Representation of the function f(x)=-2x2+8x-6

Mathematics

1 answer:

Kaylis [27]2 years ago

8 0

X-intercepts: (1,0), (3,0)
Y-intercepts: (-6,0)

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2 years ago

What is the inverse of the function f(x) = 2x - 10?

aliya0001 [1]

Answer:

$h(x) = \frac{1}{2} x+ 5$

Step-by-step explanation:

To find the inverse of a function, simply switch the 'x' and 'y' variables. Substitute in 'y' in the place of f(x) for this purpose:

y = 2x - 10

Switch positions:

x = 2y - 10

Add '10' to both sides to begin simplifying:

x + 10 = 2y

Divide both sides by 2:

$y= \frac{x+10}{2}$

This can be rewritten as:

$y = \frac{1}{2} x+ 5$

Therefore, the inverse of the function is:

$h(x) = \frac{1}{2} x+ 5$

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2 years ago

Suppose triangle ABC has vertices at A(1, 0), B(10, 0), and C(2, 6). After a 60° counterclockwise rotation about the origin, ver

Artemon [7]

Check the picture attached.

Let OB be the radius of circle with center O.

Let B' be the image of B after the described rotation

OB and OB' are sides of the equilateral triangle OBB'.

The x coordinate of B' is the midpoint of OB, that is 5.

In the right triangle B', point (5, 0) and B:

Distance point (5, 0) to B is 5
|B'B|=|OB|=10

so by the pythagorean theorem:

$a= \sqrt{ 10^{2} - 5^{2} } = \sqrt{ 2^{2} *5^{2} - 5^{2} }= \sqrt{5^{2}(4-1)}=5 \sqrt{3}$ units

Answer: $5 \sqrt{3}$