All categories

4 years ago

Which graph represents the function of f(x) 9x^2 + 9x - 18 / 3x + 6

Mathematics

1 answer:

Irina-Kira [14]4 years ago

7 0

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

$f(x)=\frac{9x^{2}+9x-18}{3x+6}$

Remember that in a quotient, the denominator cannot be equal to zero

The value of x cannot be equal to x=-2

Simplify the expression

Using a graphing tool

The roots of the quadratic equation in the numerator are

x=-2 and x=1

$9x^{2}+9x-18=9(x+2)(x-1)$

Simplify the denominator

$3x+6=3(x+2)$

substitute in the original expression

$f(x)=\frac{9(x+2)(x-1)}{3(x+2)}$

Simplify

$f(x)=3(x-1)$

$f(x)=3x-3$

Is the equation of a line

The y-intercept is the point (0,-3) (value of the function when x is equal to zero)

The x-intercept is the point (1,0) (value of x when the value of the function is equal to zero)

Graph the line, but remember that the value of x cannot be equal to -2

The graph in the attached figure

You might be interested in

What is the equation of the line that passes through the point (-6, -2) and has a slope of 1/6

Levart [38]

<h2>Answer:</h2>

Step 1: Determine b by using the point (-6,-2), the given slope, and the slope intercept formula, y = mx + b.

$y = mx + b\\\\-2 = \frac{1}{6}(-6) + b\\\\-2 = -1 + b\\\\-1 = b$

Step 2: Now that we have b, we can determine the equation of the line.

$y = \frac{1}{6}x -1$

I didn't use + (-1) because b is negative. Therefore you need to change the equation from y = 1/6x + (-1) to y = 1/6x - 1.

4 0

3 years ago

Please help someone

DiKsa [7]

The first equation is x = -1

The second and third equations are no solution

The third equation is all rel numbers.

We can tell each one by solving them. In the first one, you get the following.

4 + x = -8x - 5 ----> Add 8x to both sides

4 + 9x = -5 ----> Subtract 4 from both sides

9x = -9 ----> Divide both sides by 9

x = -1

For the middle two, when you attempt to solve, you get untrue statements. This shows there are no solutions. See the example below.

7 + 2x = 2x - 7 ----> Subtract 2x from both sides

7 = -7 (UNTRUE)

And for the last one, each term cancels out, which shows that we have all real solutions.

-3x + 3 = 3( 1 - x) ----> Distribute the 3

-3x + 3 = 3 - 3x ----> Add 3x to both sides

3 = 3 (TRUE)

8 0

3 years ago

Question 3 of 10

Fantom [35]

Answer:

true

Step-by-step explanation:

heat exhaustion and heatstroke can be counted as serious form of heat injury

3 0

3 years ago

Use the two patterns below

Svetradugi [14.3K]

Let's say u put those 2 patterns onto a graph it would be (x,y) (3,5). same for the next (6,10). I'm sorry if this didn't help I'm trying though

5 0

3 years ago

Molly and Torry like to eat ice cream sandwiches. In one week, Molly ate 555 ice cream sandwiches, and Torry ate nnn ice cream s

Svetradugi [14.3K]

Answer:

The equation is 5 + n = 12 and Torry ate 7 ice cream sandwiches.

Step-by-step explanation:

Given:

Molly and Torry like to eat ice cream sandwiches. In one week, Molly ate 5 ice cream sandwiches, and Torry ate n ice cream sandwiches. They ate a total of 12 ice cream sandwiches all together.

Now, to write an equation to describe this situation and to find number of ice cream sandwiches Torry eat.

Molly ate = 5 ice cream sandwiches.

Torry ate = $n$ ice cream sandwiches.

Total ice cream sandwiches = 12.

So, to write an equation of this situation:

$5+n=12$

Now, to find the number of ice cream Torry ate:

$5+n=12$

Subtracting both sides by 5 we get:

$n=7.$

Torry ate = 7 ice cream sandwiches.

Therefore, the equation is 5 + n = 12 and Torry ate 7 ice cream sandwiches.

4 0

3 years ago

Read 2 more answers