Find the equation for the line that passes through the point (−2,5), and that is perpendicular to the line with the equation x=−4.

Answer:

a.

b.

c.

Step-by-step explanation:

In a, the -1 means inverse of f(x). To find the inverse, you rewrite the equation in terms of x and y. You replace the x with y and y with x. Then you solve for y.

In b, all you have to do is plug in -9 into f(x).

In c, you plug in -9 into inverse function f.

i don't know specifically what you are looking for but:

Direction: Opens Up

Vertex: (1, -1)

Axis of Symmetry: x = 1

and i attached the graph

Answer:  x = √(((-F - 4)^2)/16 - 1/2) + (F + 4)/4 or x = (F + 4)/4 - √(((-F - 4)^2)/16 - 1/2)

Step-by-step explanation:

Solve for x:

F x = 2 x^2 - 4 x + 1

Subtract 2 x^2 - 4 x + 1 from both sides:

-2 x^2 + F x + 4 x - 1 = 0

Collect in terms of x:

-1 + x (F + 4) - 2 x^2 = 0

Divide both sides by -2:

1/2 + 1/2 x (-F - 4) + x^2 = 0

Subtract 1/2 from both sides:

1/2 x (-F - 4) + x^2 = -1/2

Add 1/16 (-F - 4)^2 to both sides:

1/16 (-F - 4)^2 + 1/2 x (-F - 4) + x^2 = 1/16 (-F - 4)^2 - 1/2

Write the left hand side as a square:

(1/4 (-F - 4) + x)^2 = 1/16 (-F - 4)^2 - 1/2

Take the square root of both sides:

1/4 (-F - 4) + x = √(1/16 (-F - 4)^2 - 1/2) or 1/4 (-F - 4) + x = -√(1/16 (-F - 4)^2 - 1/2)

Subtract 1/4 (-F - 4) from both sides:

x = √(((-F - 4)^2)/16 - 1/2) + (F + 4)/4 or 1/4 (-F - 4) + x = -√(1/16 (-F - 4)^2 - 1/2)

Subtract 1/4 (-F - 4) from both sides:

Answer: x = √(((-F - 4)^2)/16 - 1/2) + (F + 4)/4 or x = (F + 4)/4 - √(((-F - 4)^2)/16 - 1/2)

Answer:

208.02 m

Explanation:

When the model rocket lands, y = 0; therefore, the equation becomes

Using the quadratic formula we solve for x.

Which simplifies to give

Hence, we have the solutions

since lengths cannot be negative, we choose x = 208.02 as our answer.

Hence, the model rocket lands 208.02 m from the starting point.

Answer:

Class Boundary = 1 between the sixth and seventh classes.

Step-by-step explanation:

              Lengths (mm)                   Frequency

1.                  140 - 143                                  1

2.                 144 - 147                                 16

3.                 148 - 151                                 71

4.                 152 - 155                              108

5.                 156 - 159                               83

6.                 160 - 163                                18

7.                  164 - 167                                 3

The class boundary between two classes is the numerical value between the starting value of the higher class, which is 164 for the 7th class in this case, and the ending value of the class of the lower class, which is 163 for the 6th class in this case.

Therefore the class boundary between the sixth and seventh classes

= 164 - 163  = 1

Therefore Class Boundary = 1.

It can be seen that class boundary for the frequency distribution is 1.

If we take the difference between the lower limits of one class and the lower limit of the next class then we will get the class width value.

Therefore, Class width,

w = lower limit of second class - lower limit of first class

   = 144 - 140

   = 4

Answer:

Yes

Step-by-step explanation:

'

Yes, this F(x) is a polynomial function involving the first and null integer powers of x:  x^0 and x^1.

Final answer:

Yes, f(x) = 7 - 2x is a polynomial function because it satisfies the general form of a polynomial, which requires that every term is in the form ax^n for nonnegative integer n.

Explanation:

Yes, the function f(x) = 7-2x is indeed a polynomial function. A polynomial function is a function such as a quadratic, a cubic, a quartic, and so on, for which the function is of the form f(x) = ax^n, where n is a nonnegative integer. In this case, f(x) = 7-2x can be more comprehensively written as f(x) = -2x^1 + 7x^0, which reflects the general form of a polynomial function.

Learn more about polynomial function here:

brainly.com/question/31908293

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