16. Simplify: look at picture
please give detailed steps!!

Answer:

Step-by-step explanation:

[tex]u_{n+1}=u_n+n+5\\\Longrightarrow\ u_{n+2}=u_{n+1}+(n+1)+5\\u_{n+2}-u_{n+1}=u_{n+1}+n+1+5-u_n-n-5\\u_{n+2}=2u_{n+1}-u_n+1\\u_{n+3}=2u_{n+2}-u_{n+1}+1\\\\u_{n+3}-u_{n+2}=2u_{n+2}-u_{n+1}+1 -2u_{n+1}+u_n-1\\\\u_{n+3}-3u_{n+2}+3u_{n+1}-u_n=0\\\\\\Equation\ caract\' eristique:\\r^3-3r^2+3r-1=0\\(r-1)^3=0\\\\\boxed{u_n=a+b*n+c*t^2}\\\\u_1=5\\u_2=11\\u_3=18\\u_4=a+4*b+16*c=26\\u_5=a+5*b+25*c=35\\u_6=a+6*b+36*c=45\\\\[/tex]

a=0

b=9/2

c=1/2

Proof:

n=1 ==> u_1=1/2*(9+1)=5

n=2 ==> u_2=2/2*(9+2)=11

n=3 ==> u_3=3/2*(9+3)=18

n=4 ==> u_=4/2*(9+4)=26

n=5 ==> 5/2*(9+5)=35

n=6 ==> 6/2*(9+6)=45

...

Answer: i have found one that calculates differences when given a sigma with a sigma rule, you could adjust the formula for patterns, if you create a sigma equation and then apply the formulas and then make up a pattern that falls within it, knowing the connection is they go up in the same numbers or knowing it and for some patterns being able to solve it.  when given such a sigma problem such as n=1 sigma 3 is the end point 7n-1 is the rule, we would use the value of n until the end point 3, but consider 7n-1 equal to 6+13+20 which equals 39 since 7*1-1=6 and 7*2-1=13, 7*3-1=20 and 6+13+20 is 39. remeber it is equal to that since we plug the value of n from the starting point to the end point of any sigma. a1=7*n-1=6,a2=7*2-1=13,  7*3-1=21 is what you should manipulate for another sigma problem that calculates the diffrence of a sequence as well as its total. the one equation that calculates the total of your patterns is:∑_(n=0)^20▒〖7n-0=140〗

the ones i know to find that represent the patterns in terms of what it would be in the nth term is 58ns it represents what the pattern would be in the nth terms but it is not equal to the pattern.

    finding the nth term by looking for an expression to use for the nth term is the same as finding an expression representing the nth term. the nth term is is the numerical difference in the given series with the letter n on the right of that and the number from the beginning of a series in some cases. one more thing for a negative number at the beginning of a pattern you get the missing number i.e the numerical difference on the left and then and the function of the first number. for example:  there is a pattern going from -1 to 19 so the pattern would be -1, 3, 7,11, 15,19. the numerical difference is 4, n is the letter that would come after and -1 , -1 is a function in the area of nth term since the whole expression would be 4n subtracted by 1 and subtraction is a function, a function is a operation in mathes.          

Step-by-step explanation:        

11-5=6

18-11=7

26-35

45-35=10

6+7+35+10=13+45=58 (the differences added up)

5+11+18, 26+35+45​=140        

Answer:

y = 3x - 11

Step-by-step explanation:

2y+4=6x

2y = 6x - 4

y = 3x - 2

y = 3x + b

1 = 3(4) + b

1 = 12 + b

-11 = b

Answer:

Step-by-step explanation:

7(x - y + 3)

=> 7 × x - 7 × y + 7 × 3

=> 7x - 7y + 21

Answer:

[tex]7(x - y + 3) = 7x - 7y + 21 \\ thank \: you[/tex]

Step-by-step explanation:

=11/3×1/14

=3.67×0.07

=0.2568

Answer:

x = 1

Step-by-step explanation:

5 = 2 + 3x

=> 5 - 2 = 3x

=> 3 = 3x

=> 3/3 = x

=> 1 = x

Answer:

x=1

Step-by-step explanation:

5=2+3x

5=3x+2

-2   -2

3=3x

/3  /3

x=1

hope this helps

brainliest pls?

