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Black_prince [1.1K]
3 years ago
13

Which table shows y as DIRECTLY PROPORTIONAL to x?

Mathematics
1 answer:
klemol [59]3 years ago
7 0

Answer:

Option B gives the directly proportional relation.  

Step-by-step explanation:

If a function can be written as in the form y = kx ........... (1), where x is the independent variable, y is the dependent variable and k is the proportionality constant.

Now, from the given four tables in options, the table in option B only satisfies this relation between x and y.

The ordered pairs in the option B are (1,0.5), (2,1), (3,1.5) and (4,2).

Now, take any two pairs of coordinates and find the equation of the function that satisfies all four points.

Taking (1,0.5) and (2,1) points, the equation of the straight line will be  

\frac{y - 1}{1 - 0.5} = \frac{x - 2}{2 - 1}

⇒ 2(y - 1) = x - 2

⇒ 2y = x

⇒ y = \frac{1}{2} x ............. (2)

Therefore, this equation (2) is similar to equation (1) and hence this table is directly proportional relationship. (Answer)

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2, 6, 18, 54. 162,...
grigory [225]

9514 1404 393

Answer:

  \text{c. }f(n)=3f(n-1);f(1)=2

Step-by-step explanation:

The first term is 2, so part of the recursive definition is ...

  f(1) = 2

The common ratio is 6/2 = 3, so each term is 3 times the previous one. That part of the recursive definition is ...

  f(n) = 3·f(n -1)

These two parts of the definition match choice C.

3 0
2 years ago
An animal shelter recently held an adoption event and found homes for 48 of their shelter animals. If they found home for 80% of
Elden [556K]
There were 60 animals before the event.
5 0
3 years ago
Determine the amount needed such that when it comes time for retirement, an individual can make monthly withdraws in the amount
DochEvi [55]

Lets solve the problem through compound interest formula,

The number of months are 360

The account pay interest rate is  5.1 %compounded monthly.

The amount withdraws each month is $2154

The value of n  is 360.

The value of  is<em> i</em> is 5.1%

So,

P = A [(1+i)^n]-1/i(1+i)^n\\\\P = $2,154 [(1+(0.051/12))^30*12] - 1 / (0.051/12)(1+(0.051/12))^30*12\\\\P = $396,721.78

Hence the value of principal is $396721.78

Learn more about Compound interest on:

brainly.com/question/18456266

#SPJ4

7 0
2 years ago
Simplify by combining like terms 4b-7m -4m +5b
meriva

Answer:

9b-11m

Step-by-step explanation:

add 4b and 5b then add -4m and -7m

3 0
3 years ago
Read 2 more answers
a step on a stairway is at least 8 inches high. Write and solve an inequality to represent the minimum number of steps between f
11111nata11111 [884]
The hight of the step is 

h ≥ 8 inches

If we take that in one feet we have twelve inches

The hight between floors are H=10ft = 120 inches

If we named number of steps with n, the appropriate inequality is

n ≤ 120/8 => n ≤ 15 

Good luck!!!!
6 0
3 years ago
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