the general formula:

d_{n+1}-d_n=2(d_n-d_{n-1})

This means that

d_{n+1}=d_n+2(d_n-d_{n-1})

By applying this formula recursively, we can find the 7th term, which is the distance travelled on the 7th day:

d_1=1\\d_2=1.3\\d_3=1.9\\d_4=3.1\\d_5=3.1+2\cdot 1.2=5.5\\d_6=5.5+2\cdot 2.4=10.3\\d_7=10.3+2\cdot 4.8=19.9 mi

So, the  distance travelled on the 7th day is 19.9 miles.

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Sam works 1/5 hour at the register of a store. He works 2/3 hour in the back stock room and 1/2 hour helping customers. How many
AleksandrR [38]

Answer:

Sam worked  \frac{41}{30}  hours that day (fractional answer)

Step-by-step explanation:

The total number of hours Sam worked is the sum of all the three hours given.

Let's add the first 2 using LCM and then add that result with the last.

Firstly:

\frac{1}{5}+\frac{2}{3}\\=\frac{1(3)+2(5)}{15}\\=\frac{13}{15}

Now,

\frac{13}{15}+\frac{1}{2}\\=\frac{13(2)+1(15)}{30}\\=\frac{41}{30}

The hours worked by Sam is 41/30 hours (fractional answer).

7 0
3 years ago
Write an equation in slop intercept form (y=mx+b) for the line that has a slope (m) of 12 and passes though the point (3,20)
navik [9.2K]

Answer:

y=12x-4

Step-by-step explanation:

To find the slope intercept form, we know the m(slope) but we need to find b.

y and x is given to us, so we can find b.

Plug in the numbers provided into the slope intercept form.

y=mx+b

20=(12)(2)+b

20=24+b

To find b, we have to get b by itself. So, we subtract both sides by 24.

-4=b

Now that we found b, we can plug this into the equation.

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2 years ago
I want the answer to this problem<br> 3(x+2)-x=38
maks197457 [2]

Answer:

x = 16

Step-by-step explanation:

3(x+2)-x=38

Distribute

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Combine like terms

2x+6 = 38

Subtract 6 from each side

2x+6-6 = 38-6

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Divide each side by 2

2x/2 = 32/2

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5 0
2 years ago
Read 2 more answers
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