A function f is defined by f(x) = 3x + 1. Find
a. f(0)=
c. f(2)=
F(-2)

To rationalize essentially means to get rid of the radical.

The trick to all of these it to multiply the top and bottom by a radical that will turn the radical you have into the square root of a perfect square.

Part a: [tex]\dfrac{1}{2\sqrt{5}}[/tex]

One approach that will always work, but not be the smallest radical, is to just multiply by the radical that is already there.

In the case of [tex]\dfrac{1}{2\sqrt{5}}[/tex], you can multiply the top and bottom by [tex]\sqrt{5}[/tex], so you'll really do this:

     [tex]\dfrac{1}{2\sqrt{5}}\cdot\dfrac{\sqrt{5}}{\sqrt{5}} = \dfrac{1\cdot\sqrt{5}}{2\sqrt{5}\sqrt{5}}[/tex]

But in the bottom, [tex]\sqrt{5}\cdot\sqrt{5} = \sqrt{25}=5[/tex], so your work finishes out like this:

    [tex]\dfrac{1\cdot\sqrt{5}}{2\sqrt{5}\sqrt{5}} = \dfrac{\sqrt{5}}{2\sqrt{25}} = \dfrac{\sqrt{5}}{2\cdot5} = \dfrac{\sqrt{5}}{10}[/tex]

Part b: [tex]\dfrac{4}{5\sqrt{2}}[/tex]

In the case of [tex]\dfrac{4}{5\sqrt{2}}[/tex], you can multiply the top and bottom by [tex]\sqrt{2}[/tex], so you'll really do this:

     [tex]\dfrac{4}{5\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}[/tex]

But in the bottom, [tex]\sqrt{2}\cdot\sqrt{2} = \sqrt{4}=2[/tex], so your work finishes out like this:

    [tex]\dfrac{4}{5\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{4\sqrt{2}}{5\sqrt{4}}=\dfrac{4\sqrt{2}}{5\cdot{2}}=\dfrac{4\sqrt{2}}{10}[/tex]

Sometimes the fraction can be reduced, so this should be reduced to [tex]\dfrac{2\sqrt{2}}{5}[/tex].

Looking at all the others, they'll follow this same approach and they will all reduce at the end.

Here's part c, for one more example.

Part c: [tex]\dfrac{3}{3\sqrt{2}}[/tex]

In the case of [tex]\dfrac{3}{3\sqrt{2}}[/tex], you can multiply the top and bottom by [tex]\sqrt{2}[/tex], but you should also reduce the initial fraction first.

     [tex]\dfrac{3}{3\sqrt{2}} = \dfrac{1}{1\cdot\sqrt{2}} = \dfrac{1}{\sqrt{2}}[/tex]

And now proceed with rationalizing:

    [tex]\dfrac{1}{\sqrt{2}} \cdot\dfrac{\sqrt{2}}{\sqrt{2}}[/tex]

But in the bottom, [tex]\sqrt{2}\cdot\sqrt{2} = \sqrt{4}=2[/tex], so your work finishes out like this:

    [tex]\dfrac{1}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{1\cdot\sqrt{2}}{\sqrt{4}}=\dfrac{\sqrt{2}}{{2}}[/tex]

And you're done.

Hopefully that helps you finish the rest of those.

To check your answers, here is the answer key for the rest:

part d:[tex]\dfrac{2\sqrt{6}}{5}[/tex]

part e:[tex]\dfrac{4\sqrt{2}}{3}[/tex]

part f:[tex]\dfrac{4\sqrt{5}}{7}[/tex]

part g:[tex]\dfrac{5\sqrt{10}}{3}[/tex]

part d:[tex]\dfrac{5\sqrt{2}}{3}[/tex]

Answer:

Step-by-step explanation:

