Is this a function yes or no

Find the intercept of g(n)=-2(3n-1)(2n+1)

vaieri [72.5K]

To find the intercepts of this give function of g(n), we have to find both the points present on the axis. That is, X-Intercept axial or axis point and the Y-Intercept axial or axis point and apply the zero factor principle to get the actual points on the graph for both the respective intercepts. Let me make it simpler, by showing the whole process via the LaTeX interpreter equation editor.

The X-Intercept is that actual point present in the graphical interpretation where the Y-axis is taken as zero, this makes us to point out the position of X-Intercept points on its X-axis and Y-axis. Take the variable "n" as the variable of "x", it will not change any context or such, we can take any variables for calculations, it does not hinder the processing of Intercepts for the axial points on a graph.

$\boxed{\mathbf{\therefore \quad -2(3x - 1)(2x + 1) = 0}}$

By the zero factor principle, both of them can be separately calculated as a zero on their either sides of the expression.

$\mathbf{\therefore \quad 3x - 1 = 0}$

$\mathbf{3x - 1 + 1 = 0 + 1}$

$\mathbf{3x = 1}$

$\mathbf{\dfrac{3x}{3} = \dfrac{1}{3}}$

$\mathbf{\therefore \quad x = \dfrac{1}{3}}$

Similarly, for the second X-Intercept point for the value of 0 in the Y-axis or Y axial plane in a 2 dimensional Graphical representation is going to be, As per the zero factor principle:

$\mathbf{\therefore \quad 2x + 1 = 0}$

$\mathbf{2x + 1 - 1 = 0 - 1}$

$\mathbf{2x = - 1}$

$\mathbf{\dfrac{2x}{2} = \dfrac{- 1}{2}}$

$\mathbf{\therefore \quad x = -\dfrac{1}{2}}$

Then the X-Intercept here becomes with our provided points as:

$\boxed{\mathbf{\underline{X-Intercept: \quad \Bigg(\dfrac{1}{3}, \: 0 \Bigg), \: \: \: \: \Bigg(-\dfrac{1}{2}, \: 0 \Bigg)}}}$

Therefore, for our Y-Intercept axial point the X axial plane will instead turn out to be a value with zero on a Graphical representation to obtain the actual points for Y-axis and the Y-Intercept for x = 0 as a point on the graph itself.

Just substitute the value of "0" in "x" axis as a variable on the provided expression. Therefore:

$\boxed{\mathbf{= -2(3 \times 0 - 1) (2 \times 0 + 1)}}$

$\mathbf{y = - 2 (0 - 1) (0 + 1)}$

$\mathbf{y = - 2 (- 1) (0 + 1)}$

$\mathbf{y = - 2 (- 1) \times 1}$

$\mathbf{y = 2 \times 1 \times 1}$

$\mathbf{\therefore \quad y = 2}$

Then, the Y-Intercept would definitely be as per the X-axis lying on the point of zero.

$\boxed{\mathbf{\underline{Y-Intercept: \quad \big(0, \: 2 \big)}}}$

The final coordinating points for X-Intercept and Y-Intercept for their X-axis and Y-axis will be.

$\boxed{\mathbf{\underline{X \: Intercepts: \: \: \Bigg(\dfrac{1}{3}, \: 0 \Bigg), \: \: \: \: \Bigg(-\dfrac{1}{2}, \: 0 \Bigg); \: \: Y \: Intercepts: \: \: \big(0, \: 2 \big)}}}$

Hope it helps.

6 0

3 years ago

Solve for x. 4(7x−3)−6=6−4(3x−7) Enter your answer in the box.

olasank [31]

4(7x−3)−6=6−4(3x−7)

Distributive property

28x - 12 - 6 = 6 - 12x + 28

28x - 18 = -12x + 34

28x + 12x = 34 + 18

40x = 52

x = 52/40

x = 13/10

or

x = 1 3/10 (mixed number: 1 and 3/10)

5 0

2 years ago

How many different ways can you choose 2 vowels out of the box, if there are 5 vowels in the box and order matters.

Brums [2.3K]

I think you could change it 25 times

5 0

2 years ago

Solve:

Natalija [7]

Answer: It took 18 Months for Michelle to collect 59 dolls.

Explanation:
First, let’s right an equation for this. Michelle started with 5 dolls in a bar collection (I have no clue what that is but i’ll roll with it), and each month she bought 3 more, so 5 dolls plus the 3 dolls per month equals 59 at some point.

5 dolls + 3 dolls per month = 59 dolls
OR
5 + 3m = 59

The point of this question is to find how many months (m) it took in order to get to 59 dolls and there’s multiple ways you can do this:

1) just plug in random numbers into m to see how long it takes to get to 59 [this option might take a while]

2) Try to isolate m (get every number out of the equation) to find out the value of m. [I’m most familiar with this way]

First, subtract 5 from 5 in the equation in order to get rid of it, since we’re trying to get all whole numbers out of the equation and only have m left. You subtract 5 from 59 since the equal sign is kind of like a mirrror, whatever you do to one side you have to do to the other. So, 5-5 is 0, and 59- is 54.

Now you’re left with 3m=54. In order to isolate the m, divide 3 by 3 to get rid of the 3, then divide 54 by 3, which is 18.

In order to check your work, plug 18 into m just to see if it works or not:

5+3m=59 —-> 5+ 3(18)= 59

3 times 18 is 54, plus 5 is 59. So, Mi hells took 18 months to collect her 59 dolls. Hope this helped!

3 0

2 years ago

Are the set of all square numbers under 50 and the set of all triangular numbers that are less than 50 disjoint?

Alina [70]

Answer:

No, the two sets are not disjoint.

Step-by-step explanation:

Set of triangular numbers to 50: 1, 3, 6, 10, 15, 21, 28, 36, 45

Set of square numbers to 50: 1, 4, 9, 16, 25, 36, 49

They have 1 and 36 in common, so they are not disjoint, or in other words, they have some of the same numbers.

7 0

3 years ago