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3 years ago

What is the inverse of f(x)=x^-9

1 answer:

3 0

$y = \frac{1}{x^9}\\yx^9 = 1\\x^9 = \frac{1}{y}\\x = \sqrt[9]{\frac{1}{y}}\\Therefore, \ f^{-1}(x)=\sqrt[9]{\frac{1}{x}}.$

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A farmer has a bale of hay with a mass of 36 kg. How many milligrams of hay are in the bale?

Roman55 [17]

I got 36000000 . Hope this helps

7 0

2 years ago

Graph f(x) =-2x^+16x-30 by factoring to find the solutions, then find the coordinates of the vertex, and the axis of symmetry. I

fredd [130]

Answer:

Observe attached image

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

Axis of symmetry:

 $x =4$ 

Step-by-step explanation:

First factorize the function

$f (x) = -2x ^ 2 + 16x-30$

Take -2 as a common factor.

$-2(x ^ 2 -8x +15)$

Now factor the expression $x ^ 2 -8x +15$

You must find two numbers that when you add them, obtain the result -8 and multiplying those numbers results in 15.

These numbers are -5 and -3

Then we can factor the expression in the following way:

$f (x) = -2(x-5)(x-3)$

The quadratic function cuts the x-axis at x = 3 and at x = 5.

Now we find the coordinates of the vertex.

For a function of the form $ax ^ 2 + bx + c$ the x coordinate of its vertex is:

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

In the function $f (x) = -2x ^ 2 + 16x-30$

$a = -2\\b = 16\\c = 30$

Then the vertice is:

$x = \frac{-16}{2(-2)}\\\\x = 4$

The y coordinate of the symmetry axis is

$y = f (4) = -2 (4) ^ 2 +16 (4) -30\\\\y = 2$

The axis of symmetry is a vertical line that cuts the parabola in two equal halves. This axis of symmetry always passes through the vertex.

Then the axis of symmetry is the line

$x = 4$

The solutions and the vertice written as ordered pairs are:

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

6 0

3 years ago

Which of the following equations is equivalent to y-3x=4 ?

lina2011 [118]

Answer:

y=3x+4

idk what it has to be equivalent to...I just put it in y-intercept form

Step-by-step explanation:

7 0

3 years ago

If the length of a rectangle is 3 and the width is 2, the length of the diagonal is a 13 b 5 c √5 d √13

trasher [3.6K]

Answer:

The length of the rectangle is 12cm and the area of the rectangle is 60cm2.

Explanation:

By definition, the angles of a rectangle are right. Therefore, drawing a diagonal creates two congruent right triangles. The diagonal of the rectangle is the hypotenuse of the right triangle. The sides of the rectangle are the legs of the right triangle. We can use the Pythagorean Theorem to find the unknown side of the right triangle, which is also the unknown length of the rectangle.

Recall that the Pythagorean Theorem states that the sun of the squares of the legs of a right triangle is equal to the square of the hypotenuse. a2+b2=c2

52+b2=132

25+b2=169

25−25+b2=169−25

b2=144

√b2=√144

b=±12

Since the length of the side is a measured distance, the negative root is not a reasonable result. So the length of the rectangle is 12 cm.

The area of a rectangle is given by multiplying the width by the length.

A=(5cm)(12cm)

A=60cm2

3 0

3 years ago

Note angles not necessarily drawn to scale

kondaur [170]

Answer:

Step-by-step explanation:

Angles CGE and 30° are vertical angles.

Thus, Angle CGE is thus 30°.

Angle CGE and Angle x are complementary, so x = 90° - 30° = 60°

7 0

3 years ago

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