(a) 1/(2 sqrt5) x (sqrt 5)/(sqrt5) = (sqrt 5)/10

(b) 4/(5bsqrt2) x (sqrt2)/(sqrt2) = (4sqrt2)/10 = (2sqrt2)/5

(c) 3/(3 sqrt2) x (sqrt2)/(sqrt2) =(sqrt2)/2

(d) 12 /(5 sqrt6) x (sqrt6)/(sqrt6) = (12sqrt6)/30 = (2sqrt6)5

(e) 8/(3 sqrt2) x (sqrt2)/(sqrt2) = (8 sqrt2)/6 = (4 sqrt2)/3

(f) 20/(7 sqrt5) x (sqrt5)/(sqrt5) = (20 sqrt5)/35 = (4 sqrt5)/7

(g) 50/(3 sqrt10) x (sqrt10)(sqrt10) = (50 sqrt10)/30 = (5sqrt10)/3

(h) 10/(3 sqrt2) x (sqrt2)/(sqrt2) = (10 sqrt2)6 = (5 sqrt2)/3

Answer:

omg so many Q's

Step-by-step explanation:

Answer:

i dont get it

Step-by-step explanation:

Step-by-step explanation:

ratio

to

sind = d/e

sinf = f/e

Answer:

$135

Step-by-step explanation:

120+(12*1.25)

120+15

135

Answer: It depends on how you put it in the calculator

Step-by-step explanation:

11x10=110

110-12=98

93/3 = 32.66

Answer:

[tex] \rm y = x + 16 [/tex]

Step-by-step explanation:

A function is given to us and we need to write the inverse of the function in slope intercept form . The given function is ,

[tex]\rm\implies f(x) = x - 16 [/tex]

Let ,

[tex]\rm\implies y = f(x)[/tex]

So that ,

[tex]\rm\implies y = x - 16 [/tex]

Interchange x and y ,

[tex]\rm\implies x = y - 16 [/tex]

Solve for y ,

[tex]\rm\implies y = x + 16[/tex]

Now replace ,

[tex]\rm\implies y = f^{-1}(x) [/tex]

We have ,

[tex]\rm\implies f^{-1}(x) = x+16 [/tex]

And in slope intercept form ,

[tex]\rm\implies \boxed{\pink{\frak {y = x +16}}}[/tex]

Answer:

sorry I don't remember bye I will try to remember

Answer:

180

Step-by-step explanation:

2:3 = 300

2x +3x = 300

5x = 300

x = 300/5

x= 60

2X60= 120 (girls)

3X60= 180 (boys)

if u want to to check whether the ans is correct then try adding your outcomes 120+180 that is = 300 . so the correct ans is 180.

Answer:

3

Step-by-step explanation:

Answer:

multiply by -1

Step-by-step explanation:

Slope intercept form : y = mx + b

-4x + 2y  =  10                  Solve the equation for y

+4x        = +4x    

    2y = 4x + 10

      y = 4x/2 + 10/2           Divide all terms by 2

    multiply by -1                   Simply

Answer: D

30 60 90 trinagle rules

a=8

b=a sqaure root of 3 or 8square root of 3

c=2a or 2*8 or c=16

Step-by-step explanation:

Step-by-step explanation:

sin30°=8/c

1/2=8/c

8×2=c

16=c

tan30°=8/b

[tex] \frac{1}{ \sqrt{3} } = \frac{8}{b} \\ 8 \sqrt{3} = b[/tex]

option. d

The number of order of each aircraft is an illustration of simultaneous equations.

You should order 7 Airbus A330-300s, 5 Boeing 767-300ERs and 9 Boeing Dreamliner 787-9s

To do this, we make use of the following representations:

From the question, we have the following equations

[tex]\mathbf{330A + 270B + 240C = 5850}[/tex] ----the number of passengers

[tex]\mathbf{B + C = 2A}[/tex] --- the relationship between the number of planes

[tex]\mathbf{250A + 200B + 240C =4950 }[/tex] --- the budget

Make A the subject in [tex]\mathbf{B + C = 2A}[/tex]

[tex]\mathbf{A=\frac{1}{2}(B + C)}[/tex]

Substitute [tex]\mathbf{A=\frac{1}{2}(B + C)}[/tex] in [tex]\mathbf{330A + 270B + 240C = 5850}[/tex]

[tex]\mathbf{330 \times \frac{1}{2}(B + C) + 270B + 240C = 5850}[/tex]

[tex]\mathbf{165B + 165C + 270B + 240C = 5850}[/tex]

[tex]\mathbf{435B + 405C = 5850}[/tex]

Divide through by 15

[tex]\mathbf{29B + 27C = 390}[/tex]

Make C the subject

[tex]\mathbf{C = \frac{390 - 29B}{27}}[/tex]

Substitute [tex]\mathbf{A=\frac{1}{2}(B + C)}[/tex] in [tex]\mathbf{250A + 200B + 240C =4950 }[/tex]

[tex]\mathbf{250 \times \frac{1}{2}(B + C) + 200B + 240C =4950 }[/tex]

[tex]\mathbf{125B + 125C + 200B + 240C =4950 }[/tex]

[tex]\mathbf{325B + 365C =4950 }[/tex]

Divide through by 5

[tex]\mathbf{65B + 73C =990}[/tex]

Substitute [tex]\mathbf{C = \frac{390 - 29B}{27}}[/tex]

[tex]\mathbf{65B + 73\times\frac{390 - 29B}{27} =990}[/tex]

Multiply through by 27

[tex]\mathbf{65B \times 27+ 73\times(390 - 29B) =990 \times 27}[/tex]

[tex]\mathbf{1755B+ 28470 - 2117B =26730}[/tex]

Collect like terms

[tex]\mathbf{1755B- 2117B =26730 - 28470}[/tex]

[tex]\mathbf{-362B =-1740}[/tex]

Solve for B

[tex]\mathbf{B =\frac{1740}{362}}[/tex]

[tex]\mathbf{B =5}[/tex] --- approximated

Substitute [tex]\mathbf{B =5}[/tex] in [tex]\mathbf{C = \frac{390 - 29B}{27}}[/tex]

[tex]\mathbf{C = \frac{390 - 29 \times 5}{27}}}[/tex]

[tex]\mathbf{C = \frac{245}{27}}}[/tex]

[tex]\mathbf{C = 9}[/tex] --- approximated

Recall that: [tex]\mathbf{A=\frac{1}{2}(B + C)}[/tex]

So, we have:

[tex]\mathbf{A = \frac{1}{2} \times (5 + 9)}[/tex]

[tex]\mathbf{A = \frac{1}{2} \times 14}[/tex]

[tex]\mathbf{A = 7}[/tex]

Hence, you should order 7 Airbus A330-300s, 5 Boeing 767-300ERs and 9 Boeing Dreamliner 787-9s

Read more about simultaneous equations at:

https://brainly.com/question/16763389

Answer:

Step-by-step explanation:

g(n) = 2n + 3

h(n) = n − 1

(g * h)(n) = g(h(n))

= g(n − 1)

= 2(n − 1) + 3

= 2n − 2 + 3

= 2n + 1

Answer:

2a) because they are continuous lines that don't intercept

Step-by-step explanation:

Answer:

2a) They all have the slope of 2x.

2b) R) y = 2x-3

2c) R is the lowest line because the b value (-3) has the least value out of the 3 choices.

Answer

yc(T)=y"+y'-6y=0

Step-by-step explanation:

Answer:

5/28

Step-by-step explanation:

[tex] \frac{1}{4} + \frac{4}{7} = \frac{7 + 16}{28} = \frac{23}{28} \\ 1 - \frac{23}{28} = \frac{5}{28} [/tex]

Answer:

The answer is A

Step-by-step explanation:

A is equal to the amount of students that were absent.

Answer:

82.2

Step-by-step explanation:

The difference is subtracting:

678 - 595.8 = 82.2

Answer:

82.2

Step-by-step explanation:

Check the image below.

