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Svetradugi [14.3K]
2 years ago
10

when 8 is subtracted from a certain number and the result is multiplied by 3 the final answer is 21. What is the original number

Mathematics
2 answers:
Bingel [31]2 years ago
6 0

Answer: The original number is 15.

Step-by-step explanation:

LuckyWell [14K]2 years ago
6 0

Answer:

15

Step-by-step explanation:

(x-8)*3=21

x-8=21/3

x-8=7

x=7+8

x=15

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What are the x-coordinates of the solutions to this system of equations? x2 + y2 = 100 y = x + 2
kiruha [24]

Answer:

x = - 8, x = 6

Step-by-step explanation:

Given the 2 equations

x² + y² = 100 → (1)

y = x + 2 → (2)

Substitute y = x + 2 into (1)

x² + (x + 2)² = 100

x² + x² + 4x + 4 = 100

2x² + 4x + 4 = 100 ( subtract 100 from both sides )

2x² + 4x - 96 = 0 ( divide through by 2 )

x² + 2x - 48 = 0 ← in standard form

(x + 8)(x - 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 6 = 0 ⇒ x = 6

6 0
3 years ago
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.

8 0
2 years ago
How do I solve : COT pi/4 ...?
Wewaii [24]
Cot x = cos x / sin x
cot π/4 = cot 45° = cos 45° / sin 45°
We know that sin 45° and sin 45° have the same value:
cos 45° = sin 45° = √2 / 2;
cos 45° / sin 45° = √2/2 : √2/2 = 1
Answer:
cot π/4 = 1
3 0
3 years ago
Which expression is equivalent to (3x^5+8x^3)-(7x^2-6x^3)
inn [45]

Answer: look at the picture that the answer to it

Step-by-step explanation: Hope this help :D

7 0
3 years ago
A patio 44, feet wide is being constructed next to a house. To drain water off the patio and away from the house, a slope of 1/2
navik [9.2K]

Answer:

the total difference in height will be 22 inches

Step-by-step explanation:

since the slope is 0.5 inch per foot, and the patio is 44 feet wide, the end of the patio will be 0.5 x 44 = 22 inches lower

the slope measures how much the height (Y axis) will change as the length (X axis) increases by 1 unit. In this case, since the height decreases as the length increases the slope is negative.  

3 0
3 years ago
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