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vampirchik [111]
3 years ago
9

write a symbolic rule to represent the relalationship in which the output variable y is 12 less then the input variable x. what

is the output corresponding to an input value of 41?
Mathematics
2 answers:
klemol [59]3 years ago
7 0

Answer:

the value of output is 29

Step-by-step explanation:

the output variable y is 12 less then the input variable x.

Input variable is x, output variable is y

output values = input variable - 12

now plug in the variable in the equation

output values = input variable - 12

y=x-12

Given the input value is 41

Substitute 41 for x

y=41-12=29

the value of output is 29

Butoxors [25]3 years ago
3 0

Answer:the output corresponding to an input value of 41 is 29

Step-by-step explanation:

The input variable is represented by x.

The output variable is represented by y.

The output variable y is 12 less then the input variable x. The symbolic rule to represent the relationship would be expressed as

x = y + 12

If the input value is 41, to determine the corresponding output value, we would substitute x = 41 into the equation, x = y + 12. It becomes

41 = y + 12

y = 41 - 12 = 29

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(2pm^-1q^0)^-4 • 2m ^-1 p^3 / 2pq^2
Montano1993 [528]

Answer:

\dfrac{m^3}{16p^2q^2}

Step-by-step explanation:

Given:

(2pm^{-1}q^0)^{-4}\cdot \dfrac{ 2m^{-1} p^3}{2pq^2}

1.

m^{-1}=\dfrac{1}{m}

2.

q^0=1

3.

2pm^{-1}q^0=2p\cdot \dfrac{1}{m}\cdot 1=\dfrac{2p}{m}

4.

(2pm^{-1}q^0)^{-4}=\left(\dfrac{2p}{m}\right)^{-4}=\left(\dfrac{m}{2p}\right)^4=\dfrac{m^4}{(2p)^4}=\dfrac{m^4}{16p^4}

5.

m^{-1}=\dfrac{1}{m}

6.

2m^{-1} p^3=2\cdot \dfrac{1}{m}\cdot p^3=\dfrac{2p^3}{m}

7.

\dfrac{ 2m^{-1} p^3}{2pq^2}=\dfrac{\frac{2p^3}{m}}{2pq^2}=\dfrac{2p^3}{m}\cdot \dfrac{1}{2pq^2}=\dfrac{p^2}{mq^2}

8.

(2pm^{-1}q^0)^{-4}\cdot \dfrac{ 2m^{-1} p^3}{2pq^2}=\dfrac{m^4}{16p^4}\cdot \dfrac{p^2}{mq^2}=\dfrac{m^3}{16p^2q^2}

8 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
WILL GIVE 97 POINTS AND MARK BRAINLIEST
julia-pushkina [17]

Answer:

There is no fundamental difference between a “rotation” and an “orbit” and or "spin". The key distinction is simply where the axis of the rotation lies, either within or outside of a body in question. This distinction can be demonstrated for both “rigid” and “non rigid” bodies.

Step-by-step explanation:

thats what google says, hope it helps

3 0
3 years ago
To which subset of real numbers does the number 1/5 belong
Travka [436]
1/5 is an expression that represents 1÷5= .2
Since the return decimal equivalent doesn't go on forever and has a finite end, this is a member of the rational number set.
4 0
3 years ago
How many solutions are there to the equation below 9x + 27 = 9( x + 2 ) + 9
Nataly [62]

Let's solve the equation:

9x+27 = 9(x+2)+9 ← Distribute 9 to the x and 2

9x+27 = 9x+18+9 ← Combine like terms

9x+27 = 9x + 27 ← Subtract 27 from both sides

9x = 9x


Infinitely many solutions would be correct because no matter what x is, it will always equal each other the both sides of the equation because it is 9 times x on both sides.


7 0
3 years ago
Read 2 more answers
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