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Darya [45]
3 years ago
6

If y varies directly with x in the following table problem, find the constant of variation (k) and write the equation x 6,9,12,1

5 Y 10,15,20,25
Mathematics
1 answer:
Kobotan [32]3 years ago
4 0
We are told that y varies directly with x.
Therefore
y = k*x
where
k = the constant of variation

The given table and the ratio of k=y/x is shown below.

  x     y        k
--- ------ --------
  6   10  1.667
  9   15  1.667
 12  20  1.667
 15  25  1.667

Answer:
k = 1.667
y = 1.667x

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What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?
Trava [24]

Answer:

\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}

Step-by-step explanation:

The explicit formula for a geometric sequence:

a_n=a_1r^{n-1}

a_n - n-th term

a_1 - first term

r - common ratio

r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}

We have

a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...

The common ratio:

r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}

<h2>It's not a geometric sequence.</h2>

If a_3=-\dfrac{1}{16} then the common ratio is r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}

Put to the explicit formula:

a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}

Put a_n=\dfrac{1}{1024} and solve for <em>n </em>:

-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1

\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6

5 0
3 years ago
How do i find the inverse function of h(x) =(5-2x^2)/(3x+10)
sergeinik [125]
Inverse function: you need to exchange the position of x and y, in other words,

x = (5-2y^2)/(3y+10) , then, if you need a representation of y with respect to x, then you need to perform some math.
5 0
3 years ago
Find the perimeter of a circle O
ExtremeBDS [4]

The formula for finding the perimeter of a circle is P = 2 x 3.14 x r

The perimeter would be 2 x 3.14 x 14

The perimeter is 87.92 cm


6 0
3 years ago
PLEASE HELP WITH NUMBER 11 ASAP!!!! (Please show how you got the answer)
Alex777 [14]

Answer:

Triangle B is right

Step-by-step explanation:

Using the converse theorem of Pythagoras.

If the square of the longest side in a triangle equals the sum of the squares of the other 2 sides then the triangle is right.

Triangle A

longest side squared = 36² = 1296

26² + 18² = 676 + 324 = 1000 ≠ 1296

Hence triangle A is not right

Triangle B

longest side squared = 25² = 625

20² + 15² = 400 + 225 = 625 ← correct

Hence triangle B is right


7 0
3 years ago
What's the slope of (-5, -3) and (5,3)
MAVERICK [17]

Answer:

10/6

Step-by-step explanation:

all you have to do is divide x2 or 5 in this case - x2 or -5 with y2 or 3 - y1 or 3 so it would be

(5--5)/(3--3)

and 2 negatives are a positive so it would turn to

5+5/3+3   or    10/6

please rate 5 stars i would really appreciate it

8 0
3 years ago
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