Answer:

no solutions

Step-by-step explanation:

[tex]4x + y = 24 - - - (a) \\ y = - 4x + 24 - - - (b)[/tex]

substitute for y in (a) with (b):

[tex]4x + ( - 4x + 24) = 24 \\ 0x = 0[/tex]

Answer:

infinite solutions

Step-by-step explanation:

substitute y in the first equation

4x+(-4x+24)=24

4x and -4x cancel out

24/24=1

or solve for x, you should also get 1

Answer:

The inverse of the function is

[tex]{ \underline{f {}^{ - 1}(x) = \sqrt{ \frac{x + 4}{2} } }}[/tex]

Step-by-step explanation:

let the inverse of f(x) be m:

[tex]m = {2x}^{2} - 4 [/tex]

take 4 to the left hand side ( changes sign to positive ):

[tex]m + 4 = {2x}^{2} \\ \frac{m + 4}{2} = {x}^{2} [/tex]

take a square root on all sides:

[tex] \sqrt{ \frac{m + 4}{2} } = \sqrt{ {x}^{2} } \\ \\ x = \sqrt{ \frac{m + 4}{2} } [/tex]

substitute x in place of m:

[tex] {f}^{ - 1} (x) = \sqrt{ \frac{x + 4}{2} } [/tex]

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The statement of proportionality tells you ...

  m = kr³

The values in the fourth column can tell the value of k:

  k = m/r³ = 6.75/1.5³ = 2

Then we have ...

  m = 2r³

Solving for r gives ...

  m/2 = r³

  r = ∛(m/2)

These two relations were used to fill in the spaces in the table. (It is convenient to let a spreadsheet do the calculations.)

Answer:

B. 50%

Step-by-step explanation:

7/20 = 35%

35% + 15% = 50%

100% - 50% = 50%

white → 15%

red → 7/20 · 100% = 35/100 · 100% = 35%

blue → 100% - 35% - 15% = 50%

Answer: B)

Answer:

1/12

Step-by-step explanation:

7/12 - 1/2

~Find common denominators

7/12 - 6/12

~Subtract

1/12

Best of Luck!

Answer:

2x + 2y - 4

Step-by-step explanation:

The opposite sides are congruent so perimeter (P) is

P = 2(x + 2) + 2(y - 4)

  = 2x + 4 + 2y - 8

  = 2x + 2y - 4

Answer:

48, 49, 50

Step-by-step explanation:

x + x+1 + x+2 = 147

3x + 3 = 147

3x = 147 - 3

x = 144/3

x = 48

Answer:

x = -2 or 5

Step-by-step explanation:

y = (x-3)/((x-5)(x+2))

y is undefined when the denominator is zero.

Answer:

14

Step-by-step explanation:

√36+√64

√36=6

√64=8

6+8

14

THANK YOU

9514 1404 393

Answer:

  Marsha and Anthony

Step-by-step explanation:

Here a negative bank balance represents a debt. The larger the magnitude of the negative number, the more debt it represents. A positive bank balance corresponds to no debt.

Anthony and Marsha -- no debt . . . . smallest debt

Sara -- $90 in debt . . . . smallest non-zero debt

Sean -- $208 in debt

On those with non-zero debt, Sara has the smallest debt. Overall, Anthony and Marsha have the smallest debt: zero debt.

Answer: symmetric on the x-axis only.

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

According to the rules of segment addition, AB+BC=AC.

Since the length of AB is x+5, length of BC is 2x+10, and total length of AC is 33, we can create the equation: (x+5) + (2x+10) = 33.

To solve, we combine like terms: 3x + 15 = 33.

Subtract 15 from both sides: 3x = 18.

Divide both sides by 3: x = 6.

