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denis-greek [22]

4 years ago

11

Find the slope of the line that contains points (a,c) and (m,c)

1 answer:

Natalija [7]4 years ago

5 0

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~{{ a}} &,&{{ c}}~) 
% (c,d)
&&(~{{ m}} &,&{{ c}}~)
\end{array}
\\\\\\
% slope = m
slope = {{ m}}\implies 
\cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{c-c}{m-a}\implies \cfrac{0}{m-a}\implies 0$

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a square lawn has a perimeter of 36 meters and a circular exercise run has a circumference of 36 meters which shape will give ri

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3 years ago

Compare the function ƒ(x) = –x2 + 4x – 5 and the function g(x), whose graph is shown. Which function has a greater absolute maxi

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A)<em> g(x) </em>has a greater absolute maximum.

Step-by-step explanation:

Given graph of g(x) which is a Parabola

1. Opens downwards

2. The absolute maximum (vertex) is at around (3.5, 6)

i.e. value of absolute maximum is 6.

Another function:

$f(x) =-x^{2}+4x-5$

Let us convert it to vertex form to find its vertex.

Taking - sign common:

$f(x) =-(x^{2}-4x+5)$

Now, let us try to make it a whole square,

Writing 5 as 4+1:

$f(x) =-(x^{2}-4x+4+1)\\\Rightarrow f(x) =-((x^{2}-2 \times 2\times x+2^2)+1)\\\Rightarrow f(x) =-((x-2)^{2}+1)\\\Rightarrow f(x) =-(x-2)^{2}-1$

Please refer to attached graph of f(x).

We know that, vertex form of a parabola is given as:

$f (x) = a(x - h)^2 + k$

Comparing the equations we get:

a = -1 (Negative value of <em>a</em> means the parabola opens downwards)

h = 2, k = -1

Vertex of f(x) is at (2, -1) i.e. value of absolute maximum is -1

and

Vertex of g(x) is at (3.5, 6)

i.e. value of absolute maximum is 6.

Hence, correct answer is:

A)<em> g(x) </em>has a greater absolute maximum.

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3 years ago