What is the fraction in decimal form? 11/20

Use the factors of the function and the y-intercept to find the standard form of the equation representing Jared’s function. Typ

Georgia [21]

The y-intercept of a function is the point where the graph crosses the $\mathbf{y = x^3 + 2x^2 - 193x - 270 }$

The factors of the Jared's graph are: (x - 10), (x + 3) and (x + 9)
The y-intercept is -13.5
The standard equation of the function is: $\mathbf{y = x^3 + 2x^2 - 193x - 270 }$

(a) The factors

First, we write out the points where the function cross the x-axis.

The points are:

$\mathbf{x = 10}$

$\mathbf{x = -3}$

$\mathbf{x = -9}$

Equate the above points to 0

$\mathbf{x -10 = 0}$

$\mathbf{x +3 = 0}$

$\mathbf{x +9 = 0}$

Hence, the factors are: (x - 10), (x + 3) and (x + 9)

(b) The y-intercept

This is the point where the graph crosses the y-axis.

From the attached graph, the graph crosses the y-axis at -13.5.

Hence, the y-intercept is -13.5

(c) The standard form

In (a), we have:

$\mathbf{x -10 = 0}$

$\mathbf{x +3 = 0}$

$\mathbf{x +9 = 0}$

Multiply the above equations

$\mathbf{(x - 10) \times (x + 3) \times (x + 9) = 0 \times 0 \times 0}$

$\mathbf{(x - 10) \times (x + 3) \times (x + 9) = 0 }$

Expand

$\mathbf{(x - 10) \times (x^2 + 3x + 9x + 27) = 0 }$

$\mathbf{(x - 10) \times (x^2 + 12x + 27) = 0 }$

Expand

$\mathbf{x^3 + 12x^2 + 27x - 10x^2 - 220x - 270 = 0 }$

Collect like terms

$\mathbf{x^3 + 12x^2 - 10x^2+ 27x - 220x - 270 = 0 }$

$\mathbf{x^3 + 2x^2 - 193x - 270 = 0 }$

Replace 0 with y

$\mathbf{y = x^3 + 2x^2 - 193x - 270 }$

Hence, the standard form is: $\mathbf{y = x^3 + 2x^2 - 193x - 270 }$

Read more about graphs and functions at:

brainly.com/question/18806107

3 0

3 years ago

Please help me with this question

Setler [38]

Step-by-step explanation:

${ ({y}^{2} )}^{4} . \: {( {y}^{3}) }^{2}$

Since,

${ ({a}^{x} )}^{y} = {a}^{xy}$

Hence,

${y}^{2 \times 4} . {y}^{3 \times 2}$

$= {y}^{8} . {y}^{6}$

Since,

${a}^{x} . {a}^{y} = {a}^{x + y}$

Hence,

$= {y}^{8 + 6}$

$= {y}^{14} (ans)$

6 0

3 years ago

I need help asap plz Its 9th grade problem

IgorLugansk [536]

Y=1/2x-2 on the graph -2 would be the y intercept and x/y is slope so to find y as one you go in the middle of -2 and four

7 0

2 years ago

The coordinates below represent two linear equations.

marshall27 [118]

Look at the first line in the first problem.
x y
–6 –6
–4 –3
find the slope:
y2-y1 / x2-x1
-3+6 / -4+6
3 / 2
the slope is 3/2. now plug this into point-slope form, along with one of the ordered pairs. i'll use (-4,-3) because the numbers are smaller.
y-y1=m(x-x1)
y+3=3/2(x+4)
y+3=3/2x+6
y=3/2x+3

now do the same for the other line.
x y
0 3
2 6
actually, this one's convenient, because it tells you the y-intercept is 3 (when an ordered pair has a 0 as its x coordinate, that means its on the y axis). so we just have to find the slope.
y2-y1 / x2-x1
6-3 / 2-0
3/2
the line is y=3/2x+3. it's the same line as before. that means there are infinitely many solutions, because there are an infinite amount of points where the lines "cross" each other (since they lie on top of each other).

follow the same procedure for the next problem. if the equations turn out to be the same, it has infinite solutions. if the two lines have the same slope but different intercepts, that means they're parallel, and have no solution since the lines will never intersect. if the lines have different slopes, they will have one solution. and it makes no sense for lines to intersect at two different points, so you can ignore that option altogether.

hope this helps

6 0

3 years ago

HElp please. I will give 5 stars and thanks.

Amanda [17]

The probability of not spinning an even number should be two out of three or 2/3. because there is only 1 even number (2).

5 0

3 years ago