Answer:
You dare challenge me...
Step-by-step explanation:
Gaius Julius Caesar was a Roman general and statesman who played a critical role in the events that led to the demise of the Roman Republic and the rise of the Roman Empire. In 60 BC, Caesar, Crassus and Pompey formed the First Triumvirate, a political alliance that dominated Roman politics for several years.
Answer:
![x = - 1 + \sqrt{17}\\and\\x = - 1 - \sqrt{17}\\](https://tex.z-dn.net/?f=x%20%3D%20-%201%20%2B%20%5Csqrt%7B17%7D%5C%5Cand%5C%5Cx%20%3D%20-%201%20-%20%5Csqrt%7B17%7D%5C%5C)
Step-by-step explanation:
given equation
![x^2 +2x +1 = 17](https://tex.z-dn.net/?f=x%5E2%20%2B2x%20%2B1%20%3D%2017)
subtracting 17 from both sides
![x^2 +2x +1 = 17\\x^2 +2x +1 -17= 17-17\\x^2 +2x - 16 = 0\\](https://tex.z-dn.net/?f=x%5E2%20%2B2x%20%2B1%20%3D%2017%5C%5Cx%5E2%20%2B2x%20%2B1%20-17%3D%2017-17%5C%5Cx%5E2%20%2B2x%20-%2016%20%3D%200%5C%5C)
the solution for quadratic equation
is given by
x = ![x = -b + \sqrt{b^2 - 4ac} /2a \\\\and \ \\-b - \sqrt{b^2 - 4ac} /2a](https://tex.z-dn.net/?f=x%20%3D%20-b%20%2B%20%5Csqrt%7Bb%5E2%20-%204ac%7D%20%2F2a%20%5C%5C%5C%5Cand%20%5C%20%5C%5C-b%20-%20%5Csqrt%7Bb%5E2%20-%204ac%7D%20%2F2a)
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in our problem
a = 1
b = 2
c = -16
![x =( -2 + \sqrt{2^2 - 4*1*-16}) /2*1 \\x =( -2 + \sqrt{4 + 64}) /2\\x =( -2 + \sqrt{68} )/2\\x = ( -2 + \sqrt{4*17} )/2\\x = ( -2 + 2\sqrt{17} )/2\\x = - 1 + \sqrt{17}\\and\\\\x = - 1 - \sqrt{17}\\](https://tex.z-dn.net/?f=x%20%3D%28%20-2%20%2B%20%5Csqrt%7B2%5E2%20-%204%2A1%2A-16%7D%29%20%2F2%2A1%20%5C%5Cx%20%3D%28%20-2%20%2B%20%5Csqrt%7B4%20%20%2B%2064%7D%29%20%2F2%5C%5Cx%20%3D%28%20-2%20%2B%20%5Csqrt%7B68%7D%20%29%2F2%5C%5Cx%20%3D%20%28%20-2%20%2B%20%5Csqrt%7B4%2A17%7D%20%29%2F2%5C%5Cx%20%3D%20%20%28%20-2%20%2B%202%5Csqrt%7B17%7D%20%29%2F2%5C%5Cx%20%3D%20-%201%20%2B%20%5Csqrt%7B17%7D%5C%5Cand%5C%5C%5C%5Cx%20%3D%20-%201%20-%20%5Csqrt%7B17%7D%5C%5C)
thus value of x is
![x = - 1 + \sqrt{17}\\and\\x = - 1 - \sqrt{17}\\](https://tex.z-dn.net/?f=x%20%3D%20-%201%20%2B%20%5Csqrt%7B17%7D%5C%5Cand%5C%5Cx%20%3D%20-%201%20-%20%5Csqrt%7B17%7D%5C%5C)
Answer:
- vertex (3, -1)
- y-intercept: (0, 8)
- x-intercepts: (2, 0), (4, 0)
Step-by-step explanation:
You are being asked to read the coordinates of several points from the graph. Each set of coordinates is an (x, y) pair, where the first coordinate is the horizontal distance to the right of the y-axis, and the second coordinate is the vertical distance above the x-axis. The distances are measured according to the scales marked on the x- and y-axes.
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<h3>Vertex</h3>
The vertex is the low point of the graph. The graph is horizontally symmetrical about this point. On this graph, the vertex is (3, -1).
<h3>Y-intercept</h3>
The y-intercept is the point where the graph crosses the y-axis. On this graph, the y-intercept is (0, 8).
<h3>X-intercepts</h3>
The x-intercepts are the points where the graph crosses the x-axis. You will notice they are symmetrically located about the vertex. On this graph, the x-intercepts are (2, 0) and (4, 0).
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<em>Additional comment</em>
The reminder that these are "points" is to ensure that you write both coordinates as an ordered pair. We know the x-intercepts have a y-value of zero, for example, so there is a tendency to identify them simply as x=2 and x=4. This problem statement is telling you to write them as ordered pairs.
Answer:
Coefficient
Step-by-step explanation:
If it is 10a^3 (10 times the variable "a" cubed), then 10 is the coefficient.
Answer: IDK sssrry
Step-by-step explanation: