What is the result of dividing x3−7 by x + 2?

Write functions for each of the following transformations using function notation. Choose a different letter to represent each f

kupik [55]

Answer:

$(a)\ T_{a,b} =(x +a,y+b)$

$(b)\ F_{y\ axis} = (-x,y)$

$(c)\ F_{x\ axis} = (x,-y)$

$(d)\ R_{o,90^o} = (-y,x)$

$(e)\ R_{o,180^o} = (-x,-y)$

$(f)\ R_{o,270^o} = (y,-x)$

Step-by-step explanation:

Solving (a): Translate a units right, b units up

When a function is translated a units right, the number of units will be added to the x coordinate

When a function is translated b units up, the number of units will be added to the y coordinate.

So, we have:

$T_{a,b} =(x +a,y+b)$

Solving (b): Reflect across y-axis

When a function is translated across the y-axis, the x coordinate gets negated.

So, we have:

$F_{y\ axis} = (-x,y)$

Solving (c): Reflect across x-axis

When a function is translated across the x-axis, the y coordinate gets negated.

So, we have:

$F_{x\ axis} = (x,-y)$

Solving (d): 90 degrees rotation counterclockwise

When a function is rotated 90 degrees counterclockwise, the y-coordinates gets negated and then swapped with the x-coordinate.

So, we have:

$R_{o,90^o} = (-y,x)$

Solving (e): 180 degrees rotation counterclockwise

When a function is rotated 180 degrees counterclockwise, the coordinates are negated.

So, we have:

$R_{o,180^o} = (-x,-y)$

Solving (f): 270 degrees rotation counterclockwise

When a function is rotated 270 degrees counterclockwise, the x-coordinates gets negated and then swapped with the y-coordinate.

So, we have:

$R_{o,270^o} = (y,-x)$

6 0

3 years ago

Amanda has 4 liters of juice and some glasses. She will pour 1/4 liter of juice into each glass. What is the total number of gla

scZoUnD [109]

Answer:

16 glasses

Step-by-step explanation:

If 1 glass = 1/4 liter of juice

then 16 glasses = 4 liters of juice

because 4 divided by 1/4 = 16

8 0

3 years ago

Definitions and examples of rational, irrational, and nonzero numbers

omeli [17]

Rational are number that dont repeat and you can make it into a fraction

irrational are numbers that go on forever and never stop

4 0

2 years ago

A small regional carrier accepted 19 reservations for a particular flight with 17 seats. 14 reservations went to regular custome

Ludmilka [50]

Answer:

(a) The probability of overbooking is 0.2135.

(b) The probability that the flight has empty seats is 0.4625.

Step-by-step explanation:

Let the random variable X represent the number of passengers showing up for the flight.

It is provided that a small regional carrier accepted 19 reservations for a particular flight with 17 seats.

Of the 17 seats, 14 reservations went to regular customers who will arrive for the flight.

Number of reservations = 19

Regular customers = 14

Seats available = 17 - 14 = 3

Remaining reservations, n = 19 - 14 = 5

P (A remaining passenger will arrive), p = 0.52

The random variable X thus follows a Binomial distribution with parameters n = 5 and p = 0.52.

(1)

Compute the probability of overbooking as follows:

P (Overbooking occurs) = P(More than 3 shows up for the flight)

$=P(X>3)\\\\={5\choose 4}(0.52)^{4}(1-0.52)^{5-4}+{5\choose 5}(0.52)^{5}(1-0.52)^{5-5}\\\\=0.175478784+0.0380204032\\\\=0.2134991872\\\\\approx 0.2135$

Thus, the probability of overbooking is 0.2135.

(2)

Compute the probability that the flight has empty seats as follows:

P (The flight has empty seats) = P (Less than 3 shows up for the flight)

$=P(X$

Thus, the probability that the flight has empty seats is 0.4625.

4 0

3 years ago

1. Write the three temperatures in order from least to greatest. Explain how you put

Bess [88]

Answer:

-24, -2, 6

Step-by-step explanation:

Look at the arrow graph below; the more the dot is on the left means the more less number, the more the dot is on the right it means the more greater number. Sorry if my explanation is confusing.

8 0

2 years ago