Choose the appropriate transformation for the figure<br> Picture above ***

Expand the following using either the Binomial Theorem or Pascal’s Triangle. You must show your work for credit. (x - 3)^5

Rudiy27

I used bionomial expansion up to and including the term $x^{3}$

$(-3 + x)^{5}$

$-3^{5} (1 + -\frac{1}{3}x) ^{5}$

$-243 (1 + -\frac{1}{3}x) ^{5}$

n = 5
x = $- \frac{1}{3}x$

Binomial expansion:

$1 + nx + \frac{n(n-1) x^{2} }{2!} + \frac{n(n-1)(n-2) x^{3} }{3!}$

Therefore:

$1 + (5*- \frac{1}{3}x) + \frac{5(4) (- \frac{1}{3}x)^{2} }{2} + \frac{5(4)(3) (- \frac{1}{3}x)^{3} }{6}$

=

$1 - \frac{5}{3} x + \frac{10}{9} x^{2} - \frac{10}{27} x^{3} 

$

Multiply by -243

=

$-243 + 405x - 270x^{2} + 90 x^{3} 
$

3 0

3 years ago

Read 2 more answers

Is y= -9/5x + 1/5 perpendicular to y= 5/9x + 2/9

Lunna [17]

The given lines are perpendicular

Step-by-step explanation:

if Two lines are perpendicular then their slopes are

m $m_{1}=-\frac{1}{m_{2}}$

Where m₁ is slope of first line and m₂ is the slope of second line.

Since the lines are in slope-point form the standard form is:

$y=mx+b$

where m is the slope

The slope of first line y= -9/5x + 1/5 is: m₁ = -9/5

The slope of second line y= 5/9x + 2/9 is: m₂= 5/9

So, m $m_{1}=-\frac{1}{m_{2}}$ i.e $-\frac{9}{5}=\frac{5}{9}$

So, The given lines are perpendicular

Keywords: Perpendicular lines, slope

Learn more about Perpendicular lines at:

#learnwithBrainly

3 0

3 years ago

Please help asap (:

Korolek [52]

For this case we first define the variable:
x = number of terms.
The equation that models the problem is:
f (x) = 3.4 - 0.6x
We have then that the first four terms are:
x = 1
f (1) = 3.4 - 0.6 (1) = 3.4 - 0.6 = 2.8
x = 2
f (2) = 3.4 - 0.6 (2) = 3.4 - 1.2 = 2.2
x = 3
f (3) = 3.4 - 0.6 (3) = 3.4 - 1.8 = 1.6
x = 4
f (4) = 3.4 - 0.6 (4) = 3.4 - 2.4 = 1
Answer:
The rule for the sequence is:
f (x) = 3.4 - 0.6x
option 1

7 0

4 years ago

Read 2 more answers

fam can swim a lap in 29 2/5 seconds. cuteboujee can swim a lap in 28.7 seconds. how much faster can cuteboujee swim a lap than

natima [27]

Answer:

0.7 seconds

Step-by-step explanation:

You have to subtract both lap times, but before doing so you need to know what 2/5 is in decimal form. To do so, you must do 2 divided by 5, getting 0.4 seconds as it's a fraction converting to decimal. This means Fam swam 29.4 seconds, which instead of 2/5, you have 0.4 as your converted answer, so you would substitute it after 29. Then, you would do 29.40 subtracted by 28.7 and get 0.7 seconds as your answer to find out the difference of their swim times.

3 0

4 years ago

What is the answer to<br><br> 6x–2x+8=20

11111nata11111 [884]

Answer:

x = 3

Step-by-step explanation:

First, simplify by subtracting 2x from 6x:

6x - 2x + 8 = 20

4x + 8 = 20

Then, solve for x:

4x + 8 = 20

4x = 12

x = 3

So, the answer is x = 3

5 0

3 years ago

Choose the appropriate transformation for the figure Picture above ***