Answer:

-28

Step-by-step explanation:

You have to do the parenthesis 1st, then the [tex]\frac{8}{3}[/tex], and multiply the result :D

Answer:

Step-by-step explanation:

Answer:

D. -1 < x < 3

Step-by-step explanation:

The given function is negative between the x - intercepts  -1 and  3.

Your choice is correct.

Answer:

[tex]\begin{cases}n+d = 27\\0.05n+0.10d = 2.75\\\end{cases}[/tex]

====================================================

Explanation:

n = number of nickels

d = number of dimes

The n and d are placeholders for positive whole numbers.

Since we have 27 coins, we know that n+d = 27. The two subcounts must add to the grand total of 27. That explains how the first equation is set up.

The second equation is set up by looking at the dollar amount each group of coin brings in.

0.05n = amount of money in dollars the nickels bring in

0.10d =  amount of money in dollars the dimes bring in

0.05n+0.10d = total amount of money in dollars = 2.75

The single curly brace to the left of the equations tells the reader we're dealing with a system of equations. The equations are tied together.

BTW,,

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[tex]just \: comment \: if \: you \: want[/tex]

#bunnysquad

#bunnysquadinbrainly

Answer:

pls mark my brainliest because you didn't wriitten coorect question

Step-by-step explanation:

The movement of the ping pong ball follows a exponential progression.

1. Ping pong ball

The given parameters are:

[tex]\mathbf{a = 235}[/tex] --- the initial height

[tex]\mathbf{r = 75\%}[/tex] --- the common ratio

(a) The expression after bouncing k times

To do this, we make use of

[tex]\mathbf{T_n = a \times r^n}[/tex]

So, we have:

[tex]\mathbf{T_n = 235 \times (0.75)^n}[/tex]

In this case; k = n.

So, the equation becomes

[tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]

Hence, the expression for the k-th bounce is: [tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]

(b) The height after bouncing 6 times

This means that k = 6.

So, we have:

[tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]

[tex]\mathbf{T_6 = 235 \times (0.75)^6}[/tex]

[tex]\mathbf{T_6 = 41.82}[/tex]

Hence, the height after the 6th bounce is 41.82 ft

(c) The total distance after the 12th bounce

First, we calculate the total height after the 12th bounce using:

[tex]\mathbf{S_k = \frac{a(1 - r^k)}{1 - r}}[/tex]

So, we have:

[tex]\mathbf{S_k = \frac{235 \times (1 - 0.75^{12})}{1 - 0.75}}[/tex]

[tex]\mathbf{S_k = \frac{235 \times (0.968)}{0.25}}[/tex]

[tex]\mathbf{S_k = 909.92}[/tex]

So, the total distance is:

[tex]\mathbf{Distance = 2 \times S_k - a}[/tex]

[tex]\mathbf{Distance = 2 \times 909.92 - 235}[/tex]

[tex]\mathbf{Distance = 1584.84}[/tex]

Hence, the total distance after the 12th bounce is 1584.84ft.

(2) Cell division

The given parameters are:

[tex]\mathbf{r = 2/2hr}[/tex] --- rate

[tex]\mathbf{a = 120}[/tex] --- initial number of cells

[tex]\mathbf{t = 18}[/tex] --- number of 2 hours is a day and a half

So, the number of bacteria is:

[tex]\mathbf{T_t = ar^t}[/tex]

This gives

[tex]\mathbf{T_t = 120 \times 2^{18}}[/tex]

[tex]\mathbf{T_t = 31457280}[/tex]

Hence, there will be 31457280 bacteria after a day and a half.

Read more about exponential functions at:

https://brainly.com/question/11487261

Answer:

The intersection of the x and y axis is one point one the line, another one is (1, 1). The range of y<x is below the line I just described.

Step-by-step explanation:

Answer:

A credit card is a payment card issued to users to enable the cardholder to pay a merchant for goods and services based on the cardholder's accrued debt.

Step-by-step explanation:

Answer:

So, I believe n/2 may be even and 3n+1 is odd. They succumb to 3n if that helps.

Step-by-step explanation:

I'm not certain on what to do but I hope this helps some what.