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Tanzania [10]
2 years ago
8

Which equation is in standard form and represents a line with the slope -1 through the point (-3,5)

Mathematics
1 answer:
Step2247 [10]2 years ago
8 0
\bf \begin{array}{ccccccccc}
&&x_1&&y_1\\
%  (a,b)
&&(~ -3 &,& 5~) 
\end{array}
\\\\\\
% slope  = m
slope =  m\implies -1
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-5=-1[x-(-3)]
\\\\\\
y-5=-1(x+3)\implies 
y-5=-x-3
\\\\\\
x+y=5-3\implies \stackrel{standard~form}{x+y=2}
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Answer:

(5/2, 29/2), and this represents a maximum

Step-by-step explanation:

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The formula for the axis of symmetry (which passes through the vertex) is

x = -b/ [2a].  Here, a = -2; b = 10.  Therefore, the axis of symmetry is

x = -10/ [2(-2)] = -10/(-4) = 5/2

Evaluate the function g(x) = -2x^2 + 10x + 2 at x = 5/2 to determine the y-coordinate of the vertex:

g(5/2) = -2(5/2)^2 + 10(5/2) + 2, or

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The vertex is thus (5/2, 29/2), and this represents a maximum, because the coefficient of the x^2 term is negative (the curve opens downward).

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Please mark for Brainliest!! :D Thanks!!

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