1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Oksanka [162]
3 years ago
10

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

Mathematics
1 answer:
vaieri [72.5K]3 years ago
6 0
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.
You might be interested in
Which statements are true regarding the symmetry of the isosceles trapezoid? Check all that apply.
Ad libitum [116K]

Answer:

1, 3, and 5

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Need help finding D=___
lesya692 [45]
A straight line is 180 degrees and 144 is on a straight line. So, 180-144 which is 36. So, now we know 2 angles and the Degrees of a triangle is 180 degrees.
36+76+d= 180 D= 68
4 0
3 years ago
A school sells raffle tickets to raise money for a charity the money raised from selling raffle tickets, m, is represented by th
irina1246 [14]
P= M÷T , Price equals money raised divided by number of tickets sold
7 0
3 years ago
|4-24x|=52 absolute value
Verdich [7]
|4-24x|=52
24x=56
2.333~ is your answer
8 0
3 years ago
Mark and Don are planning to sell each other their marble collections at a garage sale. If Don has 1 more than 3 times the numbe
Volgvan

Answer: Mark has 28 marbles while Don has 85 marbles.

Step-by-step explanation:

Let x represent the number of marbles that Mark has.

Let y represent the number of marbles that Don has.

If Don has 1 more than 3 times the number of marbles Mark has, it means that

y = 3x + 1

The total number of marbles is 113. It means that

x + y = 113- - - - - - - - - - - - 1

Substituting y = 3x + 1 into equation 1, it becomes

x + 3x + 1 = 113

4x + 1 = 113

4x = 113 - 1 = 112

x = 112/4

x = 28

y = 3x + 1 = 3 × 28 + 1

y = 85

4 0
3 years ago
Other questions:
  • Jessie had a piece of cardboard that is 8.5 inches by 11 inches. She makes a picture frame with the cardboard box by cutting out
    6·2 answers
  • What are the three types of solutions possible when solving an inequality
    5·1 answer
  • Find the value of L. Perimeter = 20. Width is 6. So what is L? On a square
    15·2 answers
  • How many inches is 100 meters
    7·2 answers
  • Find x 4 over 3 = 8 over x
    8·1 answer
  • The side lengths 9, 13, and 17 form a triangle. true or false please answer ill do anything
    14·1 answer
  • This is my sister's work, please help. will give brainliest. DON'T GIVE STUPID ANSWERS, I WILL REPORT
    14·1 answer
  • Graph the line: y= 1/3x-2​
    14·2 answers
  • I need help with this important question it's for a important grade​
    15·1 answer
  • A small local bakery pre-ordered apple and pumpkin pies to be picked up the day before Thanksgiving. Apple pies were $15 each an
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!