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adell [148]
3 years ago
11

You begin with $90 in your savings account and your friend begins

Mathematics
2 answers:
Colt1911 [192]3 years ago
7 0

Answer:

F(f) = 15t + 35 represents the total amount of savings your friend would make in t weeks.

F(d) = 10t + 90 represents the total amount of saving you, darian, would make in t weeks.

When you graph the equations, plugging in different values for t, you can see that the graphs  intersect at (11,200). This means that at 11 weeks, both you and your friend have the same amount of money saved up, $200.  They will not have the same amount of money in 10 weeks.

BlackZzzverrR [31]3 years ago
6 0

Answer:

<h3>a. y=10x+90</h3>

y=15x+35

<h3>b. Your friend is wrong.</h3>

Step-by-step explanation:

If you begin with $90 and add $10 each week, then we express it as

y=10x+90

Where x refers to weeks and y refers to the total amount of money in you savings account.

On the other hand, your friend begins with $35 and deposits $15 each week, the equation that expresses your friend's savings is

y=15x+35

Therefore, the sytem of linear equation that models this situation is

y=10x+90

y=15x+35

The graph attached shows this system. There you can notice that the solution is (11, 200), which means in 11 weeks both will have the same amount saved.

Therefore, your friend is wrong, because after 10 weeks you won't have the same amount.

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Step-by-step explanation:

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It is desired to pile some logs in layers so that the top layer contains one log, the next layer contains two logs, the next lay
Hitman42 [59]

Answer:

Yes all of the logs can be used in such a grouping.

We'll have <u>19 logs</u> in the bottom row (and have 19 rows)

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

Explanation:

Let n be the number of layers. Let T(n) represent how many logs there are total.

  • If you have 1 layer, then you have 1 log. So we can say that T(1) = 1.
  • If there are n = 2 layers, then we have 1 log on top of two other logs, which leads to 1+2 = 3 logs total. This shows that T(2) = 3.
  • If there are n = 3 layers, then we have 1 log on top of 2 which are on top of 3 at the very bottom. We have 1+2+3 = 6 logs total. So T(3) = 6.
  • Having n = 4 layers gives 1+2+3+4 = 10 logs. So T(4) = 10
  • Having n = 5 layers gives 1+2+3+4+5 = 15 logs. So T(5) = 15

This process continues for however long you like. The sequence 1,3,6,10,15 is the set of triangular numbers, since the logs form a triangular or pyramid shape when stacked this way. To get the nth value in the triangular number sequence, use this formula

T(n) = 0.5*n*(n+1)

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

For example, let's say we wanted to find how many logs there were in the fifth layer

T(n) = 0.5*n*(n+1)

T(5) = 0.5*5*(5+1)

T(5) = 15

This matches from earlier.

The purpose of bringing in a formula is to see if we can get T(n) = 190 for some integer n.

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

T(n) = 0.5*n*(n+1)

190 = 0.5*n*(n+1)

190*2 = n(n+1)

380 = n^2+n

0 = n^2+n-380

n^2+n-180 = 0

Applying the quadratic formula will lead to the two solutions: n = -20 and n = 19. We ignore the negative value of n as we can't have a negative number of rows. Therefore, n = 19 is the only valid solution here.

If we wanted to stack 190 logs in this triangular pyramid fashion, then we'll need to have 19 rows. The bottom row will have 19 logs.

----------

Check:

1+2+3+4+5+6+7+8+9+10 = 55

11+12+13+14+15+16+17+18+19 = 135

55+135 = 190

Or you could say,

T(n) = 0.5*n*(n+1)

T(19) = 0.5*19*(19+1)

T(19) = 190

Either way, the answer is confirmed.

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2 years ago
Consider the following equation. y = 1/3x + 10. Which of the following lines is perpendicular to the one a above ?
seraphim [82]

Answer:

D. Y=3x+10

Step-by-step explanation:

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3 years ago
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