Since there is no single number we can add to one number in the sequence to get to the next one, this is not arithmetic. That means it's geometric, if it's a sequence at all. To get from 2 to 6 we multiply by 3. To get from 6 to 18 we multiply by 3. To get from 18 to 54 we multiply by 3. Therefore, this is in fact geometric and the common ratio is 3. The standard form of a geometric explicit formula is

$A_n=a_1(r)^{n-1$ where n is the position of a number in the sequence, a1 is the first number in the sequence, and r is the common ratio. We have then

a1 = 2 and r = 3. Therefore, the explicit formula is

$A_n=2(3)^{n-1$ and you can use this to find the value of any number in the sequence. Very handy; much more so than the recursive formula, which requires that all the numbers in a sequence be found in order in order to get to a desired value.

6 0

3 years ago

Complete the table of values for the equation, 16x + 4y = 12.

Ann [662]

The x-y coordinates for the given equation are: (-2,11),(-1,7),(0,3), (1,-1) and (2,-5).

<h3>Linear Function</h3>

A linear function can be represented by a line. The standard form for this equation is: ax+b , for example, y=2x+7. Where:

a= the slope;
b=the constant term that represents the y-intercept.

The given equation is 16x + 4y = 12. For solving this question, you should replace the given values of x for finding the values of y.

Thus,

For x= -2, the value of y will be:

16*(-2)+4y=12

-32+4y=12

4y=12+32

4y=44

y=11

For x= -1, the value of y will be:

16*(-1)+4y=12

-16+4y=12
4y=12+16
4y=28
y=7

For x= 0, the value of y will be:

16*(0)+4y=12

0+4y=12
4y=12
4y=12
y=3

For x= 1, the value of y will be:

16*(1)+4y=12

16+4y=12
4y=12-16
4y=-4
y= -1

For x= 2, the value of y will be:

16*(2)+4y=12

32+4y=12
4y=12-32
4y=-20
y= -5

Read more about the linear equation here:

brainly.com/question/1884491

#SPJ1

7 0

1 year ago

Geometry help! Please prove the following is a square with full explanation, I'm really lost.

Hoochie [10]

We have to show that this is a square, meaning all the sides are perpendicular and the same distance.

A(3,4), B(2,-2), C(-4,-1), D(-3,5)

For each side we calculate the squared distance and the slope. We don't have to bother to take the square root. We'll subtract the points first because that difference, called the direction vector, goes into both the calculation of the slope and of the distance.

AB=B-A=(2 - 3, -2 - 4) = (-1, -6). slope=-6/-1=6 AB²=(-1)²+(-6)²=37

BC=C-B=(-6, 1). slope=1/-6=-1/6. BC²=(-6)²+1²

CD=D-C=(1, 6). slope=6/1=6 CD²=1²+6²=37

DA=A-D=(6,-1) slope=-1/6 DA²=37

We see the negative reciprocal slopes, alternating between 6 and -1/6, indicating perpendicular sides. We see they all have squared distance 37. Equal perpendicular sides proves its a square.

If we do these problems enough we learn: There's no point taking the square root. In fact, there's really no point computing the slopes and the squared distances; we can see it's a square from the pattern of the direction vectors of the sides: (-1, -6) (-6, 1) (1, 6) (6,-1)

5 0

3 years ago

F=G(m1-m2)/d2 solve formula for m1 plz... thank you

antoniya [11.8K]

1. f = g(m1 - m2)/d2

2. f d2 = g(m1 - m2)

3. f d2/g + m1 - m2

4. f d2/g + m2 = m1

5. [Answer] m1 = f d2/g + m2

6 0

3 years ago

What is C in -43=-5c+4(2c+7)​

What is C in -43=-5c+4(2c+7)