You start off by looking at which operation to do first. According to PMDAS (parentheses, multiplication, division, adding, and subtracting) you would do division first so
220-450/3
220-150
Then you complete the rest
220-150=70
Hopefully this helps! :)
4/10 and 10/25 are equivalent to 2/5.
Hope this helps!
ANSWER
The zeros of
![y = x(x + 2)(x + 5)](https://tex.z-dn.net/?f=y%20%3D%20x%28x%20%2B%202%29%28x%20%2B%205%29)
are
![x=0,x=-2,x=-5](https://tex.z-dn.net/?f=x%3D0%2Cx%3D-2%2Cx%3D-5)
EXPLANATION
The given function is
![y = x(x + 2)(x + 5)](https://tex.z-dn.net/?f=y%20%3D%20x%28x%20%2B%202%29%28x%20%2B%205%29)
To find the zeros of the above function, we just have to equate the function to zero and solve for x.
![x(x + 2)(x + 5) = 0](https://tex.z-dn.net/?f=x%28x%20%2B%202%29%28x%20%2B%205%29%20%3D%200)
This implies that,
![x = 0 \: \: or \: x + 2 = 0 \:or \: x + 5 = 0](https://tex.z-dn.net/?f=x%20%3D%200%20%5C%3A%20%5C%3A%20or%20%5C%3A%20x%20%2B%202%20%3D%200%20%5C%3Aor%20%5C%3A%20x%20%2B%205%20%3D%200)
![x = 0 \: \: or \: x = - 2\:or \: x = - 5](https://tex.z-dn.net/?f=x%20%3D%200%20%5C%3A%20%5C%3A%20or%20%5C%3A%20x%20%3D%20-%202%5C%3Aor%20%5C%3A%20x%20%3D%20-%205)
To graph the above function, we need to consider the multiplicity.
We can see that the multiplicity of the roots are odd. This means that, the graph crosses the x-axis at each x-intercept.
We also need to consider the position of the graph on the following intervals,
![x < - 5](https://tex.z-dn.net/?f=x%20%3C%20-%205)
When
![x = - 10](https://tex.z-dn.net/?f=x%20%3D%20-%2010)
![y = - 10( - 8)( - 5) \: < \: 0](https://tex.z-dn.net/?f=y%20%3D%20-%2010%28%20-%208%29%28%20-%205%29%20%5C%3A%20%3C%20%5C%3A%200)
The graph is below the x-axis.
![- 5 \: < \: x \: < \: - 2](https://tex.z-dn.net/?f=%20-%205%20%5C%3A%20%3C%20%5C%3A%20x%20%5C%3A%20%3C%20%5C%3A%20-%202)
When
![x = - 3](https://tex.z-dn.net/?f=x%20%3D%20-%203)
![y = - 3(2)( - 1) \: > 0](https://tex.z-dn.net/?f=y%20%3D%20-%203%282%29%28%20-%201%29%20%5C%3A%20%3E%200)
The graph is above the x-axis.
![- 2 \: < \: x < \: 0](https://tex.z-dn.net/?f=%20-%202%20%5C%3A%20%3C%20%5C%3A%20x%20%3C%20%5C%3A%200)
when
![x = - 1](https://tex.z-dn.net/?f=x%20%3D%20-%201)
![y = -1(1)(4) \: < \: 0](https://tex.z-dn.net/?f=y%20%3D%20-1%281%29%284%29%20%5C%3A%20%3C%20%5C%3A%200)
The graph is below the x-axis.
Finally the interval,
![x \: > \: 0](https://tex.z-dn.net/?f=x%20%5C%3A%20%3E%20%5C%3A%200)
when
![x = 1](https://tex.z-dn.net/?f=x%20%3D%201)
![y = 1(3)(6) \: > \: 0](https://tex.z-dn.net/?f=y%20%3D%201%283%29%286%29%20%5C%3A%20%3E%20%5C%3A%200)
The graph is above the x-axis.
We can now use the above information to sketch graph as shown in the diagram above.
The equation for a rational function with: Vertical asymptotes at x = 2 and x = -4. x-intercepts at x = 1 and x = 4. y-intercept at 9 is
![y=-36\frac{(x - 1) (x - 4)}{(x - 2) (x +4)}](https://tex.z-dn.net/?f=y%3D-36%5Cfrac%7B%28x%20-%201%29%20%28x%20-%204%29%7D%7B%28x%20-%202%29%20%28x%20%2B4%29%7D)
<h3>How to determine the equation for a
rational function</h3>
<u>information gotten from the question</u>
From the question given above, the following data were obtained:
- Vertical asymptotes at x = 2 and x = -4
- x-intercepts at x = 1 and x = 4
- y-intercept at 9
- y =?
Rational function means that the equation will be a fraction
The rational function that models the Vertical asymptotes at x = 2 and x = -4. x-intercepts at x = 1 and x = 4. y-intercept at 9 is written as follows
The numerator
x-intercepts at x = 1 and x = 4
x = 1 ⇒ (x - 1)
x = 4 ⇒ (x - 4)
This means the equation will have (x - 1) (x - 4) as the numerator
The denominator
Vertical asymptotes at x = 2 and x = -4
x = 2 ⇒ (x - 2)
x = -4 ⇒ (x + 4)
This means the equation will have (x - 2) (x + 4) as the denominator
y-intercept at 9
expressing the functions derived already gives
![y=a\frac{(x - 1) (x - 4)}{(x - 2) (x +4)}](https://tex.z-dn.net/?f=y%3Da%5Cfrac%7B%28x%20-%201%29%20%28x%20-%204%29%7D%7B%28x%20-%202%29%20%28x%20%2B4%29%7D)
substituting x = 0 and y = 9 and solving gives a
![9=a\frac{(0 - 1) (0 - 4)}{(0 - 2) (0 +4)}](https://tex.z-dn.net/?f=9%3Da%5Cfrac%7B%280%20-%201%29%20%280%20-%204%29%7D%7B%280%20-%202%29%20%280%20%2B4%29%7D)
![9=a\frac{(4)}{(-8)}](https://tex.z-dn.net/?f=9%3Da%5Cfrac%7B%284%29%7D%7B%28-8%29%7D)
4a = 9 * -8
a = -36
The equation of the rational function is ![y=-36\frac{(x - 1) (x - 4)}{(x - 2) (x +4)}](https://tex.z-dn.net/?f=y%3D-36%5Cfrac%7B%28x%20-%201%29%20%28x%20-%204%29%7D%7B%28x%20-%202%29%20%28x%20%2B4%29%7D)
Learn more on equation for a rational function at :
brainly.com/question/28032338
#SPJ1