(e) If f(x+3) = f(x) + f(5) then prove that: f(2)= 0 and f(5) = -f(-1)

Answers

Answer 1

Answer:

See below.

Step-by-step explanation:

f(x + 3) = f(x) + f(5)    (Given) so:

f(2 + 3) = f(2) + f(5)

and f(2) = f(2 + 3)  - f(5)

= f(5) - f(5) = 0.

f(-1) = f(-1 +3) - f(5)

= f(2) - f(5)

= f(-3)

So - f(-1) = f(3)

Also:

f(5) = f(x + 3) - f(x)

= f(x + 3 - x)

= f(3).

But f(3) = -f(-1)  ( shown above),

So f(5) = -f(-1).


Related Questions

A parkingmeter charges$2 perhour.As a driverparks hercar,she noticesthat the parkingmeterhas15 minutesremainingonitfromthe previousdriver whousedthe parking spot.Ifthedriverinsertsd dollarsintotheparkingmeter and theparkingmeter has 3 hoursremainingon itas a result,write an equationtosolve ford?

Answers

Answer:

3 = 0.25 + 0.5d

Step-by-step explanation:

Given that:

Amount charged per hour = $2

Time left before inserting $d = 15 minutes

Total time after inserting $d = 3 hours

Total time of 3 hours = time left by previous driver + hours purchased with $d

$2 = 1 hour

$d = x

2x = d

x = d/2 ; 0.5d

Since 15 minutes is left before inserting $d

15 minutes to hour ; 15/60 = 0.25

Total time of 3 hours = time left by previous driver + hours purchased with $

3 = 0.25 + 0.5d

find the slope, m and y-intercept of the line y=4x

Answers

Answer:

The answer is m=4

Step-by-step explanation:

Although it may not look like it this equation is in slope-intercept form. The slope-intercept form of a linear equation is:  

y = m x + b

Where m  is the slope and  b  is the y-intercept value.

Therefore:

The slope is:  

m = 4

The  y -intercept is:  b = 0  or  ( 0 , 0 )

The slope of the line is 4 and the y-intercept is 0.

We are given that;

Line equation y=4x

Now,

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

To find the slope and y-intercept of the line y = 4x, we can compare it with the slope-intercept form and identify the values of m and b.

In this case, m = 4 and b = 0.

So, the slope of the line is 4 and the y-intercept is 0.

This means that the line passes through the origin (0,0) and rises 4 units for every 1 unit it moves to the right.

Therefore, by slope answer will be 4 and 0.

Learn more about slope here:

https://brainly.com/question/2503591

#SPJ6

 

Emma is saving to buy a video game console that costs $249. She already saved $60 and plans to save $22 per week. After how many weeks will she have saved enough money for the video game console?

Answers

Answer: about 8.6 weeks

Step-by-step explanation:

PLS HELP ME. WILL GIVE BRAINLYNESS TO FIRST AND CORRECT ANSWER.

Answers

Answer: A = 379.94

Step-by-step explanation:

first round 11.3 to 11

11^2=121

121x3.14=379.94

A = 379.94

Answer:I got 380.13 hopes this helps

Step-by-step explanation:

8(-a+4)=-6a-8+8a
Can y’all help me

Answers

Answer:

a = 14.4

Step-by-step explanation:

8a/8 = a       8(-a+4)/8=-a+4      equation is now    -a+4=-6a-8

-6a/-6 = a      -a/-6=1/6a    equation is now   1/6a + 4 = a-8

a-8 + 8 = a      1/6a + 4 + 8 = 1/6a + 12     equation is now     a = 1/6a+12

5/6 are left of the variable  12/5=2.4    12 + 2.4 = 14.4

|6 - 3| simplify this answer please

Answers

Answer:

3

Step-by-step explanation:

the bracket just makes it a positive number so if it was 3-6 then it would still be 3 because of brackets

Given that f(x)=2x-1, find f(3)

Answers

Answer:

  5

Step-by-step explanation:

Put 3 where x is and do the arithmetic.

  f(x) = 2x -1

  f(3) = 2·3 -1 = 6-1

  f(3) = 5

Jessica bought 4 packages of birthday invitations for 16.95 per package including tax each package contained 12 birthday invitations one stamp coast 0.44 she plans to split the cost evenly with her mother how much money will Jessica mother need to give to Jessica

Answers

Answer:

Jessica's mum will give her 44.46

Step-by-step explanation:

To solve this, we will first of all need to get the total cost of sending the birthday invitations across. After that, we can now split the cost into two.

Cost of sending birthday invitations:

Package cost = 16.95

Number of packages bought = 4

total sum spent on packages = 4 X 16.95 = 67.8

Each package contains 12 invitations.

There are 4 packages.

Total number of invitations = 12 X 4 = 48 invitations

One stamp cost 0.44.

Putting stamps on all 48 invitations will cost 0.44 X 48 = 21.12

Therefore the total cost will be  the total sum spent on packages +the total sum spent on stamps = 67.8 + 21.12 = 88.92

Her mum has agreed to pay half of this cost which is 88.92 / 2 = 44.46

Question 8
Translate and Solve
Twelve more than seven times a number equals the number less six. What is the answer not equation?

Answers

Answer:

-3

Step-by-step explanation:

12 + 7x = x - 6

7x - x = -6 - 12

6x = -18

x = -3

The translation of the given statement is 12 + 7n < 6.

What is inequality ?

Inequality is a form of comparing two non equal quantities.It has four types less than, less than or equal to and greater than, greater than equal to.

According to the given question we have to translate a given statement into a numerical expression.

Given, Twelve more than seven times a number equals the number less six.

Let the number be denoted by 'n'.

Twelve more than 7 times a number is 12 + 7n is less than 6.

12 + 7n < 6.

7n < 6 - 12

7n < -6

n < -6/7.

learn more about inequality here :

https://brainly.com/question/20383699

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Sequence: 2, 6, 10,_,_ _.
What are the next two numbers in the sequence?
A 14, 18
B
16, 24
C 14, 20
12, 16

Answers

The next two numbers in the sequence are 14 and 18

Answer:

A. it goes up by 4 each time so 4 to 10 would be 14 and 4 up from that would be 18

In 1999, the price of unleaded fuel was $1.09. In 2015, the price of unleaded fuel is $1.89. What is the percent change ​

Answers

Answer:

73.39%

Step-by-step explanation:

Initial price

$1.09

Later price

$1.89

Percent change:

(1.89 - 1.09)/1.09 × 100% =0.7339 × 100% =73.39%

Right how do we write 10 hundredths in standard form

Answers

Answer:

Thus, ten hundredths in standard form (or standard notation) is 0.1. We call it 'one-tenth', it's a small number of less than 1.

Step-by-step explanation:

Hope this Helps

Answer:

0.1

that is 10 hundredths in standard form

Deb ate 15 strawberries.
Amir ate 5 fewer strawberries than Deb.
How many strawberries did Amir eat?
strawberries
help pls quick

Answers

Amir at 10 strawberries

Explanation:
Less= subtract
15-5=10

Answer:

I think 15

Step-by-step explanation:

I don't have enough finger so I used my toes.

You spent $36 buying $9 storage crates
and $3 notebooks. This situation can be
modeled by the equation 9x + 3y = 36.
Find the x- and y-intercepts. Graph
the equation.

Answers

Answer:

y-intercept=-4

x-intercept=12

Andy rode his bicycle 2
3
miles on Monday and 1
10
miles on
Tuesday

Answers

He rode 33 miles your welcome

3.a shoe store marks up its merchandise by 8%. what was the selling price of a pair of shoes whose wholesale price is $24.50?

Answers

Answer:

Hi there!

Your answer is:

26.46$ selling price

Step-by-step explanation:

.08 markup

Original price= 24.5

24.5+ (.08*24.5)

26.46$

ivy bought 10 packs of cups for her holiday party. a pack of medium cups costs $1.80 and a pack of large cups costs $2.40. she paid a total of $21.60. how many packs of each size cup did she buy?

Answers

Hope this helps!
I just did this right now and this is the correct way.

Helps me solve this problem please

Answers

Answer:

-4 hope it helps :)

Step-by-step explanation:

Step-by-step explanation:

mark as brainlistyour answer is -4

Given f(x)=-3x+2, solve for x when f(x)=-1

Answers

Answer:

-1

Step-by-step explanation:

(3 * -1) +2

The answer is 5
-3(-1) + 2
3+2=5

The College Bookstore is having a back-to-school sale the t-shirts that are usually sell for $34.50 are marked down to $20.70 what percent off are they

Answers

Answer:

40% off

Step-by-step explanation:

What is the number 7 1/3 written as an improper fraction?

Answers

Answer:

22/3

Step 1: Multiply 7 by 3.

7 x 3 = 21

Step 2: Add 1.

21 + 1 = 22.

Answer = 22/3

Answer:

22/3

Step-by-step explanation:

7 * 3 = 21

21 + 1 = 22

22/3

To make this an improper fraction you need to multiply the denominator by the whole number. Then add the sum of that to the numerator.

Hope this helps! :)

(C) In the past 9 days, Lena has received the following numbers of email advertisements per day:
40, 41, 42, 43, 46, 48, 50, 52, 85.
Which measure should be used to summarize the data?
Mean
Median
Mode

Answers

median -46
mode-40,41,42,43,46,48,50,52,85
mean-49.666

⚠️PLEASE HELP⚠️

1. A 16 oz box of cereal for $3.36 or a 24 oz box for $5.52

2. 3 lbs. of ground beef for $3.87 or 5 lbs. for $6.25 EUS

3. A package of 18 pens for $6.84 or a package of 30 for $8.40

4. A 16 oz can of soup for $1.99 or a 24 oz can for $3.99 es des

5. A 14 oz bottle of ketchup for $1.69 or a 12 oz bottle for $1.29 orations

6. A package of 3 batteries for $4.80 or a package of 12 for $14.76 le Drive

7. A 7 lb. bag of dog food for $10.92 or a 10 lb bag for $12.99 ​

Answers

Answer:

Step-by-step explanation:

nvhnyhrn uk s*d

Find the area of the shape shown in Figure 1 and type your answer into the box below in units squared.

15 points!! ill also give you a brainliest if you get it right!

Answers

Answer:

34 unit squared

Step-by-step explanation:

4*12 then divide 2

4*5 then divide by 2

add two values together and get 34

Answer:

24

Step-by-step explanation:

A=bh x (1/2)

base times height divided by two

Solve the equation for a, when b=4 and c=5

[tex]17+2b-4c=4(a-7)-3[/tex]

Answers

The answer to the equation is a=9

What is the value of x?​

Answers

Answer:

x = 98

Step-by-step explanation:

x = 53 + 45

x = 98

note: the measure of an ext. angle of a triangle is equal to the sum of the two non-adjacent interior angles.

Answer:

98

sum of angle in this triangle = 180

180-(53+45) = 82

so, the third angle is 82 degrees.

moving forward, the third angle (82 degrees) and angle x are straight line angle,

therefore, x + 82 = 180

x =180-82

x=98

A calculator screen shows a number in scientific notation as 1.16E‒7. Write this number in standard form.

Answers

Remember from now on :

E = 10

Let's solve now....

[tex]1.16 \times {10}^{ - 7} = [/tex]

[tex]116 \times {10}^{ - 9} = [/tex]

[tex]0.000000116[/tex]

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

22. Restaurants At Morgan's Fine Cuisine, meals are served a la carte. That is, each
item on the menu is priced separately. Jackie and Ted Parris went to Morgan's to
celebrate their anniversary. Jackie ordered prime rib, 2 side dishes, and a roll. Ted
ordered prime rib, 3 side dishes, and 2 rolls. Jackie's meal came to $36 and Ted's
meal came to $44. If the prime rib is three times as expensive as a side dish, what
is the cost of each item?

Answers

Answer: Cost of a side dish = $ 7

Cost of a roll = $1

Cost of prime rib = $21

Step-by-step explanation:

Let x = cost of a side dish , y= cost of a roll

Then, cost of a prime rib = 3x

Jackie's meal : prime rib, 2 side dishes, and a roll, it came to $36

i.e. 3x+2x +y = 36

⇒ 5x+y=36   (i)

Ted's meal : prime rib, 3 side dishes, and 2 rolls, it came to $44.

i.e. 3x+3x +2y = 44

⇒6x+2y=44

⇒ 3x+ y= 22   (ii)  [divide both sides by 2]

Subtract (ii) from (i), we get

2x= 14

⇒ x=7               [divide both sides by 2]

Put x=7 in (ii), 3(7)+y=22

⇒ 21+y=22

⇒  y =22-21

⇒ y= 1

So, cost of a side dish = $ 7

cost of a roll = $1

cost of prime rib = 3x $7 = $21

Plz only answer if ur sure about the answer :)

Answers

Answer:

66r+77   |    -14k+9

Step-by-step explanation:

i gotchu big daddy

HELLLOOOO THIS IS DUE HELP

Answers

Answer:

RS=13

Step-by-step explanation:

RS+ST=RT

2w+1+w-1=18

3w=18

w=6

RS= 2w+1= 2(6)+1= 12+1= 13

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