10) 11
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Answer: The graph of g(x) will be shifted 2 units left and 1 unit down compared to the parabola, f(x).
Step-by-step explanation:
Answer:
C. 5,166
Step-by-step explanation:
because of the word product, it means multiplication
Answer:
k = -3/4
Step-by-step explanation:
The lines will be parallel if their slopes are equal. To find the slope of each line, write its equation in slope-intercept form (y = mx + b). In other words, solve each equation for y and look at the coefficient of x.
2x + 3y = 4k
3y = -2x + 4k
y = (-2/3)x + 4k/3
The slope of the first line is -2/3.
x - 2ky = 7
-2ky = -x + 7
y = [1/(2k)]x - 7/(2k)
The slope of the second line is 1/(2k).
If the slopes are equal, then
1/(2k) = -2/3
Multiply by 2k.
1 = (-2/3)(2k) = (-4/3)k
1 = (-4/3)k
k = -3/4
A + b = 0
ab = √(5)
since b = -a, subst into other equation
ab = √5
a(-a) = √5
-a² = √5
a² = - √5
a =± (5)^(1/4)·i
so our two zeros are (5)^(1/4) · i and -(5)^(1/4) · i.
Our polynomial has equation
![y = \left( x - 5^{1/4} \cdot \mathrm{i}\right) \left( x + 5^{1/4} \cdot \mathrm{i}\right)](https://tex.z-dn.net/?f=y%20%3D%20%5Cleft%28%20x%20-%205%5E%7B1%2F4%7D%20%5Ccdot%20%5Cmathrm%7Bi%7D%5Cright%29%20%5Cleft%28%20x%20%2B%205%5E%7B1%2F4%7D%20%5Ccdot%20%5Cmathrm%7Bi%7D%5Cright%29%20)
difference of squares: (x + y)(x - y) = x² - y² so
![\\ y = (x)^2 - \left( 5^{1/4} \cdot \mathrm{i} \right)^2 \\ y = x^2 - 5^{1/2} \cdot i^2 \\ y = x^2 + 5 ^{1/2} = x^2 + \sqrt{5}](https://tex.z-dn.net/?f=%5C%5C%20y%20%3D%20%28x%29%5E2%20-%20%5Cleft%28%205%5E%7B1%2F4%7D%20%5Ccdot%20%5Cmathrm%7Bi%7D%20%5Cright%29%5E2%20%5C%5C%0Ay%20%3D%20x%5E2%20-%205%5E%7B1%2F2%7D%20%5Ccdot%20i%5E2%20%5C%5C%0Ay%20%3D%20x%5E2%20%2B%205%20%5E%7B1%2F2%7D%20%3D%20x%5E2%20%2B%20%5Csqrt%7B5%7D)
your polynomial is
y = x² + √(5)
y = x^2 + sqrt(5)