9514 1404 393

Answer:

  see attached. red = reflected; blue = rotated

Step-by-step explanation:

The relevant coordinate transformations are ...

  (x, y) ⇒ (x, -y) . . . . . reflection over the x-axis

  (x, y) ⇒ (y, -x) . . . . . rotation 90° CW

In the attached figure, the red triangle A'B'C' is reflected. The blue triangle A"B"C" is rotated.

__

Additional comment

Learning to visualize these transformations can take a little practice. It can help to draw the figure on a graph, trace it on another piece of paper or transparency, then move the copy to the new position relative to the old axes.

For reflection across the x-axis, the x-axis of the copy is aligned with the original, but the copy is flipped over so the old +y axis is aligned with the -y axis, and vice versa.

For rotation 90° CW, what was the +y axis becomes aligned with the +x axis, and what was the +x axis becomes aligned with the -y axis. That is, the figure is rotated 90° CW about the origin so anything in the first quadrant is moved to the 4th quadrant.

Step-by-step explanation:

it is unclear what is meant by f1 and f2. do you mean f' and f'' ?

I don't think so, as you mentioned algebra 2.

so, is it just a way to identify different functions ? like function 1 vs. function 2 ?

if that's the case, then both functions represent lines.

both lines go through the origin.

but as their slopes are of same size but different sign, one is actually the mirrored version of the other one (mirrored around the x-axis).

FYI - the created visible pattern (4 lines emanating from the origin) would also indicate that the visible pattern (but not the functions) is also mirrored around the y-axis.

The required domain is [tex]\{-3,5,7\}[/tex].

Given:

A set of ordered pairs is:

[tex]A=\{(-3,2),(5,4),(7,-3)\}[/tex]

To find:

The domain of the given set of ordered pairs.

Solution:

Domain is the set of input values.

In the set of ordered pairs [tex](x,y)[/tex], then the set of all the [tex]x[/tex]-values is domain and the set of all the [tex]y[/tex]-values is range.

We have,

[tex]A=\{(-3,2),(5,4),(7,-3)\}[/tex]

In the above set of ordered pairs, the x-values are [tex]-3,5,7[/tex].

[tex]Domain=\{-3,5,7\}[/tex]

Therefore, the domain of the given set of ordered pairs is [tex]\{-3,5,7\}[/tex].

Learn more:

https://brainly.com/question/3269807

Answer:

He is correct.

Step-by-step explanation:

[tex]\frac{35}{49} =\frac{5}{7}[/tex]

Answer:

The midpoint is (-5,1.5)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2

( -3+-7)/2 = -10/2 = -5

To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2

( -2+5)/2 = 3/2 = 1.5

The midpoint is (-5,1.5)

Answer:

(0.5, -1)

Step-by-step explanation:

Answer:-6+6=0

Step-by-step explanation: basically just put the sentence into an equation.

d=degrees farenheit

-6d+6d =0d

Answer:

if ur wondering on how to solve it u should solve it by an equation.

Step-by-step explanation:

just make sure to explain us answer and the answer is 6+6=0

Answer:16 q

Step-by-step explanation:

Answer:

3.2=6

4.2=8

5.2=10

the scale factor is 2

Answer:

x =  1 /2

Step-by-step explanation:

isolate the variable by dividing each side by factors that dont contain the variable

decimal form will be: x =  0.5

hope that helps>3

Answer:

There are [tex]2^{20}[/tex] subsets of [tex]A[/tex]

Step-by-step explanation:

Using the formula for the number of subsets of a given (finite) set, the number of subsets of [tex]A[/tex] is

[tex]2^{n(A)}=2^{20}[/tex]

Answer:

r = 1

Step-by-step explanation:

Given the equation of proportion

y = rx ← r is the constant of proportionality

Divide both sides by x

[tex]\frac{y}{x}[/tex] = r

Choose any ordered pair from the table

Using x = 5.8 and y = 5.8 , then

r = [tex]\frac{5.8}{5.8}[/tex] = 1