Using the domain, it is found that x = -8 is excluded for the product.
The domain of a function is the <u>set that contains all possible input values</u>.
- In a fraction, the <u>denominator cannot be 0</u>.
In this problem, there are two fractions, and the points outside the domain, that is, the roots of the denominators, are excluded.
For the first fraction, they are:
![3x^2 + 6x = 0](https://tex.z-dn.net/?f=3x%5E2%20%2B%206x%20%3D%200)
![3x(x + 2) = 0](https://tex.z-dn.net/?f=3x%28x%20%2B%202%29%20%3D%200)
![3x = 0 \rightarrow x = 0](https://tex.z-dn.net/?f=3x%20%3D%200%20%5Crightarrow%20x%20%3D%200)
![x + 2 = 0 \rightarrow x = -2](https://tex.z-dn.net/?f=x%20%2B%202%20%3D%200%20%5Crightarrow%20x%20%3D%20-2)
Hence, x = -2(not an option) is excluded.
- x = 0 can be factored with the numerator of the second fraction, so not excluded.
For the second fraction, the roots of the denominator are:
![x^2 + 11x + 24 = 0](https://tex.z-dn.net/?f=x%5E2%20%2B%2011x%20%2B%2024%20%3D%200)
Which is a quadratic equation with <u>coefficients</u>
, hence:
![\Delta = b^2 - 4ac = 11^2 - 4(1)(24) = 121 - 96 = 25](https://tex.z-dn.net/?f=%5CDelta%20%3D%20b%5E2%20-%204ac%20%3D%2011%5E2%20-%204%281%29%2824%29%20%3D%20121%20-%2096%20%3D%2025)
![x_1 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{-11 - 5}{2} = -8](https://tex.z-dn.net/?f=x_1%20%3D%20%5Cfrac%7B-b%20-%20%5Csqrt%7B%5CDelta%7D%7D%7B2a%7D%20%3D%20%5Cfrac%7B-11%20-%205%7D%7B2%7D%20%3D%20-8)
![x_2 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{-11 + 5}{2} = -3](https://tex.z-dn.net/?f=x_2%20%3D%20%5Cfrac%7B-b%20%2B%20%5Csqrt%7B%5CDelta%7D%7D%7B2a%7D%20%3D%20%5Cfrac%7B-11%20%2B%205%7D%7B2%7D%20%3D%20-3)
x = -3 can be factored with the numerator of the first fraction, so only x = -8 is excluded.
A similar problem is given at brainly.com/question/13136492
Answer:
Part A: 90; Part B: 24.
Step-by-step explanation:
The number of blueberry muffins is 40% of the total number of muffins.
Part A: There are 36 blueberry muffins. This is 40% of the unknown number of muffins, x; this gives us
36 = 0.4x
Divide both sides by 0.4:
36/0.4 = 0.4x/0.4
90 = x
There were 90 total muffins.
Part B: 40% of the total number of muffins, 60, gives us the unknown number of blueberry muffins:
0.4(60) = x
24 = x
There were 24 blueberry muffins.
Answer:
3500
Step-by-step explanation:
2/100=70/?
2*35=70
35*100=3500
Answer:
r = <u>A</u><u> </u><u>-</u><u> </u><u>p</u>
pn
Step-by-step explanation:
A = P(1 + nr)
A = P+ Pnr
pnr = A - p
r = <u>A</u><u> </u><u>-</u><u> </u><u>p</u>
pn
9514 1404 393
Answer:
y = -0.50x -2.50
Step-by-step explanation:
The perpendicular line will have a slope that is the opposite reciprocal of the slope of the given line:
m = -1/2
The given point can be used with this slope in the point-slope equation for a line:
y -k = m(x -h) . . . . . line with slope m through point (h, k)
y +5 = -1/2(x -5)
y = -1/2x +5/2 -5
y = -0.50x -2.50