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3 years ago

E^2x -2e^x -24=0 please answer fast

Mathematics

1 answer:

serg [7]3 years ago

3 0

Answer:

x = ln6

Step-by-step explanation:

e^2x - 2e^x - 24 = 0

a = e^x

=> a^2 - 2a - 24 = 0

=> (a + 4)(a - 6) = 0

=> a = -4 => e^x = -4 (invalid because e^x > 0)

=> a = 6 => e^x = 6 => x = ln6

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3 years ago

What are the coordinates of the vertex of the function f(x)=x^2+10x−3? (–5, –28) (–5, 28) (5, –28) (5, 28)

polet [3.4K]

Answer:

(-5,-28)

Step-by-step explanation:

Given

$f(x)=x^2+10x - 3$

Required

Find the coordinates of the vertex

Given that the function is a quadratic function;

The general form of a quadratic function is

$f(x)= ax^2+bx +c$

By comparison;

$a = 1\ b = 10\ and\ c = -10$

To calculate the coordinates of the vertex;

we start by calculating the x-coordinate;

$x = \frac{-b}{2a}$

Substitute 10 for b and 1 for a

$x = \frac{-10}{2*1}$

$x = \frac{-10}{2}$

$x = -5$

Substitute $x = -5$ in the given function;

$y=x^2+10x - 3$

$y=(-5)^2+10*-5 - 3$

$y=25-50 - 3$

$y=-28$

<em>Hence, the coordinates of the vertex is (-5,-28)</em>

6 0

4 years ago

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LUCKY_DIMON [66]

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Let's simplify that:

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4 years ago